diff --git a/cryptographie/Analyse_bigramme.ipynb b/cryptographie/Analyse_bigramme.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..64ca38ff2d328a65bef8ed1ae51e55ed6b0345d2
--- /dev/null
+++ b/cryptographie/Analyse_bigramme.ipynb
@@ -0,0 +1,2062 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "b175e3e7",
+ "metadata": {},
+ "source": [
+ "# Calculer les fréquences des bigrammes d'une lettre dans une chaîne de caractères"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "42942619",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "POS_A = ord('A')#la position du A\n",
+ "POS_a = ord('a')#la position du a\n",
+ "POS_E = ord('E')#la position du E\n",
+ "POS_O = ord('O')#la position du O\n",
+ "POS_U = ord('U')#la position du U\n",
+ "POS_I = ord('I')#la position du I\n",
+ "\n",
+ "NB_CARS = 27 # le nombre de caractères pour les bigrammes\n",
+ "\n",
+ "\n",
+ "def pos_char(c):\n",
+ " '''\n",
+ " Donne la position du caractère dans l'alphabet\n",
+ " return -1 si le charactère n'est pas une lettre\n",
+ " '''\n",
+ " if 'a' <= c <= 'z':\n",
+ " p = ord(c) - POS_a\n",
+ " elif 'A' <= c <= 'Z':\n",
+ " p = ord(c) - POS_A\n",
+ " elif c in 'éèêÉÊÊ':\n",
+ " p = POS_E - POS_A\n",
+ " elif c in 'ôÔ':\n",
+ " p = POS_O - POS_A\n",
+ " elif c in 'ûÛùÙ':\n",
+ " p = POS_U - POS_A\n",
+ " elif c in 'îÎ':\n",
+ " p = POS_I - POS_A\n",
+ " elif c in ' .,:!?;':#ponction\n",
+ " p = -1\n",
+ " else:\n",
+ " p = -2\n",
+ " \n",
+ " p = p + 1\n",
+ "\n",
+ " return p\n",
+ "\n",
+ "def char_at_pos(p):\n",
+ " '''\n",
+ " Donne le caractère à la postion p\n",
+ " Exemples\n",
+ " char_at_pos(0)\n",
+ " >>> \" \"\n",
+ " char_at_pos(2)\n",
+ " >>> \"B\"\n",
+ " '''\n",
+ " if p==0:\n",
+ " return \" \"\n",
+ " else:\n",
+ " return chr(p+POS_A-1)\n",
+ "\n",
+ "def calc_bigrammes(texte):\n",
+ " \n",
+ " bigrammes= [[0]*NB_CARS for i in range(NB_CARS)] # nombre d'apparitions de chaque lettre\n",
+ " N = 0 # compte le nombre total de lettres\n",
+ " p2 = pos_char(texte[0])\n",
+ " for car in texte[1:]:\n",
+ " p1, p2 = p2, pos_char(car) # positions des caractères qui se suivent\n",
+ " \n",
+ " # fait des statistiques seulement sur des caractères alphabétiques\n",
+ " # et la ponctuation\n",
+ " if p1 != -1 and p2 != -1:\n",
+ " N = N + 1 # compte le nombre de caractères total du texte\n",
+ " bigrammes[p1][p2] += 1 # compte le nombre de bigramme (p1,p2)\n",
+ " \n",
+ " # Normalisation : calcule les fréquences\n",
+ " for i in range(NB_CARS):\n",
+ " for j in range(NB_CARS):\n",
+ " bigrammes[i][j] = bigrammes[i][j]/N\n",
+ " \n",
+ " return bigrammes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6f1f3b19",
+ "metadata": {},
+ "source": [
+ "### Test de la fonction"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "e06169b5",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# permet de lire le contenu du fichier texte\n",
+ "livre_fichier = open(\"Notre-Dame_de_Paris.txt\", \"r\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "28fdcb41",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# permet de mettre le contenu entier du fichier texte dans une unique chaîne de caractères\n",
+ "texte_livre = livre_fichier.read()\n",
+ "texte_livre = texte_livre.replace('\\n', ' ')#remplace les sauts à la ligne \"\\n\" par des espaces \" \"."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "433a8089",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "livre_fichier.close()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "45c9c0d3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "bigrammes_livre = calc_bigrammes(texte_livre)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "681c84a2",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# transformer la liste en dictionnaire\n",
+ "dic_bigrammes = {}#{chr(k+POS_A) : freq_livre[k] for k in range(NB_CARS)}\n",
