From d4ae1476f36caa47a8530747d00d4bf77706e305 Mon Sep 17 00:00:00 2001 From: Florian Mathieu Date: Wed, 25 Sep 2024 10:23:27 +0200 Subject: [PATCH] =?UTF-8?q?1er=20not=C3=A9?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Recursivité/TP_1.ipynb | 7783 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 7783 insertions(+) create mode 100644 Recursivité/TP_1.ipynb diff --git a/Recursivité/TP_1.ipynb b/Recursivité/TP_1.ipynb new file mode 100644 index 0000000..e749ad0 --- /dev/null +++ b/Recursivité/TP_1.ipynb @@ -0,0 +1,7783 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Récursivité et Programmation Dynamique\n", + "\n", + "# La reproduction des lapins\n", + "\n", + "Nous allons utiliser 2 grandes méthodes de programmation que nous allons appliquer à un problème célèbre et récurrent dans le milieu de la programmation.\n", + "\n", + "En 1202, Leonardo Fibonacci publie un ouvrage dans lequel il traite d'un problème simple et concret : la croissance d'une population de lapins. Il s'agit de savoir comment contrôler la population des clapiers et quand vendre ses lapins, etc.\n", + "\n", + "Voici le fonctionnement simplifié de cette reproduction :\n", + "\n", + "1. On compte les lapins par **couple**\n", + "2. **Chaque mois** chaque couple de lapins matures donne naissance à 1 couple de jeunes lapins immatures\n", + "3. Après 2 mois les jeunes couples devienent matures et engendrent à leur tour un jeune couple immature\n", + "4. On étudie la croissance de la population tous les mois : n est le nombre de mois\n", + "\n", + "| n | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |\n", + "|:------------------------------:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:--:|:--:|:--:|:--:|\n", + "| nb couples matures | 0 | 0 | 0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 |\n", + "| nb couples immatures 1er mois | 0 | 1 | 0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 |\n", + "| nb couples immatures 2ème mois | 0 | 0 | 1 | 0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 |\n", + "| nb couples | 0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 |\n", + "\n", + "- Complétez les mois manquants en respectant les règles de reproduction.\n", + "\n", + "- En vous inspirant de la méthode que vous avez employée pour compléter le tableau ci-dessus, écrivez une fonction `lapinoux(n)` qui retourne le nombre de couples de lapin obtenus au mois n.\n", + "- Testez votre fonction pour des valeurs de n entre 0 et 10." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pour n=0 le nombre de couples vaut:0\n", + "Pour n=1 le nombre de couples vaut:1\n", + "Pour n=2 le nombre de couples vaut:1\n", + "Pour n=3 le nombre de couples vaut:2\n", + "Pour n=4 le nombre de couples vaut:3\n", + "Pour n=5 le nombre de couples vaut:5\n", + "Pour n=6 le nombre de couples vaut:8\n", + "Pour n=7 le nombre de couples vaut:13\n", + "Pour n=8 le nombre de couples vaut:21\n", + "Pour n=9 le nombre de couples vaut:34\n", + "Pour n=10 le nombre de couples vaut:55\n" + ] + } + ], + "source": [ + "def lapinoux(n: int) -> int:\n", + " \"\"\" Calcule le nombre de couples de lapins au bout de n mois (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " \n", + " nb_couples_matures = 0\n", + " nb_couples_immatures1 = 1\n", + " nb_couples_immatures2 = 0\n", + " \n", + " for i in range(n+1):\n", + " nb_couples_matures += nb_couples_immatures2\n", + " nb_couples_immatures2 = nb_couples_immatures1\n", + " nb_couples_immatures1 = nb_couples_matures\n", + " \n", + " return nb_couples_matures\n", + "\n", + "def lapinoux_base(n: int) -> int:\n", + " \"\"\" Calcule le nombre de couples de lapins au bout de n mois (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " \n", + " if n <= 0 : return 0\n", + " nb_couples_matures = 0\n", + " nb_couples_immatures1 = 1\n", + " nb_couples_immatures2 = 0\n", + " \n", + " for i in range(2,n+1):\n", + " nb_couples_matures += nb_couples_immatures2\n", + " nb_couples_immatures2 = nb_couples_immatures1\n", + " nb_couples_immatures1 = nb_couples_matures\n", + "\n", + " return nb_couples_matures + nb_couples_immatures1 + nb_couples_immatures2\n", + "\n", + "for i in range(11):\n", + " print(f\"Pour n={i} le nombre de couples vaut:{lapinoux(i)}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "🏁 **Terminaison** : la fonction termine toujours car elle est constituée d'un boucle finie `for ... range`.\n", + "\n", + "🐌 **Complexité** : $O(n)$ car à chaque fois qu'on augmente n de 1 on ajoute un tour de boucle avec 3 affectations et 1 addition." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Suite de Fibonacci\n", + "\n", + "Comme vous êtes de bons élèves en mathématiques, il ne vous a pas échappé que ce fonctionnement pouvait se formaliser sous forme de suite mathématique qu'on nomme la **Suite de Fibonacci**.\n", + "\n", + "En effet, vous avez pu constater que pour obtenir un terme pour un mois donné, il suffisait de faire la somme des termes des 2 mois précédents : `fibo(0) = 0 ; fibo(1) = 1 ; fibo(n) = fibo(n-1) + fibo(n-2)`.\n", + "\n", + "- Reprogrammez la fonction précédente en la nommant `fibo(n)` mais cette fois en utilisant la définition de la suite ci-dessus.\n", + "\n", + "- Testez votre fonction pour des valeurs de n entre 0 et 10." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pour n=0 le nombre de couples vaut:0\n", + "Pour n=1 le nombre de couples vaut:1\n", + "Pour n=2 le nombre de couples vaut:1\n", + "Pour n=3 le nombre de couples vaut:2\n", + "Pour n=4 le nombre de couples vaut:3\n", + "Pour n=5 le nombre de couples vaut:5\n", + "Pour n=6 le nombre de couples vaut:8\n", + "Pour n=7 le nombre de couples vaut:13\n", + "Pour n=8 le nombre de couples vaut:21\n", + "Pour n=9 le nombre de couples vaut:34\n", + "Pour n=10 le nombre de couples vaut:55\n" + ] + } + ], + "source": [ + "def fibo(n: int) -> int:\n", + " \"\"\" Calcule les termes de la suite de Fibonacci (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " \n", + " if n <= 0: return 0\n", + " elif n <= 1: return 1\n", + " \n", + " un_moins_2 = 0\n", + " un_moins_1 = 1\n", + " \n", + " for i in range(2,n+1):\n", + " un = un_moins_1 + un_moins_2\n", + " un_moins_2 = un_moins_1\n", + " un_moins_1 = un\n", + " return un\n", + "\n", + "for i in range(11):\n", + " print(f\"Pour n={i} le nombre de couples vaut:{fibo(i)}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "🏁 **Terminaison** : la fonction termine toujours car elle est constituée d'un boucle finie `for ... range`.\n", + "\n", + "🐌 **Complexité** : $O(n)$ car à chaque fois qu'on augmente n de 1 on ajoute un tour de boucle avec 3 affectations et 1 addition." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Récursivité\n", + "\n", + "⚠️ En informatique une fonction peut **s'appeler elle-même**, c'est ce qu'on nomme une **fonction récursive**. Faisons un exemple pour voir :" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n", + "Lancement de la fonction recursive_infinie()\n" + ] + }, + { + "ename": "RecursionError", + "evalue": "maximum recursion depth exceeded while calling a Python object", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mRecursionError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mrecursive_infinie\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mrecursive_infinie\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m\u001b[0m in \u001b[0;36mrecursive_infinie\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mrecursive_infinie\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Lancement de la fonction recursive_infinie()\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mrecursive_infinie\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mrecursive_infinie\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "... last 1 frames repeated, from the frame below ...\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36mrecursive_infinie\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mrecursive_infinie\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Lancement de la fonction recursive_infinie()\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mrecursive_infinie\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mrecursive_infinie\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mRecursionError\u001b[0m: maximum recursion depth exceeded while calling a Python object" + ] + } + ], + "source": [ + "def recursive_infinie():\n", + " print(\"Lancement de la fonction recursive_infinie()\")\n", + " recursive_infinie()\n", + " \n", + "recursive_infinie()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vous constatez que la fonction **s'appelle elle-même** sans s'arrêter jusqu'à provoquer l'erreur : *RecursionError: maximum recursion depth exceeded while calling a Python object*. Qui se traduit littéralement par : *Ta function ne s'arrête pas gros noob !*\n", + "\n", + "⚠️ Quand nous écrivons une **fonction récursive**, il faut s'assurer que la **fonction s'arrête à coup sûr** ! Il faut donc bien écrire le ou les **cas d'arrêt**.\n", + "\n", + "Essayons cet autre exemple :" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "On est dans la fonction recursive(10)\n", + "On est dans la fonction recursive(9)\n", + "On est dans la fonction recursive(8)\n", + "On est dans la fonction recursive(7)\n", + "On est dans la fonction recursive(6)\n", + "On est dans la fonction recursive(5)\n", + "On est dans la fonction recursive(4)\n", + "On est dans la fonction recursive(3)\n", + "On est dans la fonction recursive(2)\n", + "On est dans la fonction recursive(1)\n", + "On est dans la fonction recursive(0)\n", + "C'est fini !\n" + ] + } + ], + "source": [ + "def recursive(n: int):\n", + " print(f\"On est dans la fonction recursive({n})\")\n", + " if n <= 0 :\n", + " print(\"C'est fini !\")\n", + " else :\n", + " recursive(n-1)\n", + " \n", + "recursive(10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- Écrivez la fonction `fibor(n)` pour calculer les termes de la Suite de Fibonacci en utilisant une **fonction récursive**. Pour cela vous devez utiliser le fait que `fibor(n)` doit **retourner** `fibor(n-1) + fibor(n-2)` ! Et pensez aux cas d'arrêt !\n", + "- Testez votre fonction pour des valeurs de n entre 0 et 10." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pour n=0 le nombre de couples vaut:0\n", + "Pour n=1 le nombre de couples vaut:1\n", + "Pour n=2 le nombre de couples vaut:1\n", + "Pour n=3 le nombre de couples vaut:2\n", + "Pour n=4 le nombre de couples vaut:3\n", + "Pour n=5 le nombre de couples vaut:5\n", + "Pour n=6 le nombre de couples vaut:8\n", + "Pour n=7 le nombre de couples vaut:13\n", + "Pour n=8 le nombre de couples vaut:21\n", + "Pour n=9 le nombre de couples vaut:34\n", + "Pour n=10 le nombre de couples vaut:55\n" + ] + } + ], + "source": [ + "def fibor(n: int) -> int:\n", + " \"\"\" Calcule les termes de la suite de Fibonacci récursivement (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " \n", + " if n < 2: return n\n", + " else: return fibor(n-1) + fibor(n-2)\n", + " \n", + "for i in range(11):\n", + " print(f\"Pour n={i} le nombre de couples vaut:{fibor(i)}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "🏁 **Terminaison** : la fonction termine toujours car elle est appelée récursivement avec des paramètres entiers positifs **décroissants** donc ils arriveront forcément à 0 et 1 ce qui **arrêtera les appels récursifs**.\n", + "\n", + "🐌 **Complexité** : $O(A^n)$, chaque appel de la fonction avec un nombre n plus grand déploie un arbre d'appel qui croît exponentiellement.\n", + "\n", + "Cette méthode de programmation **récursive** est séduisante car elle permet de **programmer simplement** des problèmes **difficiles** (parcours de structures, etc.). Mais elle a un gros défaut, c'est qu'elle est souvent **peu performante** en terme de **temps de calcul** et **d'efficacité mémoire**. Voyons pourquoi.\n", + "\n", + "- Ajouter à votre fonction un `print` qui permet de voir toutes les fonctions appelées. Ensuite testez `fibor(10)`" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "On calcule fibor(10)\n", + "On calcule fibor(9)\n", + "On calcule fibor(8)\n", + "On calcule fibor(7)\n", + "On calcule fibor(6)\n", + "On calcule fibor(5)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(5)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(6)\n", + "On calcule fibor(5)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(7)\n", + "On calcule fibor(6)\n", + "On calcule fibor(5)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(5)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(8)\n", + "On calcule fibor(7)\n", + "On calcule fibor(6)\n", + "On calcule fibor(5)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(5)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(6)\n", + "On calcule fibor(5)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(4)\n", + "On calcule fibor(3)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "On calcule fibor(1)\n", + "On calcule fibor(2)\n", + "On calcule fibor(1)\n", + "On calcule fibor(0)\n", + "55\n", + "fibor lancée 177 fois\n" + ] + } + ], + "source": [ + "compteur = 0\n", + "\n", + "def fibor(n: int) -> int:\n", + " \"\"\" Calcule les termes de la suite de Fibonacci récursivement (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " global compteur\n", + " compteur += 1\n", + " print(f\"On calcule fibor({n})\")\n", + " if n < 2: return n\n", + " else: return fibor(n-1) + fibor(n-2)\n", + " \n", + "print(fibor(10))\n", + "print(\"fibor lancée\", compteur, \"fois\")" + ] + }, + { + "attachments": { + "out.svg": { + "image/svg+xml": [ + "<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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" + ] + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vous constatez que la fonction `fibor` est lancée **177 fois** ! Et surtout, on calcule les mêmes valeurs plusieurs fois, par exemple on calcule **8 fois** `fibor(5)` !\n", + "\n", + "Cette image montre bien le problème pour `fibor(6)` :\n", + "\n", + "![out.svg](attachment:out.svg)\n", + "\n", + "On voit dans l'arbre des appels successifs que `fibor(4)` est calculé 2 fois et `fibor(3)` 3 fois. Ce qui est évidemment **inefficace**.\n", + "\n", + "On peut, en général, améliorer la **récursivité** en faisant de la **récursivité terminale**, mais nous approfondirons ce problème plus tard...\n", + "\n", + "⚠️ Retenons pour l'instant que la **récursivité** permet de programmer avec **simplicité et élégance** des problème **difficiles** mais souvent au **détriment de la performance**.\n", + "\n", + "# Programmation dynamique\n", + "\n", + "Le gros défaut de l'algorithme précédent est qu'il **recalcule** sans cesse les **mêmes termes** inutilement. Il existe une méthode de programmation qui répond justement à ce problème :\n", + "\n", + "⚠️ La **programmation dynamique** est une méthode de programmation qui consiste à **enregistrer des résultats de calculs intermédiaires** pour les **réutiliser plus tard afin d'éviter de les recalculer**.\n", + "\n", + "- Écrivez la fonction `fibordyn` qui calcule les termes de la suite de Fibonacci **récursivement** mais avec une **liste pour enregistrer les résultats intermédiaires** que vous consulterez avant de recommencer un calcul.\n", + "\n", + "- Testez votre fonction avec n = 10." