535 lines
11 KiB
Plaintext
535 lines
11 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Découverte de Python\n",
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"\n",
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"Dans ce cours autour de la programmation Python et de l'algorithmie, nous verons beaucoup de petits morceaux de programmes. \n",
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"\n",
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"Il est vivement recommander de ne pas faire **que** les questions poser mais aussi d'**expérimenter** par soi même."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Base de Ipython\n",
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"\n",
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"Dans les encadrés, on peut lancer des commandes Python et écrire des petits programmes.\n",
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"\n",
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"La combinaison de touche **shift+entré** permet de faire executer par l'ordinateur la ou les commandes tapées."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Boujour\n"
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]
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}
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],
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"source": [
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"print 'Boujour'"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* Modifier la commande précédente pour qu'elle n'affiche plus bonjour mais votre nom puis executer cette commande."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"La touche **entré** permet de passer à la ligne pour écrire d'autres commandes."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"bonjour\n",
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"monde\n"
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]
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}
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],
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"source": [
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"print(\"bonjour\")\n",
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"print('monde')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* Modifier le programme précédent pour qu'il affiche:\n",
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"\n",
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" Bonjour\n",
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" \n",
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" tous\n",
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" \n",
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" le \n",
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" \n",
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" monde"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Les commandes commençant par un dièze, ne seront pas executées. On appelle cela des commentaires. Nous les utiliserons pour expliquer ce que l'on fait."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"bonjour\n"
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]
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}
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],
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"source": [
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"# la commande suivante affiche Bonjour\n",
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"print('bonjour')\n",
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"# Quand on veut afficher quelque chose, on utilisera la commande print()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Les variables\n",
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"\n",
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"Les variables sont des *tirroirs* où l'on stockera des nombres, des mots, des phrases ou des choses plus compliqués. C'est ce que l'on appelle **assigner** une **valeur** à une variable ou **stocker** une valeur dans une variable."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"10\n"
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]
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}
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],
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"source": [
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"un_nombre = 10\n",
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"print(un_nombre)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* Modifier le programme précédent pour stocker 2 dans **un_nombre** "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Pour stocker des mots ou des phrases, il faut les mettre entre guillemets"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"un_mot = \"Coucou\"\n",
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"une_phrase = \"ceci est une phrase\""
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* Modifier le programme précédent pour changer le contenu des variables puis ajouter deux lignes pour afficher ce que contiennent ces variables (avec la commande **print**)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Opérations\n",
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"\n",
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"Un ordinateur ne sais **que** calculer. On peut donc lui faire faire toutes les opérations classiques "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"5\n",
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"21\n"
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]
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}
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],
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"source": [
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"print(2 + 3)\n",
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"print(4*5 + 1)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Ces simples calculs ne sont pas très interessants. La programmation devient réellement efficace quand on travail non plus avec des nombres que l'on définit par avance mais avec des nombres stockés dans des variables."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# On définit 3 variables\n",
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"a = 2\n",
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"b = 10\n",
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"c = 100"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"20\n",
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"120\n",
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"50.666666666666664\n"
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]
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}
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],
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"source": [
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"# On peut afficher des calculs avec elles\n",
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"print(a * b)\n",
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"print(a * b + c)\n",
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"print(a / 3 + c * 0.5)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"13\n",
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"3\n",
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"4\n"
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]
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}
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],
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"source": [
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"# On peut aussi stocker le résultat d'un calcul dans une variables\n",
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"d = a + b\n",