+ "for i in range(NB_CARS):\n",
+ " for j in range(NB_CARS):\n",
+ " dic_bigrammes[(char_at_pos(i),char_at_pos(j))]= bigrammes_livre[i][j]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "a9aecb5f",
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
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+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
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+ "source": [
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+ },
+ {
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+ "execution_count": 8,
+ "id": "67831663",
+ "metadata": {},
+ "outputs": [
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+ " (('Y', 'Y'), 0.0),\n",
+ " (('Z', 'B'), 0.0),\n",
+ " (('Z', 'C'), 0.0),\n",
+ " (('Z', 'D'), 0.0),\n",
+ " (('Z', 'F'), 0.0),\n",
+ " (('Z', 'G'), 0.0),\n",
+ " (('Z', 'H'), 0.0),\n",
+ " (('Z', 'J'), 0.0),\n",
+ " (('Z', 'K'), 0.0),\n",
+ " (('Z', 'L'), 0.0),\n",
+ " (('Z', 'M'), 0.0),\n",
+ " (('Z', 'N'), 0.0),\n",
+ " (('Z', 'P'), 0.0),\n",
+ " (('Z', 'Q'), 0.0),\n",
+ " (('Z', 'R'), 0.0),\n",
+ " (('Z', 'S'), 0.0),\n",
+ " (('Z', 'T'), 0.0),\n",
+ " (('Z', 'V'), 0.0),\n",
+ " (('Z', 'W'), 0.0),\n",
+ " (('Z', 'X'), 0.0),\n",
+ " (('Z', 'Y'), 0.0),\n",
+ " (('Z', 'Z'), 0.0)]"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bigrammes_triees = sorted([(key, value) for key, value in dic_bigrammes.items()],\n",
+ " key=lambda x: x[1],\n",
+ " reverse = True)\n",
+ "bigrammes_triees "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "13ee1ccd",
+ "metadata": {},
+ "source": [
+ "### Affichage visuel"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "c982ce2a",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import matplotlib.pyplot as plt "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "6d597bd8",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "<Figure size 640x480 with 2 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "c = plt.pcolor(bigrammes_livre)\n",
+ "plt.colorbar(c) \n",
+ "plt.show() "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "017c7afa",
+ "metadata": {},
+ "source": [
+ "## Cryptanalyse Cesar"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "id": "690d4446",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def dist_bigrammes(bigramme1, bigramme2):\n",
+ " ''' calcule la distance euclidienne \n",
+ " '''\n",
+ " dist = 0\n",
+ " for i in range(NB_CARS):\n",
+ " for j in range(NB_CARS):\n",
+ " dist += (bigramme1[i][j] - bigramme2[i][j])**2\n",
+ " \n",
+ " return dist**0.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "id": "30f1ab26",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def cesar_dechiffre(texte_chiffre, k):\n",
+ " texte_clair= \"\"\n",
+ " for lettre in texte_chiffre:\n",
+ " nb_chiffre = pos_char(lettre)\n",
+ " nb_clair = (nb_chiffre - k) % 26\n",
+ " lettre_clair = chr(nb_clair + POS_A)\n",
+ " texte_clair = texte_clair + lettre_clair\n",
+ " return texte_clair"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "id": "a54222f3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def casser_cesar(texte_chiffre):\n",
+ " \n",
+ " d_min = 2 # car ||a-b||=(a-b)·(a-b)=||a||+||b||-2 (a·b)=2-2 (a·b)\n",
+ " # donc toujours plus petit que 2\n",
+ " cle = 0\n",
+ " texte_dechiffre_final = texte_chiffre\n",
+ " for k in range(1,26):\n",
+ " texte_dechiffre = cesar_dechiffre(texte_chiffre, k)\n",
+ " bigramme_dechiffre = calc_bigrammes(texte_dechiffre)\n",
+ " d = dist_bigrammes(bigramme_dechiffre, bigrammes_livre)\n",
+ " \n",
+ " if d < d_min:\n",
+ " d_min = d\n",
+ " cle = k\n",
+ " texte_dechiffre_final = texte_dechiffre\n",
+ " \n",
+ " return cle, texte_dechiffre_final"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "id": "bd6f21e0",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "La clé pour déchiffrer \" INKANNWLJPN \" est 10 et le texte dechiffré est : ZEBREENCAGE\n"