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "On appelle fibor(10)\n", + "On appelle fibor(9)\n", + "On appelle fibor(8)\n", + "On appelle fibor(7)\n", + "On appelle fibor(6)\n", + "On appelle fibor(5)\n", + "On appelle fibor(4)\n", + "On appelle fibor(3)\n", + "On appelle fibor(2)\n", + "On appelle fibor(1)\n", + "On appelle fibor(0)\n", + "On appelle fibor(1)\n", + "On appelle fibor(2)\n", + "On appelle fibor(3)\n", + "On appelle fibor(4)\n", + "On appelle fibor(5)\n", + "On appelle fibor(6)\n", + "On appelle fibor(7)\n", + "On appelle fibor(8)\n", + "55\n", + "On appelle fibor(10)\n", + "On appelle fibor(9)\n", + "On appelle fibor(8)\n", + "On appelle fibor(7)\n", + "On appelle fibor(6)\n", + "On appelle fibor(5)\n", + "On appelle fibor(4)\n", + "On appelle fibor(3)\n", + "On appelle fibor(2)\n", + "55\n", + "On appelle fibor(10)\n", + "On appelle fibor(9)\n", + "On appelle fibor(8)\n", + "On appelle fibor(7)\n", + "On appelle fibor(6)\n", + "On appelle fibor(5)\n", + "On appelle fibor(4)\n", + "On appelle fibor(3)\n", + "On appelle fibor(2)\n", + "55\n" + ] + } + ], + "source": [ + "def fibordyn1(n: int) -> int:\n", + " \"\"\" Lanceur de la fonction fibor (n>=0) : initialisation du tableau de résultats \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " resultats = [None for i in range(n+2)]\n", + " resultats[0] = 0\n", + " resultats[1] = 1\n", + " return fibor1(n, resultats)\n", + "\n", + "def fibor1(n: int, resultats: list) -> int:\n", + " \"\"\" Calcule les termes de la suite de Fibonacci récursivement avec programmation dynamique (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " print(f\"On appelle fibor({n})\")\n", + "\n", + " if resultats[n] == None:\n", + " resultats[n] = fibor1(n-1, resultats) + fibor1(n-2, resultats)\n", + " \n", + " return resultats[n]\n", + "\n", + "def fibordyn2(n: int) -> int:\n", + " \"\"\" Lanceur de la fonction fibor (n>=0) : initialisation du tableau de résultats \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " resultats = [None for i in range(n+2)]\n", + " resultats[0] = 0\n", + " resultats[1] = 1\n", + " return fibor2(n, resultats)\n", + "\n", + "def fibor2(n: int, resultats: list) -> int:\n", + " \"\"\" Calcule les termes de la suite de Fibonacci récursivement avec programmation dynamique (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " print(f\"On appelle fibor({n})\")\n", + " if resultats[n] != None: return resultats[n]\n", + " if resultats[n-1] == None: resultats[n-1] = fibor2(n-1, resultats)\n", + " if resultats[n-2] == None: resultats[n-2] = fibor2(n-2, resultats)\n", + " return resultats[n-1] + resultats[n-2]\n", + "\n", + "def fibordyn3(n: int) -> int:\n", + " \"\"\" Lanceur de la fonction fibor (n>=0) : initialisation du tableau de résultats \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " resultats = [None for i in range(n+2)]\n", + " resultats[0] = 0\n", + " resultats[1] = 1\n", + " \n", + " # === Nested function ===\n", + " def fibor3(n: int) -> int:\n", + " \"\"\" Calcule les termes de la suite de Fibonacci récursivement avec programmation dynamique (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " print(f\"On appelle fibor({n})\")\n", + " \n", + " if resultats[n] != None: return resultats[n]\n", + " if resultats[n-1] == None: resultats[n-1] = fibor3(n-1)\n", + " if resultats[n-2] == None: resultats[n-2] = fibor3(n-2)\n", + " return resultats[n-1] + resultats[n-2]\n", + " # === End of nested function ===\n", + " \n", + " return fibor3(n)\n", + "\n", + "print(fibordyn1(10))\n", + "print(fibordyn2(10))\n", + "print(fibordyn3(10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "🏁 **Terminaison** : la fonction termine toujours car elle est appelée récursivement avec des paramètres entiers positifs **décroissants** donc ils arriveront forcément à 0 et 1 ce qui **arrêtera les appels récursifs**.\n", + "\n", + "🐌 **Complexité** : $O(n)$, on appelle n+1 fois la fonction `fibor()` qui contient des tests, des affectations, des additions mais aussi des **accès à des listes qui se font en temps constant en Python**.\n", + "\n", + "⚠️ Je vous conseille de faire un arbre d'appel avec `n = 5` pour comprendre exactement comment marche ce programme car c'est plus subtil qu'il n'y parait ! C'est l'occasion d'utiliser [Python Tutor](http://www.pythontutor.com/visualize.html#mode=edit) !\n", + "\n", + "# Performances\n", + "\n", + "Nous avons donc 4 algorithmes différents pour calculer la croissance de la population de nos couples de lapins. Testons leurs performances.\n", + "\n", + "- **Copier-coller** la définition de votre fonction `lapinoux` au début de la cellule ci-dessous et exécutez la cellule pour analyser les performances." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test avec n=10 - Test avec n=1010 - Test avec n=2010 - Test avec n=3010 - Test avec n=4010 - Test avec n=5010 - Test avec n=6010 - Test avec n=7010 - Test avec n=8010 - Test avec n=9010 - Test avec n=10010 - Test avec n=11010 - Test avec n=12010 - Test avec n=13010 - Test avec n=14010 - Test avec n=15010 - Test avec n=16010 - Test avec n=17010 - Test avec n=18010 - Test avec n=19010 - Test avec n=20010 - Test avec n=21010 - Test avec n=22010 - Test avec n=23010 - Test avec n=24010 - Test avec n=25010 - Test avec n=26010 - Test avec n=27010 - Test avec n=28010 - Test avec n=29010 - Test avec n=30010 - Test avec n=31010 - Test avec n=32010 - Test avec n=33010 - Test avec n=34010 - Test avec n=35010 - Test avec n=36010 - Test avec n=37010 - Test avec n=38010 - Test avec n=39010 - Test avec n=40010 - Test avec n=41010 - Test avec n=42010 - Test avec n=43010 - Test avec n=44010 - Test avec n=45010 - Test avec n=46010 - Test avec n=47010 - Test avec n=48010 - Test avec n=49010 - Test avec n=50010 - Test avec n=51010 - Test avec n=52010 - Test avec n=53010 - Test avec n=54010 - Test avec n=55010 - Test avec n=56010 - Test avec n=57010 - Test avec n=58010 - Test avec n=59010 - Test avec n=60010 - Test avec n=61010 - Test avec n=62010 - Test avec n=63010 - Test avec n=64010 - Test avec n=65010 - Test avec n=66010 - Test avec n=67010 - Test avec n=68010 - Test avec n=69010 - Test avec n=70010 - Test avec n=71010 - Test avec n=72010 - Test avec n=73010 - Test avec n=74010 - Test avec n=75010 - Test avec n=76010 - Test avec n=77010 - Test avec n=78010 - Test avec n=79010 - Test avec n=80010 - Test avec n=81010 - Test avec n=82010 - Test avec n=83010 - Test avec n=84010 - Test avec n=85010 - Test avec n=86010 - Test avec n=87010 - Test avec n=88010 - Test avec n=89010 - Test avec n=90010 - Test avec n=91010 - Test avec n=92010 - Test avec n=93010 - Test avec n=94010 - Test avec n=95010 - Test avec n=96010 - Test avec n=97010 - Test avec n=98010 - Test avec n=99010 - " + ] + }, + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "/* global mpl */\n", + "window.mpl = {};\n", + "\n", + "mpl.get_websocket_type = function () {\n", + " if (typeof WebSocket !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof MozWebSocket !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert(\n", + " 'Your browser does not have WebSocket support. 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'mouseenter',\n", + " on_mouse_event_closure('figure_enter')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseleave',\n", + " on_mouse_event_closure('figure_leave')\n", + " );\n", + "\n", + " canvas_div.addEventListener('wheel', function (event) {\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " on_mouse_event_closure('scroll')(event);\n", + " });\n", + "\n", + " canvas_div.appendChild(canvas);\n", + " canvas_div.appendChild(rubberband_canvas);\n", + "\n", + " this.rubberband_context = rubberband_canvas.getContext('2d');\n", + " this.rubberband_context.strokeStyle = '#000000';\n", + "\n", + " this._resize_canvas = function (width, height, forward) {\n", + " if (forward) {\n", + " canvas_div.style.width = width + 'px';\n", + " canvas_div.style.height = height + 'px';\n", + " }\n", + " };\n", + "\n", + " // Disable right mouse context menu.\n", + " this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n", + " event.preventDefault();\n", + " return false;\n", + " });\n", + "\n", + " function set_focus() {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'mpl-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " continue;\n", + " }\n", + "\n", + " var button = (fig.buttons[name] = document.createElement('button'));\n", + " button.classList = 'mpl-widget';\n", + " button.setAttribute('role', 'button');\n", + " button.setAttribute('aria-disabled', 'false');\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + "\n", + " var icon_img = document.createElement('img');\n", + " icon_img.src = '_images/' + image + '.png';\n", + " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", + " icon_img.alt = tooltip;\n", + " button.appendChild(icon_img);\n", + "\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " var fmt_picker = document.createElement('select');\n", + " fmt_picker.classList = 'mpl-widget';\n", + " toolbar.appendChild(fmt_picker);\n", + " this.format_dropdown = fmt_picker;\n", + "\n", + " for (var ind in mpl.extensions) {\n", + " var fmt = mpl.extensions[ind];\n", + " var option = document.createElement('option');\n", + " option.selected = fmt === mpl.default_extension;\n", + " option.innerHTML = fmt;\n", + " fmt_picker.appendChild(option);\n", + " }\n", + "\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "};\n", + "\n", + "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", + " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", + " // which will in turn request a refresh of the image.\n", + " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", + "};\n", + "\n", + "mpl.figure.prototype.send_message = function (type, properties) {\n", + " properties['type'] = type;\n", + " properties['figure_id'] = this.id;\n", + " this.ws.send(JSON.stringify(properties));\n", + "};\n", + "\n", + "mpl.figure.prototype.send_draw_message = function () {\n", + " if (!this.waiting) {\n", + " this.waiting = true;\n", + " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " var format_dropdown = fig.format_dropdown;\n", + " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", + " fig.ondownload(fig, format);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", + " var size = msg['size'];\n", + " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", + " fig._resize_canvas(size[0], size[1], msg['forward']);\n", + " fig.send_message('refresh', {});\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", + " var x0 = msg['x0'] / fig.ratio;\n", + " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", + " var x1 = msg['x1'] / fig.ratio;\n", + " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", + " x0 = Math.floor(x0) + 0.5;\n", + " y0 = Math.floor(y0) + 0.5;\n", + " x1 = Math.floor(x1) + 0.5;\n", + " y1 = Math.floor(y1) + 0.5;\n", + " var min_x = Math.min(x0, x1);\n", + " var min_y = Math.min(y0, y1);\n", + " var width = Math.abs(x1 - x0);\n", + " var height = Math.abs(y1 - y0);\n", + "\n", + " fig.rubberband_context.clearRect(\n", + " 0,\n", + " 0,\n", + " fig.canvas.width / fig.ratio,\n", + " fig.canvas.height / fig.ratio\n", + " );\n", + "\n", + " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", + " // Updates the figure title.\n", + " fig.header.textContent = msg['label'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", + " var cursor = msg['cursor'];\n", + " switch (cursor) {\n", + " case 0:\n", + " cursor = 'pointer';\n", + " break;\n", + " case 1:\n", + " cursor = 'default';\n", + " break;\n", + " case 2:\n", + " cursor = 'crosshair';\n", + " break;\n", + " case 3:\n", + " cursor = 'move';\n", + " break;\n", + " }\n", + " fig.rubberband_canvas.style.cursor = cursor;\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_message = function (fig, msg) {\n", + " fig.message.textContent = msg['message'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", + " // Request the server to send over a new figure.\n", + " fig.send_draw_message();\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", + " fig.image_mode = msg['mode'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", + " for (var key in msg) {\n", + " if (!(key in fig.buttons)) {\n", + " continue;\n", + " }\n", + " fig.buttons[key].disabled = !msg[key];\n", + " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", + " if (msg['mode'] === 'PAN') {\n", + " fig.buttons['Pan'].classList.add('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " } else if (msg['mode'] === 'ZOOM') {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.add('active');\n", + " } else {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Called whenever the canvas gets updated.\n", + " this.send_message('ack', {});\n", + "};\n", + "\n", + "// A function to construct a web socket function for onmessage handling.\n", + "// Called in the figure constructor.\n", + "mpl.figure.prototype._make_on_message_function = function (fig) {\n", + " return function socket_on_message(evt) {\n", + " if (evt.data instanceof Blob) {\n", + " /* FIXME: We get \"Resource interpreted as Image but\n", + " * transferred with MIME type text/plain:\" errors on\n", + " * Chrome. But how to set the MIME type? It doesn't seem\n", + " * to be part of the websocket stream */\n", + " evt.data.type = 'image/png';\n", + "\n", + " /* Free the memory for the previous frames */\n", + " if (fig.imageObj.src) {\n", + " (window.URL || window.webkitURL).revokeObjectURL(\n", + " fig.imageObj.src\n", + " );\n", + " }\n", + "\n", + " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", + " evt.data\n", + " );\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " } else if (\n", + " typeof evt.data === 'string' &&\n", + " evt.data.slice(0, 21) === 'data:image/png;base64'\n", + " ) {\n", + " fig.imageObj.src = evt.data;\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " }\n", + "\n", + " var msg = JSON.parse(evt.data);\n", + " var msg_type = msg['type'];\n", + "\n", + " // Call the \"handle_{type}\" callback, which takes\n", + " // the figure and JSON message as its only arguments.\n", + " try {\n", + " var callback = fig['handle_' + msg_type];\n", + " } catch (e) {\n", + " console.log(\n", + " \"No handler for the '\" + msg_type + \"' message type: \",\n", + " msg\n", + " );\n", + " return;\n", + " }\n", + "\n", + " if (callback) {\n", + " try {\n", + " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", + " callback(fig, msg);\n", + " } catch (e) {\n", + " console.log(\n", + " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", + " e,\n", + " e.stack,\n", + " msg\n", + " );\n", + " }\n", + " }\n", + " };\n", + "};\n", + "\n", + "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", + "mpl.findpos = function (e) {\n", + " //this section is from http://www.quirksmode.org/js/events_properties.html\n", + " var targ;\n", + " if (!e) {\n", + " e = window.event;\n", + " }\n", + " if (e.target) {\n", + " targ = e.target;\n", + " } else if (e.srcElement) {\n", + " targ = e.srcElement;\n", + " }\n", + " if (targ.nodeType === 3) {\n", + " // defeat Safari bug\n", + " targ = targ.parentNode;\n", + " }\n", + "\n", + " // pageX,Y are the mouse positions relative to the document\n", + " var boundingRect = targ.getBoundingClientRect();\n", + " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", + " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", + "\n", + " return { x: x, y: y };\n", + "};\n", + "\n", + "/*\n", + " * return a copy of an object with only non-object keys\n", + " * we need this to avoid circular references\n", + " * http://stackoverflow.com/a/24161582/3208463\n", + " */\n", + "function simpleKeys(original) {\n", + " return Object.keys(original).reduce(function (obj, key) {\n", + " if (typeof original[key] !