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"print(d)\n",
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"print(a)\n",
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"a = a + 1 \n",
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"print(a)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* Modifier les valeurs initiales de *a*, *b* et *c* puis executer les 3 blocks."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Exercice avec les suites\n",
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"\n",
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"Nous allons commencer à voir comment utiliser un programme pour calculer les permiers termes d'une suite.\n",
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"\n",
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"Soit $u_n$ la suite définie par\n",
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"$$u_0 = 100$$\n",
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"et \n",
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"$$ u_{n+1} = 0.4u_n + 10$$\n",
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"On veut calculer $u_3$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"22.0\n"
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]
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}
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],
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"source": [
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"# Premiere valeur de la suite (initialisation): u0\n",
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"u = 100\n",
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"# On lui applique la relation de récurrence pour avoir la deuxième valeur u1\n",
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"u = 0.4*u+10\n",
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"# On recommence jusqu'à atteindre u3\n",
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"u = 0.4*u+10\n",
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"u = 0.4*u+10\n",
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"# On affiche la valeur obtenue\n",
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"print(u)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"* Modifier le programme précédent pour calculer $u_5$\n",
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"\n",
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"* Dans le cadre suivant reprendre le programme précédent pour calculer $v_5$ pour la suite $v_n$ définie par\n",
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"$$v_0 = 10$$\n",
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"et \n",
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"$$ u_{n+1} = 5u_n -3$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Boucles\n",
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"\n",
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"Le problème c'est que si l'on veut calculer $u_{100}$, il faudra recopier un grand nombre de fois la formule de récurence ce qui n'est pas très astucieux...\n",
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"\n",
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"Pour éviter d'avoir à recopier plusieurs fois la même chose. Quand il a des répétitions à faire, nous utilisons des **boucles**.\n",
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"\n",
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"Pour faire des boucles on utilise l'instruction *for*"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"bonjour\n",
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"bonjour\n",
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"bonjour\n",
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"bonjour\n",
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"bonjour\n",
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"bonjour\n",
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"bonjour\n",
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"bonjour\n",
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"bonjour\n",
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"bonjour\n"
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]
|
||
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}
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],
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"source": [
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"for i in range(10):\n",
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" print(\"bonjour\")"
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]
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},
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{
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||
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"cell_type": "markdown",
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||
|
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"metadata": {},
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||
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"source": [
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"La fonction **range** va enumérer les nombres de 0 jusqu'à la valeur entre parenthèses.\n",
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"\n",
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"* Transformer le programme pour qu'il repète 20 fois le mot bonjour\n",
|
||
|
|
"* Remplacer \"bonjour\" par i pour voir les valeurs prises par i\n",
|
||
|
|
"\n",
|
||
|
|
"On remarquera qu'à la fin de la ligne **for**, il y a deux points puis que ce qui doit être répété est indenté (avec la touche **tab**).\n",
|
||
|
|
"\n",
|
||
|
|
"Dans l'exemple suivant nous allons faire plusieurs choses dans la boucle."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 24,
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0\n",
|
||
|
|
"bonjour\n",
|
||
|
|
"1\n",
|
||
|
|
"bonjour\n",
|
||
|
|
"2\n",
|
||
|
|
"bonjour\n",
|
||
|
|
"3\n",
|
||
|
|
"bonjour\n",
|
||
|
|
"4\n",
|
||
|
|
"bonjour\n",
|
||
|
|
"5\n",
|
||
|
|
"bonjour\n",
|
||
|
|
"6\n",
|
||
|
|
"bonjour\n",
|
||
|
|
"7\n",
|
||
|
|
"bonjour\n",
|
||
|
|
"8\n",
|
||
|
|
"bonjour\n",
|
||
|
|
"9\n",
|
||
|
|
"bonjour\n",
|
||
|
|
"fin de la boucle\n",
|
||
|
|
"12\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"un_mot = \"bonjour\"\n",
|
||
|
|
"un_nombre = 2\n",
|
||
|
|
"for i in range(10):\n",
|
||
|
|
" print(i)\n",
|
||
|
|
" print(un_mot)\n",
|
||
|
|
" un_nombre = un_nombre + 1\n",
|
||
|
|
"print(\"fin de la boucle\")\n",
|
||
|
|
"print(un_nombre)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"* recopier le programme précédent puis l'adapter pour calculer $u_{100}$"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": true
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"* écrire un programme qui calcule le n-ième terme de la suite $(w_n)$ définie par\n",
|
||
|
|
"$$w_0 = 3$$\n",
|
||
|
|
"et\n",
|
||
|
|
"$$w_{n+1} = -2u_n + 2$$"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": true
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"* Ecrire un programme qui calcule le n-ième terme de la suite (t_n) définie par\n",
|
||
|
|
"$$w_0 = 1$$\n",
|
||
|
|
"et\n",
|
||
|
|
"$$ w_{n+1} = w_n^{n} + 1$$"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": true
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 2",
|
||
|
|
"language": "python",
|
||
|
|
"name": "python2"
|
||
|
|
},
|
||
|
|
"language_info": {
|
||
|
|
"codemirror_mode": {
|
||
|
|
"name": "ipython",
|
||
|
|
"version": 2
|
||
|
|
},
|
||
|
|
"file_extension": ".py",
|
||
|
|
"mimetype": "text/x-python",
|
||
|
|
"name": "python",
|
||
|
|
"nbconvert_exporter": "python",
|
||
|
|
"pygments_lexer": "ipython2",
|
||
|
|
"version": "2.7.9"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 0
|
||
|
|
}
|