+ ]
+ }
+ ],
+ "source": [
+ "texte_chiffre_01='INKANNWLJPN'\n",
+ "cle, texte_dechiffre = casser_cesar(texte_chiffre_01)\n",
+ "print('La clé pour déchiffrer \"', texte_chiffre_01, '\" est ', cle, \n",
+ " ' et le texte dechiffré est : ', texte_dechiffre)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "id": "fbd32638",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "La clé pour déchiffrer \" LKDKSVVO \" est 11 et le texte dechiffré est : BATAILLE\n"
+ ]
+ }
+ ],
+ "source": [
+ "texte_chiffre_02='LKDKSVVO'\n",
+ "cle, texte_dechiffre = casser_cesar(texte_chiffre_02)\n",
+ "print('La clé pour déchiffrer \"', texte_chiffre_02, '\" est ', cle, \n",
+ " ' et le texte dechiffré est : ', texte_dechiffre)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "id": "ee411e60",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "La clé pour déchiffrer \" REYPKENA \" est 23 et le texte dechiffré est : VICTOIRE\n"
+ ]
+ }
+ ],
+ "source": [
+ "texte_chiffre_03='REYPKENA'\n",
+ "cle, texte_dechiffre = casser_cesar(texte_chiffre_03)\n",
+ "print('La clé pour déchiffrer \"', texte_chiffre_03, '\" est ', cle, \n",
+ " ' et le texte dechiffré est : ', texte_dechiffre)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e520793f",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0d112f3f",
+ "metadata": {},
+ "source": [
+ "## Cryptanalyse Affine"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "id": "04b2009c",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def find_inverse_Z26(x):\n",
+ " '''\n",
+ " Si l'inverse n'existe pas, 0 est retourné\n",
+ " '''\n",
+ " for k in range(1,26):\n",
+ " r = (x * k) % 26\n",
+ " if r == 1:\n",
+ " return k\n",
+ " return 0"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "id": "0118daea",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def affine_dechiffre(texte_chiffre,a,b):\n",
+ " \n",
+ " inverse = find_inverse_Z26(a) # c est l'inverse de a mod 26\n",
+ " \n",
+ " texte_clair= \"\"\n",
+ " for lettre in texte_chiffre: # Boucle\n",
+ " nb_chiffre = pos_char(lettre) # Bijection b\n",
+ " nb_clair = inverse*(nb_chiffre-b)%26 # Fonction de dechiffrement\n",
+ " lettre_clair = chr(nb_clair + POS_A) # Bijection b^-1\n",
+ " texte_clair = texte_clair + lettre_clair \n",
+ " return texte_clair"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "id": "ec6b34e6",
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'EDWDLOOH'"
+ ]
+ },
+ "execution_count": 26,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "affine_dechiffre('LCRCWXXM',9,2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "id": "9d7cd8bb",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[1, 9, 21, 15, 3, 19, 7, 23, 11, 5, 17, 25]"
+ ]
+ },
+ "execution_count": 27,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# tous les éléments qui possède une inverse dans Z26\n",
+ "INV_Z26 = [find_inverse_Z26(k) for k in range(26) if find_inverse_Z26(k)!=0]\n",
+ "INV_Z26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "id": "d22ce0c3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def casser_affine(texte_chiffre):\n",
+ " \n",
+ " d_min = 2 # car ||a-b||=(a-b)·(a-b)=||a||+||b||-2 (a·b)=2-2 (a·b)\n",
+ " # donc toujours plus petit que 2\n",
+ " cle = (1,0)\n",
+ " texte_dechiffre_final = texte_chiffre\n",
+ " for a in INV_Z26:\n",
+ " for b in range(1,26):\n",
+ " texte_dechiffre = affine_dechiffre(texte_chiffre, a,b)\n",
+ " bigramme_dechiffre = calc_bigrammes(texte_dechiffre)\n",
+ " d = dist_bigrammes(bigramme_dechiffre, bigrammes_livre)\n",
+ " \n",
+ " if d < d_min:\n",
+ " d_min = d\n",
+ " cle = (a,b)\n",
+ " texte_dechiffre_final = texte_dechiffre\n",
+ " # print((a,b), texte_dechiffre, d)\n",
+ " \n",