== 'object') {\n", + " obj[key] = original[key];\n", + " }\n", + " return obj;\n", + " }, {});\n", + "}\n", + "\n", + "mpl.figure.prototype.mouse_event = function (event, name) {\n", + " var canvas_pos = mpl.findpos(event);\n", + "\n", + " if (name === 'button_press') {\n", + " this.canvas.focus();\n", + " this.canvas_div.focus();\n", + " }\n", + "\n", + " var x = canvas_pos.x * this.ratio;\n", + " var y = canvas_pos.y * this.ratio;\n", + "\n", + " this.send_message(name, {\n", + " x: x,\n", + " y: y,\n", + " button: event.button,\n", + " step: event.step,\n", + " guiEvent: simpleKeys(event),\n", + " });\n", + "\n", + " /* This prevents the web browser from automatically changing to\n", + " * the text insertion cursor when the button is pressed. We want\n", + " * to control all of the cursor setting manually through the\n", + " * 'cursor' event from matplotlib */\n", + " event.preventDefault();\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", + " // Handle any extra behaviour associated with a key event\n", + "};\n", + "\n", + "mpl.figure.prototype.key_event = function (event, name) {\n", + " // Prevent repeat events\n", + " if (name === 'key_press') {\n", + " if (event.which === this._key) {\n", + " return;\n", + " } else {\n", + " this._key = event.which;\n", + " }\n", + " }\n", + " if (name === 'key_release') {\n", + " this._key = null;\n", + " }\n", + "\n", + " var value = '';\n", + " if (event.ctrlKey && event.which !== 17) {\n", + " value += 'ctrl+';\n", + " }\n", + " if (event.altKey && event.which !== 18) {\n", + " value += 'alt+';\n", + " }\n", + " if (event.shiftKey && event.which !== 16) {\n", + " value += 'shift+';\n", + " }\n", + "\n", + " value += 'k';\n", + " value += event.which.toString();\n", + "\n", + " this._key_event_extra(event, name);\n", + "\n", + " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", + " if (name === 'download') {\n", + " this.handle_save(this, null);\n", + " } else {\n", + " this.send_message('toolbar_button', { name: name });\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", + " this.message.textContent = tooltip;\n", + "};\n", + "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", + "\n", + "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", + "\n", + "mpl.default_extension = \"png\";/* global mpl */\n", + "\n", + "var comm_websocket_adapter = function (comm) {\n", + " // Create a \"websocket\"-like object which calls the given IPython comm\n", + " // object with the appropriate methods. Currently this is a non binary\n", + " // socket, so there is still some room for performance tuning.\n", + " var ws = {};\n", + "\n", + " ws.close = function () {\n", + " comm.close();\n", + " };\n", + " ws.send = function (m) {\n", + " //console.log('sending', m);\n", + " comm.send(m);\n", + " };\n", + " // Register the callback with on_msg.\n", + " comm.on_msg(function (msg) {\n", + " //console.log('receiving', msg['content']['data'], msg);\n", + " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", + " ws.onmessage(msg['content']['data']);\n", + " });\n", + " return ws;\n", + "};\n", + "\n", + "mpl.mpl_figure_comm = function (comm, msg) {\n", + " // This is the function which gets called when the mpl process\n", + " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", + "\n", + " var id = msg.content.data.id;\n", + " // Get hold of the div created by the display call when the Comm\n", + " // socket was opened in Python.\n", + " var element = document.getElementById(id);\n", + " var ws_proxy = comm_websocket_adapter(comm);\n", + "\n", + " function ondownload(figure, _format) {\n", + " window.open(figure.canvas.toDataURL());\n", + " }\n", + "\n", + " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", + "\n", + " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", + " // web socket which is closed, not our websocket->open comm proxy.\n", + " ws_proxy.onopen();\n", + "\n", + " fig.parent_element = element;\n", + " fig.cell_info = mpl.find_output_cell(\"
\");\n", + " if (!fig.cell_info) {\n", + " console.error('Failed to find cell for figure', id, fig);\n", + " return;\n", + " }\n", + " fig.cell_info[0].output_area.element.one(\n", + " 'cleared',\n", + " { fig: fig },\n", + " fig._remove_fig_handler\n", + " );\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_close = function (fig, msg) {\n", + " var width = fig.canvas.width / fig.ratio;\n", + " fig.cell_info[0].output_area.element.off(\n", + " 'cleared',\n", + " fig._remove_fig_handler\n", + " );\n", + "\n", + " // Update the output cell to use the data from the current canvas.\n", + " fig.push_to_output();\n", + " var dataURL = fig.canvas.toDataURL();\n", + " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", + " // the notebook keyboard shortcuts fail.\n", + " IPython.keyboard_manager.enable();\n", + " fig.parent_element.innerHTML =\n", + " '';\n", + " fig.close_ws(fig, msg);\n", + "};\n", + "\n", + "mpl.figure.prototype.close_ws = function (fig, msg) {\n", + " fig.send_message('closing', msg);\n", + " // fig.ws.close()\n", + "};\n", + "\n", + "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", + " // Turn the data on the canvas into data in the output cell.\n", + " var width = this.canvas.width / this.ratio;\n", + " var dataURL = this.canvas.toDataURL();\n", + " this.cell_info[1]['text/html'] =\n", + " '';\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Tell IPython that the notebook contents must change.\n", + " IPython.notebook.set_dirty(true);\n", + " this.send_message('ack', {});\n", + " var fig = this;\n", + " // Wait a second, then push the new image to the DOM so\n", + " // that it is saved nicely (might be nice to debounce this).\n", + " setTimeout(function () {\n", + " fig.push_to_output();\n", + " }, 1000);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'btn-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " var button;\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " continue;\n", + " }\n", + "\n", + " button = fig.buttons[name] = document.createElement('button');\n", + " button.classList = 'btn btn-default';\n", + " button.href = '#';\n", + " button.title = name;\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message pull-right';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = document.createElement('div');\n", + " buttongrp.classList = 'btn-group inline pull-right';\n", + " button = document.createElement('button');\n", + " button.classList = 'btn btn-mini btn-primary';\n", + " button.href = '#';\n", + " button.title = 'Stop Interaction';\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', function (_evt) {\n", + " fig.handle_close(fig, {});\n", + " });\n", + " button.addEventListener(\n", + " 'mouseover',\n", + " on_mouseover_closure('Stop Interaction')\n", + " );\n", + " buttongrp.appendChild(button);\n", + " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", + " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", + "};\n", + "\n", + "mpl.figure.prototype._remove_fig_handler = function (event) {\n", + " var fig = event.data.fig;\n", + " fig.close_ws(fig, {});\n", + "};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (el) {\n", + " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (el) {\n", + " // this is important to make the div 'focusable\n", + " el.setAttribute('tabindex', 0);\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " } else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager) {\n", + " manager = IPython.keyboard_manager;\n", + " }\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which === 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " fig.ondownload(fig, null);\n", + "};\n", + "\n", + "mpl.find_output_cell = function (html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i = 0; i < ncells; i++) {\n", + " var cell = cells[i];\n", + " if (cell.cell_type === 'code') {\n", + " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", + " var data = cell.output_area.outputs[j];\n", + " if (data.data) {\n", + " // IPython >= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] === html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "};\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel !== null) {\n", + " IPython.notebook.kernel.comm_manager.register_target(\n", + " 'matplotlib',\n", + " mpl.mpl_figure_comm\n", + " );\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n", + "Temps d'execution de lapinoux avec n=99010 : 0.08579590969999984\n" + ] + } + ], + "source": [ + "def lapinoux(n: int) -> int:\n", + " \"\"\" Calcule le nombre de couples de lapins au bout de n mois (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " nb_couples_immatures1 = 1\n", + " nb_couples_immatures2 = 0\n", + " nb_couples_matures = 0\n", + " \n", + " for i in range(n+1):\n", + " nb_couples_matures += nb_couples_immatures2\n", + " nb_couples_immatures2 = nb_couples_immatures1\n", + " nb_couples_immatures1 = nb_couples_matures\n", + " \n", + " return nb_couples_matures\n", + "\n", + "# Mesure du temps et tracés\n", + "import time\n", + "%matplotlib notebook\n", + "import matplotlib.pyplot as plt\n", + "\n", + "n = [i for i in range(10, 100000, 1000)]\n", + "liste_temps = []\n", + "\n", + "for i in n:\n", + " print(f\"Test avec n={i}\", end = \" - \")\n", + " temps = 0.0\n", + " nb_loops = 10\n", + " for test in range(nb_loops):\n", + " start = time.process_time()\n", + " lapinoux(i)\n", + " temps += time.process_time() - start\n", + " temps /= nb_loops\n", + " liste_temps.append(temps)\n", + "\n", + "plt.plot(n, liste_temps, label=\"lapinoux\")\n", + "plt.xlabel(\"n\")\n", + "plt.grid(True)\n", + "print(f\"\\n\\nTemps d'execution de lapinoux avec n={n[-1]} : {liste_temps[-1]}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On constate que le temps d'exécution en fonction de `n` n'est **pas linéaire** comme la complexité le laissait supposer... ???\n", + "\n", + "- **Copier-coller** la définition de votre fonction `fibo` au début de la cellule suivante et exécutez la cellule pour analyser les performances." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test avec n=10 - Test avec n=1010 - Test avec n=2010 - Test avec n=3010 - Test avec n=4010 - Test avec n=5010 - Test avec n=6010 - Test avec n=7010 - Test avec n=8010 - Test avec n=9010 - Test avec n=10010 - Test avec n=11010 - Test avec n=12010 - Test avec n=13010 - Test avec n=14010 - Test avec n=15010 - Test avec n=16010 - Test avec n=17010 - Test avec n=18010 - Test avec n=19010 - Test avec n=20010 - Test avec n=21010 - Test avec n=22010 - Test avec n=23010 - Test avec n=24010 - Test avec n=25010 - Test avec n=26010 - Test avec n=27010 - Test avec n=28010 - Test avec n=29010 - Test avec n=30010 - Test avec n=31010 - Test avec n=32010 - Test avec n=33010 - Test avec n=34010 - Test avec n=35010 - Test avec n=36010 - Test avec n=37010 - Test avec n=38010 - Test avec n=39010 - Test avec n=40010 - Test avec n=41010 - Test avec n=42010 - Test avec n=43010 - Test avec n=44010 - Test avec n=45010 - Test avec n=46010 - Test avec n=47010 - Test avec n=48010 - Test avec n=49010 - Test avec n=50010 - Test avec n=51010 - Test avec n=52010 - Test avec n=53010 - Test avec n=54010 - Test avec n=55010 - Test avec n=56010 - Test avec n=57010 - Test avec n=58010 - Test avec n=59010 - Test avec n=60010 - Test avec n=61010 - Test avec n=62010 - Test avec n=63010 - Test avec n=64010 - Test avec n=65010 - Test avec n=66010 - Test avec n=67010 - Test avec n=68010 - Test avec n=69010 - Test avec n=70010 - Test avec n=71010 - Test avec n=72010 - Test avec n=73010 - Test avec n=74010 - Test avec n=75010 - Test avec n=76010 - Test avec n=77010 - Test avec n=78010 - Test avec n=79010 - Test avec n=80010 - Test avec n=81010 - Test avec n=82010 - Test avec n=83010 - Test avec n=84010 - Test avec n=85010 - Test avec n=86010 - Test avec n=87010 - Test avec n=88010 - Test avec n=89010 - Test avec n=90010 - Test avec n=91010 - Test avec n=92010 - Test avec n=93010 - Test avec n=94010 - Test avec n=95010 - Test avec n=96010 - Test avec n=97010 - Test avec n=98010 - Test avec n=99010 - " + ] + }, + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "/* global mpl */\n", + "window.mpl = {};\n", + "\n", + "mpl.get_websocket_type = function () {\n", + " if (typeof WebSocket !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof MozWebSocket !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert(\n", + " 'Your browser does not have WebSocket support. ' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.'\n", + " );\n", + " }\n", + "};\n", + "\n", + "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = this.ws.binaryType !== undefined;\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById('mpl-warnings');\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent =\n", + " 'This browser does not support binary websocket messages. ' +\n", + " 'Performance may be slow.';\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = document.createElement('div');\n", + " this.root.setAttribute('style', 'display: inline-block');\n", + " this._root_extra_style(this.root);\n", + "\n", + " parent_element.appendChild(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message('supports_binary', { value: fig.supports_binary });\n", + " fig.send_message('send_image_mode', {});\n", + " if (fig.ratio !== 1) {\n", + " fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n", + " }\n", + " fig.send_message('refresh', {});\n", + " };\n", + "\n", + " this.imageObj.onload = function () {\n", + " if (fig.image_mode === 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function () {\n", + " fig.ws.close();\n", + " };\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "};\n", + "\n", + "mpl.figure.prototype._init_header = function () {\n", + " var titlebar = document.createElement('div');\n", + " titlebar.classList =\n", + " 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n", + " var titletext = document.createElement('div');\n", + " titletext.classList = 'ui-dialog-title';\n", + " titletext.setAttribute(\n", + " 'style',\n", + " 'width: 100%; text-align: center; padding: 3px;'\n", + " );\n", + " titlebar.appendChild(titletext);\n", + " this.root.appendChild(titlebar);\n", + " this.header = titletext;\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n", + "\n", + "mpl.figure.prototype._init_canvas = function () {\n", + " var fig = this;\n", + "\n", + " var canvas_div = (this.canvas_div = document.createElement('div'));\n", + " canvas_div.setAttribute(\n", + " 'style',\n", + " 'border: 1px solid #ddd;' +\n", + " 'box-sizing: content-box;' +\n", + " 'clear: both;' +\n", + " 'min-height: 1px;' +\n", + " 'min-width: 1px;' +\n", + " 'outline: 0;' +\n", + " 'overflow: hidden;' +\n", + " 'position: relative;' +\n", + " 'resize: both;'\n", + " );\n", + "\n", + " function on_keyboard_event_closure(name) {\n", + " return function (event) {\n", + " return fig.key_event(event, name);\n", + " };\n", + " }\n", + "\n", + " canvas_div.addEventListener(\n", + " 'keydown',\n", + " on_keyboard_event_closure('key_press')\n", + " );\n", + " canvas_div.addEventListener(\n", + " 'keyup',\n", + " on_keyboard_event_closure('key_release')\n", + " );\n", + "\n", + " this._canvas_extra_style(canvas_div);\n", + " this.root.appendChild(canvas_div);\n", + "\n", + " var canvas = (this.canvas = document.createElement('canvas'));\n", + " canvas.classList.add('mpl-canvas');\n", + " canvas.setAttribute('style', 'box-sizing: content-box;');\n", + "\n", + " this.context = canvas.getContext('2d');\n", + "\n", + " var backingStore =\n", + " this.context.backingStorePixelRatio ||\n", + " this.context.webkitBackingStorePixelRatio ||\n", + " this.context.mozBackingStorePixelRatio ||\n", + " this.context.msBackingStorePixelRatio ||\n", + " this.context.oBackingStorePixelRatio ||\n", + " this.context.backingStorePixelRatio ||\n", + " 1;\n", + "\n", + " this.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + " if (this.ratio !== 1) {\n", + " fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n", + " }\n", + "\n", + " var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n", + " 'canvas'\n", + " ));\n", + " rubberband_canvas.setAttribute(\n", + " 'style',\n", + " 'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n", + " );\n", + "\n", + " var resizeObserver = new ResizeObserver(function (entries) {\n", + " var nentries = entries.length;\n", + " for (var i = 0; i < nentries; i++) {\n", + " var entry = entries[i];\n", + " var width, height;\n", + " if (entry.contentBoxSize) {\n", + " if (entry.contentBoxSize instanceof Array) {\n", + " // Chrome 84 implements new version of spec.\n", + " width = entry.contentBoxSize[0].inlineSize;\n", + " height = entry.contentBoxSize[0].blockSize;\n", + " } else {\n", + " // Firefox implements old version of spec.\n", + " width = entry.contentBoxSize.inlineSize;\n", + " height = entry.contentBoxSize.blockSize;\n", + " }\n", + " } else {\n", + " // Chrome <84 implements even older version of spec.\n", + " width = entry.contentRect.width;\n", + " height = entry.contentRect.height;\n", + " }\n", + "\n", + " // Keep the size of the canvas and rubber band canvas in sync with\n", + " // the canvas container.\n", + " if (entry.devicePixelContentBoxSize) {\n", + " // Chrome 84 implements new version of spec.\n", + " canvas.setAttribute(\n", + " 'width',\n", + " entry.devicePixelContentBoxSize[0].inlineSize\n", + " );\n", + " canvas.setAttribute(\n", + " 'height',\n", + " entry.devicePixelContentBoxSize[0].blockSize\n", + " );\n", + " } else {\n", + " canvas.setAttribute('width', width * fig.ratio);\n", + " canvas.setAttribute('height', height * fig.ratio);\n", + " }\n", + " canvas.setAttribute(\n", + " 'style',\n", + " 'width: ' + width + 'px; height: ' + height + 'px;'\n", + " );\n", + "\n", + " rubberband_canvas.setAttribute('width', width);\n", + " rubberband_canvas.setAttribute('height', height);\n", + "\n", + " // And update the size in Python. We ignore the initial 0/0 size\n", + " // that occurs as the element is placed into the DOM, which should\n", + " // otherwise not happen due to the minimum size styling.\n", + " if (width != 0 && height != 0) {\n", + " fig.request_resize(width, height);\n", + " }\n", + " }\n", + " });\n", + " resizeObserver.observe(canvas_div);\n", + "\n", + " function on_mouse_event_closure(name) {\n", + " return function (event) {\n", + " return fig.mouse_event(event, name);\n", + " };\n", + " }\n", + "\n", + " rubberband_canvas.addEventListener(\n", + " 'mousedown',\n", + " on_mouse_event_closure('button_press')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseup',\n", + " on_mouse_event_closure('button_release')\n", + " );\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband_canvas.addEventListener(\n", + " 'mousemove',\n", + " on_mouse_event_closure('motion_notify')\n", + " );\n", + "\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseenter',\n", + " on_mouse_event_closure('figure_enter')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseleave',\n", + " on_mouse_event_closure('figure_leave')\n", + " );\n", + "\n", + " canvas_div.addEventListener('wheel', function (event) {\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " on_mouse_event_closure('scroll')(event);\n", + " });\n", + "\n", + " canvas_div.appendChild(canvas);\n", + " canvas_div.appendChild(rubberband_canvas);\n", + "\n", + " this.rubberband_context = rubberband_canvas.getContext('2d');\n", + " this.rubberband_context.strokeStyle = '#000000';\n", + "\n", + " this._resize_canvas = function (width, height, forward) {\n", + " if (forward) {\n", + " canvas_div.style.width = width + 'px';\n", + " canvas_div.style.height = height + 'px';\n", + " }\n", + " };\n", + "\n", + " // Disable right mouse context menu.\n", + " this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n", + " event.preventDefault();\n", + " return false;\n", + " });\n", + "\n", + " function set_focus() {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'mpl-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " continue;\n", + " }\n", + "\n", + " var button = (fig.buttons[name] = document.createElement('button'));\n", + " button.classList = 'mpl-widget';\n", + " button.setAttribute('role', 'button');\n", + " button.setAttribute('aria-disabled', 'false');\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + "\n", + " var icon_img = document.createElement('img');\n", + " icon_img.src = '_images/' + image + '.png';\n", + " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", + " icon_img.alt = tooltip;\n", + " button.appendChild(icon_img);\n", + "\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " var fmt_picker = document.createElement('select');\n", + " fmt_picker.classList = 'mpl-widget';\n", + " toolbar.appendChild(fmt_picker);\n", + " this.format_dropdown = fmt_picker;\n", + "\n", + " for (var ind in mpl.extensions) {\n", + " var fmt = mpl.extensions[ind];\n", + " var option = document.createElement('option');\n", + " option.selected = fmt === mpl.default_extension;\n", + " option.innerHTML = fmt;\n", + " fmt_picker.appendChild(option);\n", + " }\n", + "\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "};\n", + "\n", + "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", + " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", + " // which will in turn request a refresh of the image.\n", + " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", + "};\n", + "\n", + "mpl.figure.prototype.send_message = function (type, properties) {\n", + " properties['type'] = type;\n", + " properties['figure_id'] = this.id;\n", + " this.ws.send(JSON.stringify(properties));\n", + "};\n", + "\n", + "mpl.figure.prototype.send_draw_message = function () {\n", + " if (!this.waiting) {\n", + " this.waiting = true;\n", + " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " var format_dropdown = fig.format_dropdown;\n", + " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", + " fig.ondownload(fig, format);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", + " var size = msg['size'];\n", + " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", + " fig._resize_canvas(size[0], size[1], msg['forward']);\n", + " fig.send_message('refresh', {});\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", + " var x0 = msg['x0'] / fig.ratio;\n", + " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", + " var x1 = msg['x1'] / fig.ratio;\n", + " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", + " x0 = Math.floor(x0) + 0.5;\n", + " y0 = Math.floor(y0) + 0.5;\n", + " x1 = Math.floor(x1) + 0.5;\n", + " y1 = Math.floor(y1) + 0.5;\n", + " var min_x = Math.min(x0, x1);\n", + " var min_y = Math.min(y0, y1);\n", + " var width = Math.abs(x1 - x0);\n", + " var height = Math.abs(y1 - y0);\n", + "\n", + " fig.rubberband_context.clearRect(\n", + " 0,\n", + " 0,\n", + " fig.canvas.width / fig.ratio,\n", + " fig.canvas.height / fig.ratio\n", + " );\n", + "\n", + " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", + " // Updates the figure title.\n", + " fig.header.textContent = msg['label'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", + " var cursor = msg['cursor'];\n", + " switch (cursor) {\n", + " case 0:\n", + " cursor = 'pointer';\n", + " break;\n", + " case 1:\n", + " cursor = 'default';\n", + " break;\n", + " case 2:\n", + " cursor = 'crosshair';\n", + " break;\n", + " case 3:\n", + " cursor = 'move';\n", + " break;\n", + " }\n", + " fig.rubberband_canvas.style.cursor = cursor;\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_message = function (fig, msg) {\n", + " fig.message.textContent = msg['message'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", + " // Request the server to send over a new figure.\n", + " fig.send_draw_message();\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", + " fig.image_mode = msg['mode'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", + " for (var key in msg) {\n", + " if (!(key in fig.buttons)) {\n", + " continue;\n", + " }\n", + " fig.buttons[key].disabled = !msg[key];\n", + " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", + " if (msg['mode'] === 'PAN') {\n", + " fig.buttons['Pan'].classList.add('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " } else if (msg['mode'] === 'ZOOM') {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.add('active');\n", + " } else {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Called whenever the canvas gets updated.\n", + " this.send_message('ack', {});\n", + "};\n", + "\n", + "// A function to construct a web socket function for onmessage handling.\n", + "// Called in the figure constructor.\n", + "mpl.figure.prototype._make_on_message_function = function (fig) {\n", + " return function socket_on_message(evt) {\n", + " if (evt.data instanceof Blob) {\n", + " /* FIXME: We get \"Resource interpreted as Image but\n", + " * transferred with MIME type text/plain:\" errors on\n", + " * Chrome. But how to set the MIME type? It doesn't seem\n", + " * to be part of the websocket stream */\n", + " evt.data.type = 'image/png';\n", + "\n", + " /* Free the memory for the previous frames */\n", + " if (fig.imageObj.src) {\n", + " (window.URL || window.webkitURL).revokeObjectURL(\n", + " fig.imageObj.src\n", + " );\n", + " }\n", + "\n", + " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", + " evt.data\n", + " );\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " } else if (\n", + " typeof evt.data === 'string' &&\n", + " evt.data.slice(0, 21) === 'data:image/png;base64'\n", + " ) {\n", + " fig.imageObj.src = evt.data;\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " }\n", + "\n", + " var msg = JSON.parse(evt.data);\n", + " var msg_type = msg['type'];\n", + "\n", + " // Call the \"handle_{type}\" callback, which takes\n", + " // the figure and JSON message as its only arguments.\n", + " try {\n", + " var callback = fig['handle_' + msg_type];\n", + " } catch (e) {\n", + " console.log(\n", + " \"No handler for the '\" + msg_type + \"' message type: \",\n", + " msg\n", + " );\n", + " return;\n", + " }\n", + "\n", + " if (callback) {\n", + " try {\n", + " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", + " callback(fig, msg);\n", + " } catch (e) {\n", + " console.log(\n", + " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", + " e,\n", + " e.stack,\n", + " msg\n", + " );\n", + " }\n", + " }\n", + " };\n", + "};\n", + "\n", + "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", + "mpl.findpos = function (e) {\n", + " //this section is from http://www.quirksmode.org/js/events_properties.html\n", + " var targ;\n", + " if (!e) {\n", + " e = window.event;\n", + " }\n", + " if (e.target) {\n", + " targ = e.target;\n", + " } else if (e.srcElement) {\n", + " targ = e.srcElement;\n", + " }\n", + " if (targ.nodeType === 3) {\n", + " // defeat Safari bug\n", + " targ = targ.parentNode;\n", + " }\n", + "\n", + " // pageX,Y are the mouse positions relative to the document\n", + " var boundingRect = targ.getBoundingClientRect();\n", + " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", + " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", + "\n", + " return { x: x, y: y };\n", + "};\n", + "\n", + "/*\n", + " * return a copy of an object with only non-object keys\n", + " * we need this to avoid circular references\n", + " * http://stackoverflow.com/a/24161582/3208463\n", + " */\n", + "function simpleKeys(original) {\n", + " return Object.keys(original).reduce(function (obj, key) {\n", + " if (typeof original[key] !== 'object') {\n", + " obj[key] = original[key];\n", + " }\n", + " return obj;\n", + " }, {});\n", + "}\n", + "\n", + "mpl.figure.prototype.mouse_event = function (event, name) {\n", + " var canvas_pos = mpl.findpos(event);\n", + "\n", + " if (name === 'button_press') {\n", + " this.canvas.focus();\n", + " this.canvas_div.focus();\n", + " }\n", + "\n", + " var x = canvas_pos.x * this.ratio;\n", + " var y = canvas_pos.y * this.ratio;\n", + "\n", + " this.send_message(name, {\n", + " x: x,\n", + " y: y,\n", + " button: event.button,\n", + " step: event.step,\n", + " guiEvent: simpleKeys(event),\n", + " });\n", + "\n", + " /* This prevents the web browser from automatically changing to\n", + " * the text insertion cursor when the button is pressed. We want\n", + " * to control all of the cursor setting manually through the\n", + " * 'cursor' event from matplotlib */\n", + " event.preventDefault();\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", + " // Handle any extra behaviour associated with a key event\n", + "};\n", + "\n", + "mpl.figure.prototype.key_event = function (event, name) {\n", + " // Prevent repeat events\n", + " if (name === 'key_press') {\n", + " if (event.which === this._key) {\n", + " return;\n", + " } else {\n", + " this._key = event.which;\n", + " }\n", + " }\n", + " if (name === 'key_release') {\n", + " this._key = null;\n", + " }\n", + "\n", + " var value = '';\n", + " if (event.ctrlKey && event.which !== 17) {\n", + " value += 'ctrl+';\n", + " }\n", + " if (event.altKey && event.which !== 18) {\n", + " value += 'alt+';\n", + " }\n", + " if (event.shiftKey && event.which !== 16) {\n", + " value += 'shift+';\n", + " }\n", + "\n", + " value += 'k';\n", + " value += event.which.toString();\n", + "\n", + " this._key_event_extra(event, name);\n", + "\n", + " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", + " if (name === 'download') {\n", + " this.handle_save(this, null);\n", + " } else {\n", + " this.send_message('toolbar_button', { name: name });\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", + " this.message.textContent = tooltip;\n", + "};\n", + "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", + "\n", + "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", + "\n", + "mpl.default_extension = \"png\";/* global mpl */\n", + "\n", + "var comm_websocket_adapter = function (comm) {\n", + " // Create a \"websocket\"-like object which calls the given IPython comm\n", + " // object with the appropriate methods. Currently this is a non binary\n", + " // socket, so there is still some room for performance tuning.\n", + " var ws = {};\n", + "\n", + " ws.close = function () {\n", + " comm.close();\n", + " };\n", + " ws.send = function (m) {\n", + " //console.log('sending', m);\n", + " comm.send(m);\n", + " };\n", + " // Register the callback with on_msg.\n", + " comm.on_msg(function (msg) {\n", + " //console.log('receiving', msg['content']['data'], msg);\n", + " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", + " ws.onmessage(msg['content']['data']);\n", + " });\n", + " return ws;\n", + "};\n", + "\n", + "mpl.mpl_figure_comm = function (comm, msg) {\n", + " // This is the function which gets called when the mpl process\n", + " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", + "\n", + " var id = msg.content.data.id;\n", + " // Get hold of the div created by the display call when the Comm\n", + " // socket was opened in Python.\n", + " var element = document.getElementById(id);\n", + " var ws_proxy = comm_websocket_adapter(comm);\n", + "\n", + " function ondownload(figure, _format) {\n", + " window.open(figure.canvas.toDataURL());\n", + " }\n", + "\n", + " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", + "\n", + " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", + " // web socket which is closed, not our websocket->open comm proxy.\n", + " ws_proxy.onopen();\n", + "\n", + " fig.parent_element = element;\n", + " fig.cell_info = mpl.find_output_cell(\"
\");\n", + " if (!fig.cell_info) {\n", + " console.error('Failed to find cell for figure', id, fig);\n", + " return;\n", + " }\n", + " fig.cell_info[0].output_area.element.one(\n", + " 'cleared',\n", + " { fig: fig },\n", + " fig._remove_fig_handler\n", + " );\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_close = function (fig, msg) {\n", + " var width = fig.canvas.width / fig.ratio;\n", + " fig.cell_info[0].output_area.element.off(\n", + " 'cleared',\n", + " fig._remove_fig_handler\n", + " );\n", + "\n", + " // Update the output cell to use the data from the current canvas.\n", + " fig.push_to_output();\n", + " var dataURL = fig.canvas.toDataURL();\n", + " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", + " // the notebook keyboard shortcuts fail.\n", + " IPython.keyboard_manager.enable();\n", + " fig.parent_element.innerHTML =\n", + " '';\n", + " fig.close_ws(fig, msg);\n", + "};\n", + "\n", + "mpl.figure.prototype.close_ws = function (fig, msg) {\n", + " fig.send_message('closing', msg);\n", + " // fig.ws.close()\n", + "};\n", + "\n", + "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", + " // Turn the data on the canvas into data in the output cell.\n", + " var width = this.canvas.width / this.ratio;\n", + " var dataURL = this.canvas.toDataURL();\n", + " this.cell_info[1]['text/html'] =\n", + " '';\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Tell IPython that the notebook contents must change.\n", + " IPython.notebook.set_dirty(true);\n", + " this.send_message('ack', {});\n", + " var fig = this;\n", + " // Wait a second, then push the new image to the DOM so\n", + " // that it is saved nicely (might be nice to debounce this).\n", + " setTimeout(function () {\n", + " fig.push_to_output();\n", + " }, 1000);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'btn-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " var button;\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " continue;\n", + " }\n", + "\n", + " button = fig.buttons[name] = document.createElement('button');\n", + " button.classList = 'btn btn-default';\n", + " button.href = '#';\n", + " button.title = name;\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message pull-right';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = document.createElement('div');\n", + " buttongrp.classList = 'btn-group inline pull-right';\n", + " button = document.createElement('button');\n", + " button.classList = 'btn btn-mini btn-primary';\n", + " button.href = '#';\n", + " button.title = 'Stop Interaction';\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', function (_evt) {\n", + " fig.handle_close(fig, {});\n", + " });\n", + " button.addEventListener(\n", + " 'mouseover',\n", + " on_mouseover_closure('Stop Interaction')\n", + " );\n", + " buttongrp.appendChild(button);\n", + " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", + " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", + "};\n", + "\n", + "mpl.figure.prototype._remove_fig_handler = function (event) {\n", + " var fig = event.data.fig;\n", + " fig.close_ws(fig, {});\n", + "};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (el) {\n", + " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (el) {\n", + " // this is important to make the div 'focusable\n", + " el.setAttribute('tabindex', 0);\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " } else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager) {\n", + " manager = IPython.keyboard_manager;\n", + " }\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which === 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " fig.ondownload(fig, null);\n", + "};\n", + "\n", + "mpl.find_output_cell = function (html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i = 0; i < ncells; i++) {\n", + " var cell = cells[i];\n", + " if (cell.cell_type === 'code') {\n", + " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", + " var data = cell.output_area.outputs[j];\n", + " if (data.data) {\n", + " // IPython >= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] === html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "};\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel !== null) {\n", + " IPython.notebook.kernel.comm_manager.register_target(\n", + " 'matplotlib',\n", + " mpl.mpl_figure_comm\n", + " );\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n", + "Temps d'execution de fibo avec n=99010 : 0.08708674800000082\n" + ] + } + ], + "source": [ + "def fibo(n: int) -> int:\n", + " \"\"\" Calcule les termes de la suite de Fibonacci (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " \n", + " if n <= 1: return 1\n", + " elif n <= 0: return 0\n", + "\n", + " un_moins_2 = 0\n", + " un_moins_1 = 1\n", + " \n", + " for i in range(2,n+1):\n", + " un = un_moins_1 + un_moins_2\n", + " un_moins_2 = un_moins_1\n", + " un_moins_1 = un\n", + " return un\n", + "\n", + "# Mesure du temps et tracés\n", + "import time\n", + "%matplotlib notebook\n", + "import matplotlib.pyplot as plt\n", + "\n", + "n = [i for i in range(10, 100000, 1000)]\n", + "liste_temps = []\n", + "\n", + "for i in n:\n", + " print(f\"Test avec n={i}\", end = \" - \")\n", + " temps = 0.0\n", + " nb_loops = 10\n", + " for test in range(nb_loops):\n", + " start = time.process_time()\n", + " fibo(i)\n", + " temps += time.process_time() - start\n", + " temps /= nb_loops\n", + " liste_temps.append(temps)\n", + "\n", + "plt.plot(n, liste_temps, label=\"fibo\")\n", + "plt.xlabel(\"n\")\n", + "plt.grid(True)\n", + "print(f\"\\n\\nTemps d'execution de fibo avec n={n[-1]} : {liste_temps[-1]}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Nous obtenons des résultats identiques à la fonction précédente, ce qui est normal puisque ces fonctions sont presques identiques.\n", + "\n", + "- **Copier-coller** la définition de votre fonction `fibor` au début de la cellule suivante et exécutez la cellule pour analyser les performances." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test avec n=5 - Test avec n=7 - Test avec n=9 - Test avec n=11 - Test avec n=13 - Test avec n=15 - Test avec n=17 - Test avec n=19 - Test avec n=21 - Test avec n=23 - Test avec n=25 - Test avec n=27 - Test avec n=29 - Test avec n=31 - Test avec n=33 - Test avec n=35 - Test avec n=37 - Test avec n=39 - " + ] + }, + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "/* global mpl */\n", + "window.mpl = {};\n", + "\n", + "mpl.get_websocket_type = function () {\n", + " if (typeof WebSocket !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof MozWebSocket !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert(\n", + " 'Your browser does not have WebSocket support. ' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.'\n", + " );\n", + " }\n", + "};\n", + "\n", + "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = this.ws.binaryType !== undefined;\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById('mpl-warnings');\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent =\n", + " 'This browser does not support binary websocket messages. ' +\n", + " 'Performance may be slow.';\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = document.createElement('div');\n", + " this.root.setAttribute('style', 'display: inline-block');\n", + " this._root_extra_style(this.root);\n", + "\n", + " parent_element.appendChild(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message('supports_binary', { value: fig.supports_binary });\n", + " fig.send_message('send_image_mode', {});\n", + " if (fig.ratio !== 1) {\n", + " fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n", + " }\n", + " fig.send_message('refresh', {});\n", + " };\n", + "\n", + " this.imageObj.onload = function () {\n", + " if (fig.image_mode === 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function () {\n", + " fig.ws.close();\n", + " };\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "};\n", + "\n", + "mpl.figure.prototype._init_header = function () {\n", + " var titlebar = document.createElement('div');\n", + " titlebar.classList =\n", + " 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n", + " var titletext = document.createElement('div');\n", + " titletext.classList = 'ui-dialog-title';\n", + " titletext.setAttribute(\n", + " 'style',\n", + " 'width: 100%; text-align: center; padding: 3px;'\n", + " );\n", + " titlebar.appendChild(titletext);\n", + " this.root.appendChild(titlebar);\n", + " this.header = titletext;\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n", + "\n", + "mpl.figure.prototype._init_canvas = function () {\n", + " var fig = this;\n", + "\n", + " var canvas_div = (this.canvas_div = document.createElement('div'));\n", + " canvas_div.setAttribute(\n", + " 'style',\n", + " 'border: 1px solid #ddd;' +\n", + " 'box-sizing: content-box;' +\n", + " 'clear: both;' +\n", + " 'min-height: 1px;' +\n", + " 'min-width: 1px;' +\n", + " 'outline: 0;' +\n", + " 'overflow: hidden;' +\n", + " 'position: relative;' +\n", + " 'resize: both;'\n", + " );\n", + "\n", + " function on_keyboard_event_closure(name) {\n", + " return function (event) {\n", + " return fig.key_event(event, name);\n", + " };\n", + " }\n", + "\n", + " canvas_div.addEventListener(\n", + " 'keydown',\n", + " on_keyboard_event_closure('key_press')\n", + " );\n", + " canvas_div.addEventListener(\n", + " 'keyup',\n", + " on_keyboard_event_closure('key_release')\n", + " );\n", + "\n", + " this._canvas_extra_style(canvas_div);\n", + " this.root.appendChild(canvas_div);\n", + "\n", + " var canvas = (this.canvas = document.createElement('canvas'));\n", + " canvas.classList.add('mpl-canvas');\n", + " canvas.setAttribute('style', 'box-sizing: content-box;');\n", + "\n", + " this.context = canvas.getContext('2d');\n", + "\n", + " var backingStore =\n", + " this.context.backingStorePixelRatio ||\n", + " this.context.webkitBackingStorePixelRatio ||\n", + " this.context.mozBackingStorePixelRatio ||\n", + " this.context.msBackingStorePixelRatio ||\n", + " this.context.oBackingStorePixelRatio ||\n", + " this.context.backingStorePixelRatio ||\n", + " 1;\n", + "\n", + " this.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + " if (this.ratio !== 1) {\n", + " fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n", + " }\n", + "\n", + " var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n", + " 'canvas'\n", + " ));\n", + " rubberband_canvas.setAttribute(\n", + " 'style',\n", + " 'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n", + " );\n", + "\n", + " var resizeObserver = new ResizeObserver(function (entries) {\n", + " var nentries = entries.length;\n", + " for (var i = 0; i < nentries; i++) {\n", + " var entry = entries[i];\n", + " var width, height;\n", + " if (entry.contentBoxSize) {\n", + " if (entry.contentBoxSize instanceof Array) {\n", + " // Chrome 84 implements new version of spec.\n", + " width = entry.contentBoxSize[0].inlineSize;\n", + " height = entry.contentBoxSize[0].blockSize;\n", + " } else {\n", + " // Firefox implements old version of spec.\n", + " width = entry.contentBoxSize.inlineSize;\n", + " height = entry.contentBoxSize.blockSize;\n", + " }\n", + " } else {\n", + " // Chrome <84 implements even older version of spec.\n", + " width = entry.contentRect.width;\n", + " height = entry.contentRect.height;\n", + " }\n", + "\n", + " // Keep the size of the canvas and rubber band canvas in sync with\n", + " // the canvas container.\n", + " if (entry.devicePixelContentBoxSize) {\n", + " // Chrome 84 implements new version of spec.\n", + " canvas.setAttribute(\n", + " 'width',\n", + " entry.devicePixelContentBoxSize[0].inlineSize\n", + " );\n", + " canvas.setAttribute(\n", + " 'height',\n", + " entry.devicePixelContentBoxSize[0].blockSize\n", + " );\n", + " } else {\n", + " canvas.setAttribute('width', width * fig.ratio);\n", + " canvas.setAttribute('height', height * fig.ratio);\n", + " }\n", + " canvas.setAttribute(\n", + " 'style',\n", + " 'width: ' + width + 'px; height: ' + height + 'px;'\n", + " );\n", + "\n", + " rubberband_canvas.setAttribute('width', width);\n", + " rubberband_canvas.setAttribute('height', height);\n", + "\n", + " // And update the size in Python. We ignore the initial 0/0 size\n", + " // that occurs as the element is placed into the DOM, which should\n", + " // otherwise not happen due to the minimum size styling.\n", + " if (width != 0 && height != 0) {\n", + " fig.request_resize(width, height);\n", + " }\n", + " }\n", + " });\n", + " resizeObserver.observe(canvas_div);\n", + "\n", + " function on_mouse_event_closure(name) {\n", + " return function (event) {\n", + " return fig.mouse_event(event, name);\n", + " };\n", + " }\n", + "\n", + " rubberband_canvas.addEventListener(\n", + " 'mousedown',\n", + " on_mouse_event_closure('button_press')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseup',\n", + " on_mouse_event_closure('button_release')\n", + " );\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband_canvas.addEventListener(\n", + " 'mousemove',\n", + " on_mouse_event_closure('motion_notify')\n", + " );\n", + "\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseenter',\n", + " on_mouse_event_closure('figure_enter')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseleave',\n", + " on_mouse_event_closure('figure_leave')\n", + " );\n", + "\n", + " canvas_div.addEventListener('wheel', function (event) {\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " on_mouse_event_closure('scroll')(event);\n", + " });\n", + "\n", + " canvas_div.appendChild(canvas);\n", + " canvas_div.appendChild(rubberband_canvas);\n", + "\n", + " this.rubberband_context = rubberband_canvas.getContext('2d');\n", + " this.rubberband_context.strokeStyle = '#000000';\n", + "\n", + " this._resize_canvas = function (width, height, forward) {\n", + " if (forward) {\n", + " canvas_div.style.width = width + 'px';\n", + " canvas_div.style.height = height + 'px';\n", + " }\n", + " };\n", + "\n", + " // Disable right mouse context menu.\n", + " this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n", + " event.preventDefault();\n", + " return false;\n", + " });\n", + "\n", + " function set_focus() {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'mpl-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " continue;\n", + " }\n", + "\n", + " var button = (fig.buttons[name] = document.createElement('button'));\n", + " button.classList = 'mpl-widget';\n", + " button.setAttribute('role', 'button');\n", + " button.setAttribute('aria-disabled', 'false');\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + "\n", + " var icon_img = document.createElement('img');\n", + " icon_img.src = '_images/' + image + '.png';\n", + " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", + " icon_img.alt = tooltip;\n", + " button.appendChild(icon_img);\n", + "\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " var fmt_picker = document.createElement('select');\n", + " fmt_picker.classList = 'mpl-widget';\n", + " toolbar.appendChild(fmt_picker);\n", + " this.format_dropdown = fmt_picker;\n", + "\n", + " for (var ind in mpl.extensions) {\n", + " var fmt = mpl.extensions[ind];\n", + " var option = document.createElement('option');\n", + " option.selected = fmt === mpl.default_extension;\n", + " option.innerHTML = fmt;\n", + " fmt_picker.appendChild(option);\n", + " }\n", + "\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "};\n", + "\n", + "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", + " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", + " // which will in turn request a refresh of the image.\n", + " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", + "};\n", + "\n", + "mpl.figure.prototype.send_message = function (type, properties) {\n", + " properties['type'] = type;\n", + " properties['figure_id'] = this.id;\n", + " this.ws.send(JSON.stringify(properties));\n", + "};\n", + "\n", + "mpl.figure.prototype.send_draw_message = function () {\n", + " if (!this.waiting) {\n", + " this.waiting = true;\n", + " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " var format_dropdown = fig.format_dropdown;\n", + " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", + " fig.ondownload(fig, format);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", + " var size = msg['size'];\n", + " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", + " fig._resize_canvas(size[0], size[1], msg['forward']);\n", + " fig.send_message('refresh', {});\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", + " var x0 = msg['x0'] / fig.ratio;\n", + " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", + " var x1 = msg['x1'] / fig.ratio;\n", + " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", + " x0 = Math.floor(x0) + 0.5;\n", + " y0 = Math.floor(y0) + 0.5;\n", + " x1 = Math.floor(x1) + 0.5;\n", + " y1 = Math.floor(y1) + 0.5;\n", + " var min_x = Math.min(x0, x1);\n", + " var min_y = Math.min(y0, y1);\n", + " var width = Math.abs(x1 - x0);\n", + " var height = Math.abs(y1 - y0);\n", + "\n", + " fig.rubberband_context.clearRect(\n", + " 0,\n", + " 0,\n", + " fig.canvas.width / fig.ratio,\n", + " fig.canvas.height / fig.ratio\n", + " );\n", + "\n", + " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", + " // Updates the figure title.\n", + " fig.header.textContent = msg['label'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", + " var cursor = msg['cursor'];\n", + " switch (cursor) {\n", + " case 0:\n", + " cursor = 'pointer';\n", + " break;\n", + " case 1:\n", + " cursor = 'default';\n", + " break;\n", + " case 2:\n", + " cursor = 'crosshair';\n", + " break;\n", + " case 3:\n", + " cursor = 'move';\n", + " break;\n", + " }\n", + " fig.rubberband_canvas.style.cursor = cursor;\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_message = function (fig, msg) {\n", + " fig.message.textContent = msg['message'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", + " // Request the server to send over a new figure.\n", + " fig.send_draw_message();\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", + " fig.image_mode = msg['mode'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", + " for (var key in msg) {\n", + " if (!(key in fig.buttons)) {\n", + " continue;\n", + " }\n", + " fig.buttons[key].disabled = !msg[key];\n", + " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", + " if (msg['mode'] === 'PAN') {\n", + " fig.buttons['Pan'].classList.add('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " } else if (msg['mode'] === 'ZOOM') {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.add('active');\n", + " } else {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Called whenever the canvas gets updated.\n", + " this.send_message('ack', {});\n", + "};\n", + "\n", + "// A function to construct a web socket function for onmessage handling.\n", + "// Called in the figure constructor.\n", + "mpl.figure.prototype._make_on_message_function = function (fig) {\n", + " return function socket_on_message(evt) {\n", + " if (evt.data instanceof Blob) {\n", + " /* FIXME: We get \"Resource interpreted as Image but\n", + " * transferred with MIME type text/plain:\" errors on\n", + " * Chrome. But how to set the MIME type? It doesn't seem\n", + " * to be part of the websocket stream */\n", + " evt.data.type = 'image/png';\n", + "\n", + " /* Free the memory for the previous frames */\n", + " if (fig.imageObj.src) {\n", + " (window.URL || window.webkitURL).revokeObjectURL(\n", + " fig.imageObj.src\n", + " );\n", + " }\n", + "\n", + " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", + " evt.data\n", + " );\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " } else if (\n", + " typeof evt.data === 'string' &&\n", + " evt.data.slice(0, 21) === 'data:image/png;base64'\n", + " ) {\n", + " fig.imageObj.src = evt.data;\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " }\n", + "\n", + " var msg = JSON.parse(evt.data);\n", + " var msg_type = msg['type'];\n", + "\n", + " // Call the \"handle_{type}\" callback, which takes\n", + " // the figure and JSON message as its only arguments.\n", + " try {\n", + " var callback = fig['handle_' + msg_type];\n", + " } catch (e) {\n", + " console.log(\n", + " \"No handler for the '\" + msg_type + \"' message type: \",\n", + " msg\n", + " );\n", + " return;\n", + " }\n", + "\n", + " if (callback) {\n", + " try {\n", + " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", + " callback(fig, msg);\n", + " } catch (e) {\n", + " console.log(\n", + " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", + " e,\n", + " e.stack,\n", + " msg\n", + " );\n", + " }\n", + " }\n", + " };\n", + "};\n", + "\n", + "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", + "mpl.findpos = function (e) {\n", + " //this section is from http://www.quirksmode.org/js/events_properties.html\n", + " var targ;\n", + " if (!e) {\n", + " e = window.event;\n", + " }\n", + " if (e.target) {\n", + " targ = e.target;\n", + " } else if (e.srcElement) {\n", + " targ = e.srcElement;\n", + " }\n", + " if (targ.nodeType === 3) {\n", + " // defeat Safari bug\n", + " targ = targ.parentNode;\n", + " }\n", + "\n", + " // pageX,Y are the mouse positions relative to the document\n", + " var boundingRect = targ.getBoundingClientRect();\n", + " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", + " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", + "\n", + " return { x: x, y: y };\n", + "};\n", + "\n", + "/*\n", + " * return a copy of an object with only non-object keys\n", + " * we need this to avoid circular references\n", + " * http://stackoverflow.com/a/24161582/3208463\n", + " */\n", + "function simpleKeys(original) {\n", + " return Object.keys(original).reduce(function (obj, key) {\n", + " if (typeof original[key] !== 'object') {\n", + " obj[key] = original[key];\n", + " }\n", + " return obj;\n", + " }, {});\n", + "}\n", + "\n", + "mpl.figure.prototype.mouse_event = function (event, name) {\n", + " var canvas_pos = mpl.findpos(event);\n", + "\n", + " if (name === 'button_press') {\n", + " this.canvas.focus();\n", + " this.canvas_div.focus();\n", + " }\n", + "\n", + " var x = canvas_pos.x * this.ratio;\n", + " var y = canvas_pos.y * this.ratio;\n", + "\n", + " this.send_message(name, {\n", + " x: x,\n", + " y: y,\n", + " button: event.button,\n", + " step: event.step,\n", + " guiEvent: simpleKeys(event),\n", + " });\n", + "\n", + " /* This prevents the web browser from automatically changing to\n", + " * the text insertion cursor when the button is pressed. We want\n", + " * to control all of the cursor setting manually through the\n", + " * 'cursor' event from matplotlib */\n", + " event.preventDefault();\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", + " // Handle any extra behaviour associated with a key event\n", + "};\n", + "\n", + "mpl.figure.prototype.key_event = function (event, name) {\n", + " // Prevent repeat events\n", + " if (name === 'key_press') {\n", + " if (event.which === this._key) {\n", + " return;\n", + " } else {\n", + " this._key = event.which;\n", + " }\n", + " }\n", + " if (name === 'key_release') {\n", + " this._key = null;\n", + " }\n", + "\n", + " var value = '';\n", + " if (event.ctrlKey && event.which !== 17) {\n", + " value += 'ctrl+';\n", + " }\n", + " if (event.altKey && event.which !== 18) {\n", + " value += 'alt+';\n", + " }\n", + " if (event.shiftKey && event.which !== 16) {\n", + " value += 'shift+';\n", + " }\n", + "\n", + " value += 'k';\n", + " value += event.which.toString();\n", + "\n", + " this._key_event_extra(event, name);\n", + "\n", + " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", + " if (name === 'download') {\n", + " this.handle_save(this, null);\n", + " } else {\n", + " this.send_message('toolbar_button', { name: name });\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", + " this.message.textContent = tooltip;\n", + "};\n", + "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", + "\n", + "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", + "\n", + "mpl.default_extension = \"png\";/* global mpl */\n", + "\n", + "var comm_websocket_adapter = function (comm) {\n", + " // Create a \"websocket\"-like object which calls the given IPython comm\n", + " // object with the appropriate methods. Currently this is a non binary\n", + " // socket, so there is still some room for performance tuning.\n", + " var ws = {};\n", + "\n", + " ws.close = function () {\n", + " comm.close();\n", + " };\n", + " ws.send = function (m) {\n", + " //console.log('sending', m);\n", + " comm.send(m);\n", + " };\n", + " // Register the callback with on_msg.\n", + " comm.on_msg(function (msg) {\n", + " //console.log('receiving', msg['content']['data'], msg);\n", + " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", + " ws.onmessage(msg['content']['data']);\n", + " });\n", + " return ws;\n", + "};\n", + "\n", + "mpl.mpl_figure_comm = function (comm, msg) {\n", + " // This is the function which gets called when the mpl process\n", + " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", + "\n", + " var id = msg.content.data.id;\n", + " // Get hold of the div created by the display call when the Comm\n", + " // socket was opened in Python.\n", + " var element = document.getElementById(id);\n", + " var ws_proxy = comm_websocket_adapter(comm);\n", + "\n", + " function ondownload(figure, _format) {\n", + " window.open(figure.canvas.toDataURL());\n", + " }\n", + "\n", + " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", + "\n", + " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", + " // web socket which is closed, not our websocket->open comm proxy.\n", + " ws_proxy.onopen();\n", + "\n", + " fig.parent_element = element;\n", + " fig.cell_info = mpl.find_output_cell(\"
\");\n", + " if (!fig.cell_info) {\n", + " console.error('Failed to find cell for figure', id, fig);\n", + " return;\n", + " }\n", + " fig.cell_info[0].output_area.element.one(\n", + " 'cleared',\n", + " { fig: fig },\n", + " fig._remove_fig_handler\n", + " );\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_close = function (fig, msg) {\n", + " var width = fig.canvas.width / fig.ratio;\n", + " fig.cell_info[0].output_area.element.off(\n", + " 'cleared',\n", + " fig._remove_fig_handler\n", + " );\n", + "\n", + " // Update the output cell to use the data from the current canvas.\n", + " fig.push_to_output();\n", + " var dataURL = fig.canvas.toDataURL();\n", + " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", + " // the notebook keyboard shortcuts fail.\n", + " IPython.keyboard_manager.enable();\n", + " fig.parent_element.innerHTML =\n", + " '';\n", + " fig.close_ws(fig, msg);\n", + "};\n", + "\n", + "mpl.figure.prototype.close_ws = function (fig, msg) {\n", + " fig.send_message('closing', msg);\n", + " // fig.ws.close()\n", + "};\n", + "\n", + "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", + " // Turn the data on the canvas into data in the output cell.\n", + " var width = this.canvas.width / this.ratio;\n", + " var dataURL = this.canvas.toDataURL();\n", + " this.cell_info[1]['text/html'] =\n", + " '';\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Tell IPython that the notebook contents must change.\n", + " IPython.notebook.set_dirty(true);\n", + " this.send_message('ack', {});\n", + " var fig = this;\n", + " // Wait a second, then push the new image to the DOM so\n", + " // that it is saved nicely (might be nice to debounce this).\n", + " setTimeout(function () {\n", + " fig.push_to_output();\n", + " }, 1000);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'btn-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " var button;\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " continue;\n", + " }\n", + "\n", + " button = fig.buttons[name] = document.createElement('button');\n", + " button.classList = 'btn btn-default';\n", + " button.href = '#';\n", + " button.title = name;\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message pull-right';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = document.createElement('div');\n", + " buttongrp.classList = 'btn-group inline pull-right';\n", + " button = document.createElement('button');\n", + " button.classList = 'btn btn-mini btn-primary';\n", + " button.href = '#';\n", + " button.title = 'Stop Interaction';\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', function (_evt) {\n", + " fig.handle_close(fig, {});\n", + " });\n", + " button.addEventListener(\n", + " 'mouseover',\n", + " on_mouseover_closure('Stop Interaction')\n", + " );\n", + " buttongrp.appendChild(button);\n", + " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", + " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", + "};\n", + "\n", + "mpl.figure.prototype._remove_fig_handler = function (event) {\n", + " var fig = event.data.fig;\n", + " fig.close_ws(fig, {});\n", + "};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (el) {\n", + " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (el) {\n", + " // this is important to make the div 'focusable\n", + " el.setAttribute('tabindex', 0);\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " } else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager) {\n", + " manager = IPython.keyboard_manager;\n", + " }\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which === 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " fig.ondownload(fig, null);\n", + "};\n", + "\n", + "mpl.find_output_cell = function (html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i = 0; i < ncells; i++) {\n", + " var cell = cells[i];\n", + " if (cell.cell_type === 'code') {\n", + " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", + " var data = cell.output_area.outputs[j];\n", + " if (data.data) {\n", + " // IPython >= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] === html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "};\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel !== null) {\n", + " IPython.notebook.kernel.comm_manager.register_target(\n", + " 'matplotlib',\n", + " mpl.mpl_figure_comm\n", + " );\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n", + "Temps d'execution de fibor avec n=39 : 25.778192887666663\n" + ] + } + ], + "source": [ + "def fibor(n: int) -> int:\n", + " \"\"\" Calcule les termes de la suite de Fibonacci récursivement (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " if n <= 0: return 0\n", + " elif n <= 1: return 1\n", + " else: return fibor(n-1) + fibor(n-2)\n", + "\n", + "# Mesure du temps et tracés\n", + "import time\n", + "%matplotlib notebook\n", + "import matplotlib.pyplot as plt\n", + "n = [i for i in range(5, 40, 2)]\n", + "liste_temps = []\n", + "\n", + "for i in n:\n", + " print(f\"Test avec n={i}\", end = \" - \")\n", + " temps = 0.0\n", + " nb_loops = 3\n", + " for test in range(nb_loops):\n", + " start = time.process_time()\n", + " fibor(i)\n", + " temps += time.process_time() - start\n", + " temps /= nb_loops\n", + " liste_temps.append(temps)\n", + "\n", + "plt.plot(n, liste_temps, label=\"fibor\")\n", + "plt.xlabel(\"n\")\n", + "plt.grid(True)\n", + "print(f\"\\n\\nTemps d'execution de fibor avec n={n[-1]} : {liste_temps[-1]}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Comme prévu, le temps d'exécution est bien **exponentiel** en fonction du nombre n. Cet algorithme **récursif** est très **esthétique** dans son écriture mais c'est une **catastrophe en terme de performance** : 25 sec pour n = 39 seulement !\n", + "\n", + "- **Copier-coller** la définition de votre fonction `fibordyn` au début de la cellule suivante et exécutez la cellule pour analyser les performances." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test avec n=10 - Test avec n=35 - Test avec n=60 - Test avec n=85 - Test avec n=110 - Test avec n=135 - Test avec n=160 - Test avec n=185 - Test avec n=210 - Test avec n=235 - Test avec n=260 - Test avec n=285 - Test avec n=310 - Test avec n=335 - Test avec n=360 - Test avec n=385 - Test avec n=410 - Test avec n=435 - Test avec n=460 - Test avec n=485 - Test avec n=510 - Test avec n=535 - Test avec n=560 - Test avec n=585 - Test avec n=610 - Test avec n=635 - Test avec n=660 - Test avec n=685 - Test avec n=710 - Test avec n=735 - Test avec n=760 - Test avec n=785 - Test avec n=810 - Test avec n=835 - Test avec n=860 - Test avec n=885 - Test avec n=910 - Test avec n=935 - Test avec n=960 - Test avec n=985 - Test avec n=1010 - Test avec n=1035 - Test avec n=1060 - Test avec n=1085 - Test avec n=1110 - Test avec n=1135 - Test avec n=1160 - Test avec n=1185 - Test avec n=1210 - Test avec n=1235 - Test avec n=1260 - Test avec n=1285 - Test avec n=1310 - Test avec n=1335 - Test avec n=1360 - Test avec n=1385 - Test avec n=1410 - Test avec n=1435 - Test avec n=1460 - Test avec n=1485 - Test avec n=1510 - Test avec n=1535 - Test avec n=1560 - Test avec n=1585 - Test avec n=1610 - Test avec n=1635 - Test avec n=1660 - Test avec n=1685 - Test avec n=1710 - Test avec n=1735 - Test avec n=1760 - Test avec n=1785 - Test avec n=1810 - Test avec n=1835 - Test avec n=1860 - Test avec n=1885 - Test avec n=1910 - Test avec n=1935 - Test avec n=1960 - Test avec n=1985 - Test avec n=2010 - Test avec n=2035 - Test avec n=2060 - Test avec n=2085 - Test avec n=2110 - Test avec n=2135 - Test avec n=2160 - Test avec n=2185 - Test avec n=2210 - Test avec n=2235 - Test avec n=2260 - Test avec n=2285 - Test avec n=2310 - Test avec n=2335 - Test avec n=2360 - Test avec n=2385 - Test avec n=2410 - Test avec n=2435 - Test avec n=2460 - Test avec n=2485 - Test avec n=2510 - Test avec n=2535 - Test avec n=2560 - Test avec n=2585 - Test avec n=2610 - Test avec n=2635 - Test avec n=2660 - Test avec n=2685 - Test avec n=2710 - Test avec n=2735 - Test avec n=2760 - Test avec n=2785 - Test avec n=2810 - Test avec n=2835 - Test avec n=2860 - Test avec n=2885 - Test avec n=2910 - Test avec n=2935 - Test avec n=2960 - " + ] + }, + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "/* global mpl */\n", + "window.mpl = {};\n", + "\n", + "mpl.get_websocket_type = function () {\n", + " if (typeof WebSocket !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof MozWebSocket !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert(\n", + " 'Your browser does not have WebSocket support. ' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.'\n", + " );\n", + " }\n", + "};\n", + "\n", + "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = this.ws.binaryType !== undefined;\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById('mpl-warnings');\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent =\n", + " 'This browser does not support binary websocket messages. ' +\n", + " 'Performance may be slow.';\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = document.createElement('div');\n", + " this.root.setAttribute('style', 'display: inline-block');\n", + " this._root_extra_style(this.root);\n", + "\n", + " parent_element.appendChild(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message('supports_binary', { value: fig.supports_binary });\n", + " fig.send_message('send_image_mode', {});\n", + " if (fig.ratio !== 1) {\n", + " fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n", + " }\n", + " fig.send_message('refresh', {});\n", + " };\n", + "\n", + " this.imageObj.onload = function () {\n", + " if (fig.image_mode === 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function () {\n", + " fig.ws.close();\n", + " };\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "};\n", + "\n", + "mpl.figure.prototype._init_header = function () {\n", + " var titlebar = document.createElement('div');\n", + " titlebar.classList =\n", + " 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n", + " var titletext = document.createElement('div');\n", + " titletext.classList = 'ui-dialog-title';\n", + " titletext.setAttribute(\n", + " 'style',\n", + " 'width: 100%; text-align: center; padding: 3px;'\n", + " );\n", + " titlebar.appendChild(titletext);\n", + " this.root.appendChild(titlebar);\n", + " this.header = titletext;\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n", + "\n", + "mpl.figure.prototype._init_canvas = function () {\n", + " var fig = this;\n", + "\n", + " var canvas_div = (this.canvas_div = document.createElement('div'));\n", + " canvas_div.setAttribute(\n", + " 'style',\n", + " 'border: 1px solid #ddd;' +\n", + " 'box-sizing: content-box;' +\n", + " 'clear: both;' +\n", + " 'min-height: 1px;' +\n", + " 'min-width: 1px;' +\n", + " 'outline: 0;' +\n", + " 'overflow: hidden;' +\n", + " 'position: relative;' +\n", + " 'resize: both;'\n", + " );\n", + "\n", + " function on_keyboard_event_closure(name) {\n", + " return function (event) {\n", + " return fig.key_event(event, name);\n", + " };\n", + " }\n", + "\n", + " canvas_div.addEventListener(\n", + " 'keydown',\n", + " on_keyboard_event_closure('key_press')\n", + " );\n", + " canvas_div.addEventListener(\n", + " 'keyup',\n", + " on_keyboard_event_closure('key_release')\n", + " );\n", + "\n", + " this._canvas_extra_style(canvas_div);\n", + " this.root.appendChild(canvas_div);\n", + "\n", + " var canvas = (this.canvas = document.createElement('canvas'));\n", + " canvas.classList.add('mpl-canvas');\n", + " canvas.setAttribute('style', 'box-sizing: content-box;');\n", + "\n", + " this.context = canvas.getContext('2d');\n", + "\n", + " var backingStore =\n", + " this.context.backingStorePixelRatio ||\n", + " this.context.webkitBackingStorePixelRatio ||\n", + " this.context.mozBackingStorePixelRatio ||\n", + " this.context.msBackingStorePixelRatio ||\n", + " this.context.oBackingStorePixelRatio ||\n", + " this.context.backingStorePixelRatio ||\n", + " 1;\n", + "\n", + " this.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + " if (this.ratio !== 1) {\n", + " fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n", + " }\n", + "\n", + " var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n", + " 'canvas'\n", + " ));\n", + " rubberband_canvas.setAttribute(\n", + " 'style',\n", + " 'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n", + " );\n", + "\n", + " var resizeObserver = new ResizeObserver(function (entries) {\n", + " var nentries = entries.length;\n", + " for (var i = 0; i < nentries; i++) {\n", + " var entry = entries[i];\n", + " var width, height;\n", + " if (entry.contentBoxSize) {\n", + " if (entry.contentBoxSize instanceof Array) {\n", + " // Chrome 84 implements new version of spec.\n", + " width = entry.contentBoxSize[0].inlineSize;\n", + " height = entry.contentBoxSize[0].blockSize;\n", + " } else {\n", + " // Firefox implements old version of spec.\n", + " width = entry.contentBoxSize.inlineSize;\n", + " height = entry.contentBoxSize.blockSize;\n", + " }\n", + " } else {\n", + " // Chrome <84 implements even older version of spec.\n", + " width = entry.contentRect.width;\n", + " height = entry.contentRect.height;\n", + " }\n", + "\n", + " // Keep the size of the canvas and rubber band canvas in sync with\n", + " // the canvas container.\n", + " if (entry.devicePixelContentBoxSize) {\n", + " // Chrome 84 implements new version of spec.\n", + " canvas.setAttribute(\n", + " 'width',\n", + " entry.devicePixelContentBoxSize[0].inlineSize\n", + " );\n", + " canvas.setAttribute(\n", + " 'height',\n", + " entry.devicePixelContentBoxSize[0].blockSize\n", + " );\n", + " } else {\n", + " canvas.setAttribute('width', width * fig.ratio);\n", + " canvas.setAttribute('height', height * fig.ratio);\n", + " }\n", + " canvas.setAttribute(\n", + " 'style',\n", + " 'width: ' + width + 'px; height: ' + height + 'px;'\n", + " );\n", + "\n", + " rubberband_canvas.setAttribute('width', width);\n", + " rubberband_canvas.setAttribute('height', height);\n", + "\n", + " // And update the size in Python. We ignore the initial 0/0 size\n", + " // that occurs as the element is placed into the DOM, which should\n", + " // otherwise not happen due to the minimum size styling.\n", + " if (width != 0 && height != 0) {\n", + " fig.request_resize(width, height);\n", + " }\n", + " }\n", + " });\n", + " resizeObserver.observe(canvas_div);\n", + "\n", + " function on_mouse_event_closure(name) {\n", + " return function (event) {\n", + " return fig.mouse_event(event, name);\n", + " };\n", + " }\n", + "\n", + " rubberband_canvas.addEventListener(\n", + " 'mousedown',\n", + " on_mouse_event_closure('button_press')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseup',\n", + " on_mouse_event_closure('button_release')\n", + " );\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband_canvas.addEventListener(\n", + " 'mousemove',\n", + " on_mouse_event_closure('motion_notify')\n", + " );\n", + "\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseenter',\n", + " on_mouse_event_closure('figure_enter')\n", + " );\n", + " rubberband_canvas.addEventListener(\n", + " 'mouseleave',\n", + " on_mouse_event_closure('figure_leave')\n", + " );\n", + "\n", + " canvas_div.addEventListener('wheel', function (event) {\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " on_mouse_event_closure('scroll')(event);\n", + " });\n", + "\n", + " canvas_div.appendChild(canvas);\n", + " canvas_div.appendChild(rubberband_canvas);\n", + "\n", + " this.rubberband_context = rubberband_canvas.getContext('2d');\n", + " this.rubberband_context.strokeStyle = '#000000';\n", + "\n", + " this._resize_canvas = function (width, height, forward) {\n", + " if (forward) {\n", + " canvas_div.style.width = width + 'px';\n", + " canvas_div.style.height = height + 'px';\n", + " }\n", + " };\n", + "\n", + " // Disable right mouse context menu.\n", + " this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n", + " event.preventDefault();\n", + " return false;\n", + " });\n", + "\n", + " function set_focus() {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'mpl-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'mpl-button-group';\n", + " continue;\n", + " }\n", + "\n", + " var button = (fig.buttons[name] = document.createElement('button'));\n", + " button.classList = 'mpl-widget';\n", + " button.setAttribute('role', 'button');\n", + " button.setAttribute('aria-disabled', 'false');\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + "\n", + " var icon_img = document.createElement('img');\n", + " icon_img.src = '_images/' + image + '.png';\n", + " icon_img.srcset = '_images/' + image + '_large.png 2x';\n", + " icon_img.alt = tooltip;\n", + " button.appendChild(icon_img);\n", + "\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " var fmt_picker = document.createElement('select');\n", + " fmt_picker.classList = 'mpl-widget';\n", + " toolbar.appendChild(fmt_picker);\n", + " this.format_dropdown = fmt_picker;\n", + "\n", + " for (var ind in mpl.extensions) {\n", + " var fmt = mpl.extensions[ind];\n", + " var option = document.createElement('option');\n", + " option.selected = fmt === mpl.default_extension;\n", + " option.innerHTML = fmt;\n", + " fmt_picker.appendChild(option);\n", + " }\n", + "\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "};\n", + "\n", + "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n", + " // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n", + " // which will in turn request a refresh of the image.\n", + " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", + "};\n", + "\n", + "mpl.figure.prototype.send_message = function (type, properties) {\n", + " properties['type'] = type;\n", + " properties['figure_id'] = this.id;\n", + " this.ws.send(JSON.stringify(properties));\n", + "};\n", + "\n", + "mpl.figure.prototype.send_draw_message = function () {\n", + " if (!this.waiting) {\n", + " this.waiting = true;\n", + " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " var format_dropdown = fig.format_dropdown;\n", + " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", + " fig.ondownload(fig, format);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", + " var size = msg['size'];\n", + " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", + " fig._resize_canvas(size[0], size[1], msg['forward']);\n", + " fig.send_message('refresh', {});\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", + " var x0 = msg['x0'] / fig.ratio;\n", + " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", + " var x1 = msg['x1'] / fig.ratio;\n", + " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", + " x0 = Math.floor(x0) + 0.5;\n", + " y0 = Math.floor(y0) + 0.5;\n", + " x1 = Math.floor(x1) + 0.5;\n", + " y1 = Math.floor(y1) + 0.5;\n", + " var min_x = Math.min(x0, x1);\n", + " var min_y = Math.min(y0, y1);\n", + " var width = Math.abs(x1 - x0);\n", + " var height = Math.abs(y1 - y0);\n", + "\n", + " fig.rubberband_context.clearRect(\n", + " 0,\n", + " 0,\n", + " fig.canvas.width / fig.ratio,\n", + " fig.canvas.height / fig.ratio\n", + " );\n", + "\n", + " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", + " // Updates the figure title.\n", + " fig.header.textContent = msg['label'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", + " var cursor = msg['cursor'];\n", + " switch (cursor) {\n", + " case 0:\n", + " cursor = 'pointer';\n", + " break;\n", + " case 1:\n", + " cursor = 'default';\n", + " break;\n", + " case 2:\n", + " cursor = 'crosshair';\n", + " break;\n", + " case 3:\n", + " cursor = 'move';\n", + " break;\n", + " }\n", + " fig.rubberband_canvas.style.cursor = cursor;\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_message = function (fig, msg) {\n", + " fig.message.textContent = msg['message'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", + " // Request the server to send over a new figure.\n", + " fig.send_draw_message();\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", + " fig.image_mode = msg['mode'];\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", + " for (var key in msg) {\n", + " if (!(key in fig.buttons)) {\n", + " continue;\n", + " }\n", + " fig.buttons[key].disabled = !msg[key];\n", + " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", + " if (msg['mode'] === 'PAN') {\n", + " fig.buttons['Pan'].classList.add('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " } else if (msg['mode'] === 'ZOOM') {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.add('active');\n", + " } else {\n", + " fig.buttons['Pan'].classList.remove('active');\n", + " fig.buttons['Zoom'].classList.remove('active');\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Called whenever the canvas gets updated.\n", + " this.send_message('ack', {});\n", + "};\n", + "\n", + "// A function to construct a web socket function for onmessage handling.\n", + "// Called in the figure constructor.\n", + "mpl.figure.prototype._make_on_message_function = function (fig) {\n", + " return function socket_on_message(evt) {\n", + " if (evt.data instanceof Blob) {\n", + " /* FIXME: We get \"Resource interpreted as Image but\n", + " * transferred with MIME type text/plain:\" errors on\n", + " * Chrome. But how to set the MIME type? It doesn't seem\n", + " * to be part of the websocket stream */\n", + " evt.data.type = 'image/png';\n", + "\n", + " /* Free the memory for the previous frames */\n", + " if (fig.imageObj.src) {\n", + " (window.URL || window.webkitURL).revokeObjectURL(\n", + " fig.imageObj.src\n", + " );\n", + " }\n", + "\n", + " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", + " evt.data\n", + " );\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " } else if (\n", + " typeof evt.data === 'string' &&\n", + " evt.data.slice(0, 21) === 'data:image/png;base64'\n", + " ) {\n", + " fig.imageObj.src = evt.data;\n", + " fig.updated_canvas_event();\n", + " fig.waiting = false;\n", + " return;\n", + " }\n", + "\n", + " var msg = JSON.parse(evt.data);\n", + " var msg_type = msg['type'];\n", + "\n", + " // Call the \"handle_{type}\" callback, which takes\n", + " // the figure and JSON message as its only arguments.\n", + " try {\n", + " var callback = fig['handle_' + msg_type];\n", + " } catch (e) {\n", + " console.log(\n", + " \"No handler for the '\" + msg_type + \"' message type: \",\n", + " msg\n", + " );\n", + " return;\n", + " }\n", + "\n", + " if (callback) {\n", + " try {\n", + " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", + " callback(fig, msg);\n", + " } catch (e) {\n", + " console.log(\n", + " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", + " e,\n", + " e.stack,\n", + " msg\n", + " );\n", + " }\n", + " }\n", + " };\n", + "};\n", + "\n", + "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", + "mpl.findpos = function (e) {\n", + " //this section is from http://www.quirksmode.org/js/events_properties.html\n", + " var targ;\n", + " if (!e) {\n", + " e = window.event;\n", + " }\n", + " if (e.target) {\n", + " targ = e.target;\n", + " } else if (e.srcElement) {\n", + " targ = e.srcElement;\n", + " }\n", + " if (targ.nodeType === 3) {\n", + " // defeat Safari bug\n", + " targ = targ.parentNode;\n", + " }\n", + "\n", + " // pageX,Y are the mouse positions relative to the document\n", + " var boundingRect = targ.getBoundingClientRect();\n", + " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", + " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", + "\n", + " return { x: x, y: y };\n", + "};\n", + "\n", + "/*\n", + " * return a copy of an object with only non-object keys\n", + " * we need this to avoid circular references\n", + " * http://stackoverflow.com/a/24161582/3208463\n", + " */\n", + "function simpleKeys(original) {\n", + " return Object.keys(original).reduce(function (obj, key) {\n", + " if (typeof original[key] !== 'object') {\n", + " obj[key] = original[key];\n", + " }\n", + " return obj;\n", + " }, {});\n", + "}\n", + "\n", + "mpl.figure.prototype.mouse_event = function (event, name) {\n", + " var canvas_pos = mpl.findpos(event);\n", + "\n", + " if (name === 'button_press') {\n", + " this.canvas.focus();\n", + " this.canvas_div.focus();\n", + " }\n", + "\n", + " var x = canvas_pos.x * this.ratio;\n", + " var y = canvas_pos.y * this.ratio;\n", + "\n", + " this.send_message(name, {\n", + " x: x,\n", + " y: y,\n", + " button: event.button,\n", + " step: event.step,\n", + " guiEvent: simpleKeys(event),\n", + " });\n", + "\n", + " /* This prevents the web browser from automatically changing to\n", + " * the text insertion cursor when the button is pressed. We want\n", + " * to control all of the cursor setting manually through the\n", + " * 'cursor' event from matplotlib */\n", + " event.preventDefault();\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", + " // Handle any extra behaviour associated with a key event\n", + "};\n", + "\n", + "mpl.figure.prototype.key_event = function (event, name) {\n", + " // Prevent repeat events\n", + " if (name === 'key_press') {\n", + " if (event.which === this._key) {\n", + " return;\n", + " } else {\n", + " this._key = event.which;\n", + " }\n", + " }\n", + " if (name === 'key_release') {\n", + " this._key = null;\n", + " }\n", + "\n", + " var value = '';\n", + " if (event.ctrlKey && event.which !== 17) {\n", + " value += 'ctrl+';\n", + " }\n", + " if (event.altKey && event.which !== 18) {\n", + " value += 'alt+';\n", + " }\n", + " if (event.shiftKey && event.which !== 16) {\n", + " value += 'shift+';\n", + " }\n", + "\n", + " value += 'k';\n", + " value += event.which.toString();\n", + "\n", + " this._key_event_extra(event, name);\n", + "\n", + " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", + " return false;\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", + " if (name === 'download') {\n", + " this.handle_save(this, null);\n", + " } else {\n", + " this.send_message('toolbar_button', { name: name });\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", + " this.message.textContent = tooltip;\n", + "};\n", + "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", + "\n", + "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", + "\n", + "mpl.default_extension = \"png\";/* global mpl */\n", + "\n", + "var comm_websocket_adapter = function (comm) {\n", + " // Create a \"websocket\"-like object which calls the given IPython comm\n", + " // object with the appropriate methods. Currently this is a non binary\n", + " // socket, so there is still some room for performance tuning.\n", + " var ws = {};\n", + "\n", + " ws.close = function () {\n", + " comm.close();\n", + " };\n", + " ws.send = function (m) {\n", + " //console.log('sending', m);\n", + " comm.send(m);\n", + " };\n", + " // Register the callback with on_msg.\n", + " comm.on_msg(function (msg) {\n", + " //console.log('receiving', msg['content']['data'], msg);\n", + " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", + " ws.onmessage(msg['content']['data']);\n", + " });\n", + " return ws;\n", + "};\n", + "\n", + "mpl.mpl_figure_comm = function (comm, msg) {\n", + " // This is the function which gets called when the mpl process\n", + " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", + "\n", + " var id = msg.content.data.id;\n", + " // Get hold of the div created by the display call when the Comm\n", + " // socket was opened in Python.\n", + " var element = document.getElementById(id);\n", + " var ws_proxy = comm_websocket_adapter(comm);\n", + "\n", + " function ondownload(figure, _format) {\n", + " window.open(figure.canvas.toDataURL());\n", + " }\n", + "\n", + " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", + "\n", + " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", + " // web socket which is closed, not our websocket->open comm proxy.\n", + " ws_proxy.onopen();\n", + "\n", + " fig.parent_element = element;\n", + " fig.cell_info = mpl.find_output_cell(\"
\");\n", + " if (!fig.cell_info) {\n", + " console.error('Failed to find cell for figure', id, fig);\n", + " return;\n", + " }\n", + " fig.cell_info[0].output_area.element.one(\n", + " 'cleared',\n", + " { fig: fig },\n", + " fig._remove_fig_handler\n", + " );\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_close = function (fig, msg) {\n", + " var width = fig.canvas.width / fig.ratio;\n", + " fig.cell_info[0].output_area.element.off(\n", + " 'cleared',\n", + " fig._remove_fig_handler\n", + " );\n", + "\n", + " // Update the output cell to use the data from the current canvas.\n", + " fig.push_to_output();\n", + " var dataURL = fig.canvas.toDataURL();\n", + " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", + " // the notebook keyboard shortcuts fail.\n", + " IPython.keyboard_manager.enable();\n", + " fig.parent_element.innerHTML =\n", + " '';\n", + " fig.close_ws(fig, msg);\n", + "};\n", + "\n", + "mpl.figure.prototype.close_ws = function (fig, msg) {\n", + " fig.send_message('closing', msg);\n", + " // fig.ws.close()\n", + "};\n", + "\n", + "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", + " // Turn the data on the canvas into data in the output cell.\n", + " var width = this.canvas.width / this.ratio;\n", + " var dataURL = this.canvas.toDataURL();\n", + " this.cell_info[1]['text/html'] =\n", + " '';\n", + "};\n", + "\n", + "mpl.figure.prototype.updated_canvas_event = function () {\n", + " // Tell IPython that the notebook contents must change.\n", + " IPython.notebook.set_dirty(true);\n", + " this.send_message('ack', {});\n", + " var fig = this;\n", + " // Wait a second, then push the new image to the DOM so\n", + " // that it is saved nicely (might be nice to debounce this).\n", + " setTimeout(function () {\n", + " fig.push_to_output();\n", + " }, 1000);\n", + "};\n", + "\n", + "mpl.figure.prototype._init_toolbar = function () {\n", + " var fig = this;\n", + "\n", + " var toolbar = document.createElement('div');\n", + " toolbar.classList = 'btn-toolbar';\n", + " this.root.appendChild(toolbar);\n", + "\n", + " function on_click_closure(name) {\n", + " return function (_event) {\n", + " return fig.toolbar_button_onclick(name);\n", + " };\n", + " }\n", + "\n", + " function on_mouseover_closure(tooltip) {\n", + " return function (event) {\n", + " if (!event.currentTarget.disabled) {\n", + " return fig.toolbar_button_onmouseover(tooltip);\n", + " }\n", + " };\n", + " }\n", + "\n", + " fig.buttons = {};\n", + " var buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " var button;\n", + " for (var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " /* Instead of a spacer, we start a new button group. */\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + " buttonGroup = document.createElement('div');\n", + " buttonGroup.classList = 'btn-group';\n", + " continue;\n", + " }\n", + "\n", + " button = fig.buttons[name] = document.createElement('button');\n", + " button.classList = 'btn btn-default';\n", + " button.href = '#';\n", + " button.title = name;\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', on_click_closure(method_name));\n", + " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", + " buttonGroup.appendChild(button);\n", + " }\n", + "\n", + " if (buttonGroup.hasChildNodes()) {\n", + " toolbar.appendChild(buttonGroup);\n", + " }\n", + "\n", + " // Add the status bar.\n", + " var status_bar = document.createElement('span');\n", + " status_bar.classList = 'mpl-message pull-right';\n", + " toolbar.appendChild(status_bar);\n", + " this.message = status_bar;\n", + "\n", + " // Add the close button to the window.\n", + " var buttongrp = document.createElement('div');\n", + " buttongrp.classList = 'btn-group inline pull-right';\n", + " button = document.createElement('button');\n", + " button.classList = 'btn btn-mini btn-primary';\n", + " button.href = '#';\n", + " button.title = 'Stop Interaction';\n", + " button.innerHTML = '';\n", + " button.addEventListener('click', function (_evt) {\n", + " fig.handle_close(fig, {});\n", + " });\n", + " button.addEventListener(\n", + " 'mouseover',\n", + " on_mouseover_closure('Stop Interaction')\n", + " );\n", + " buttongrp.appendChild(button);\n", + " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", + " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", + "};\n", + "\n", + "mpl.figure.prototype._remove_fig_handler = function (event) {\n", + " var fig = event.data.fig;\n", + " fig.close_ws(fig, {});\n", + "};\n", + "\n", + "mpl.figure.prototype._root_extra_style = function (el) {\n", + " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", + "};\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function (el) {\n", + " // this is important to make the div 'focusable\n", + " el.setAttribute('tabindex', 0);\n", + " // reach out to IPython and tell the keyboard manager to turn it's self\n", + " // off when our div gets focus\n", + "\n", + " // location in version 3\n", + " if (IPython.notebook.keyboard_manager) {\n", + " IPython.notebook.keyboard_manager.register_events(el);\n", + " } else {\n", + " // location in version 2\n", + " IPython.keyboard_manager.register_events(el);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", + " var manager = IPython.notebook.keyboard_manager;\n", + " if (!manager) {\n", + " manager = IPython.keyboard_manager;\n", + " }\n", + "\n", + " // Check for shift+enter\n", + " if (event.shiftKey && event.which === 13) {\n", + " this.canvas_div.blur();\n", + " // select the cell after this one\n", + " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", + " IPython.notebook.select(index + 1);\n", + " }\n", + "};\n", + "\n", + "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", + " fig.ondownload(fig, null);\n", + "};\n", + "\n", + "mpl.find_output_cell = function (html_output) {\n", + " // Return the cell and output element which can be found *uniquely* in the notebook.\n", + " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", + " // IPython event is triggered only after the cells have been serialised, which for\n", + " // our purposes (turning an active figure into a static one), is too late.\n", + " var cells = IPython.notebook.get_cells();\n", + " var ncells = cells.length;\n", + " for (var i = 0; i < ncells; i++) {\n", + " var cell = cells[i];\n", + " if (cell.cell_type === 'code') {\n", + " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", + " var data = cell.output_area.outputs[j];\n", + " if (data.data) {\n", + " // IPython >= 3 moved mimebundle to data attribute of output\n", + " data = data.data;\n", + " }\n", + " if (data['text/html'] === html_output) {\n", + " return [cell, data, j];\n", + " }\n", + " }\n", + " }\n", + " }\n", + "};\n", + "\n", + "// Register the function which deals with the matplotlib target/channel.\n", + "// The kernel may be null if the page has been refreshed.\n", + "if (IPython.notebook.kernel !== null) {\n", + " IPython.notebook.kernel.comm_manager.register_target(\n", + " 'matplotlib',\n", + " mpl.mpl_figure_comm\n", + " );\n", + "}\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n", + "Temps d'execution de fibor avec n=2960 : 0.001542809620000014\n" + ] + } + ], + "source": [ + "def fibordyn(n: int) -> int:\n", + " \"\"\" Lanceur de la fonction fibor (n>=0) : initialisation du tableau de résultats \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + " resultats = [None for i in range(n+2)]\n", + " resultats[0] = 0\n", + " resultats[1] = 1\n", + " \n", + " # === Nested function ===\n", + " def fibor(n: int) -> int:\n", + " \"\"\" Calcule les termes de la suite de Fibonacci récursivement avec programmation dynamique (n>=0) \"\"\"\n", + " assert isinstance(n, int) and n >= 0, \"n must be integer and positive\"\n", + "\n", + " if resultats[n] != None: return resultats[n]\n", + " if resultats[n-1] == None: resultats[n-1] = fibor(n-1)\n", + " if resultats[n-2] == None: resultats[n-2] = fibor(n-2)\n", + " return resultats[n-1] + resultats[n-2]\n", + " # === End of nested function ===\n", + " \n", + " return fibor(n)\n", + "\n", + "# Mesure du temps et tracés\n", + "import time\n", + "%matplotlib notebook\n", + "import matplotlib.pyplot as plt\n", + "n = [i for i in range(10, 2985, 25)]\n", + "liste_temps = []\n", + "\n", + "for i in n:\n", + " print(f\"Test avec n={i}\", end = \" - \")\n", + " temps = 0.0\n", + " nb_loops = 100\n", + " for test in range(nb_loops):\n", + " start = time.process_time()\n", + " fibordyn(i)\n", + " temps += time.process_time() - start\n", + " temps /= nb_loops\n", + " liste_temps.append(temps)\n", + "\n", + "plt.plot(n, liste_temps, label=\"fibor\")\n", + "plt.xlabel(\"n\")\n", + "plt.grid(True)\n", + "print(f\"\\n\\nTemps d'execution de fibor avec n={n[-1]} : {liste_temps[-1]}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ici le temps d'exécution est bien **linéaire** en fonction de n.\n", + "\n", + "⚠️ Mais il y a **trop d'appels de fonctions** imbriqués et Python ne peut pas calculer au delà de n=2900.\n", + "\n", + "Malgré tout, les performances sont bien en dessous de nos premiers algorithmes car ici il faut environ 1 ms pour calculer le terme avec n=2960 alors qu'il en fallait à peine 0.25 ms avec les premiers.\n", + "\n", + "# Conclusion\n", + "\n", + "⚠️ La **récursivité** permet de résoudre **facilement** des **problèmes complexes** mais elle s'accompagne souvent de **problèmes de performances**.\n", + "\n", + "⚠️ La **programmation dynamique** permet de gagner du temps dans les algorithmes car elle consiste à **enregistrer les résultats intermédiaires calculés** afin de les **ré-utiliser plus tard** dans l'algorithme.\n", + "\n", + "Cette technique est souvent utilisée dans les problèmes **d'optimisation** car dans ce domaine, les calculs utilisent souvent **plusieurs fois les mêmes valeurs**." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": 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