+ " return cle, texte_dechiffre_final"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "id": "a8a10ff4",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "((9, 3), 'BATAILLE')"
+ ]
+ },
+ "execution_count": 29,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "casser_affine('LCRCWXXM')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "id": "461e5130",
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "((11, 4), 'BRAVOCENESTPASFACILE')"
+ ]
+ },
+ "execution_count": 30,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "casser_affine('OIDABZVQVTEMDTGDZNUV')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "id": "a030790f",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "((25, 14), 'LECOMMANDEMENTMILITAIREESTPRET')"
+ ]
+ },
+ "execution_count": 31,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "casser_affine('CJLZBBNAKJBJAUBFCFUNFWJJVUYWJU')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7e20405a",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "61148a97",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "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": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.12.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/recursivite/ex_decomposition_quatre_carres.ipynb b/recursivite/ex_decomposition_quatre_carres.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..73c300d5ea815be5af64370aba57e782abdcd9a9
--- /dev/null
+++ b/recursivite/ex_decomposition_quatre_carres.ipynb
@@ -0,0 +1 @@
+{"cells":[{"metadata":{},"cell_type":"markdown","source":"<div style='background-color: #e3a8b6;\n border: 0.5em solid black;\n border-radius: 0.5em;\n padding: 1em;'>\n <h2>Exercice</h2>\n <h1>Décomposition d'un entier positif en somme d'au plus quatre carrés</h1>\n</div>"},{"metadata":{},"cell_type":"markdown","source":"Le théorème des quatre carrés de Lagrange affirme que tout nombre entier positif `n` peut s'écrire comme la somme d'au plus quatre carrés.\n\nPar exemple, $1871 = 1 + 25 + 81 + 1764 = 1^2 + 5^2 + 9^2 + 42^2$.\n\nPour afficher une possibilité on peut donner l'algorithme suivant qui permet de décomposer un entier positif `n` en une somme d'au plus quatre carrés."},{"metadata":{},"cell_type":"markdown","source":"<div style='background-color: #f7bd83;\n border-radius: 0.5em;\n padding: 1em;\n margin: 0em 2em 0em 2em'>\n\n<p><b>Algorithme de décomposition de l'entier positif <code>n</code> en une somme d'au plus quatre carrés</b></p>\n<p><b>Début</b></p>\n<p STYLE=\"padding:0 0 0 40px;\">Si <code>n</code> est le carré d'un entier alors</p>\n<p STYLE=\"padding:0 0 0 80px;\">Retourner un tableau contenant uniquement l'élément <code>n</code></p>\n <p STYLE=\"padding:0 0 0 40px;\">Sinon</p>\n <p STYLE=\"padding:0 0 0 80px;\"><code>liste_carres</code> ← tableau contenant la liste décroissante des nombres compris entre 1 et <code>n</code> qui sont des carrés d'entiers</p>\n<p STYLE=\"padding:0 0 0 80px;\">Pour chaque élément <code>carre</code> de <code>liste_carres</code> faire</p>\n<p STYLE=\"padding:0 0 0 120px;\"><code>decompo</code> ← liste renvoyé par <code>decomposition_carres(n - carre)</code> auquel on ajoute l'élément <code>carre</code> à la fin</p>\n<p STYLE=\"padding:0 0 0 120px;\">Si longueur(<code>decompo</code>) $\\leq$ 4 alors</p>\n<p STYLE=\"padding:0 0 0 160px;\">Retourner <code>decompo</code></p>\n <p><b>Fin</b></p>\n \n</div>"},{"metadata":{},"cell_type":"markdown","source":"**(1)** 💻 Définir une fonction `est_carre` qui prend en paramètre d'entrée un entier positif `n` et qui renvoie `True` si `n` est le carré d'un entier et `False` sinon."},{"metadata":{"trusted":true},"cell_type":"code","source":"def est_carre(n):\n if round(n**0.5)**2 == n:\n return True\n else:\n return False","execution_count":5,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# Test\nnb = 9\nprint(nb, \"est-il un carre ? \", est_carre(nb))\nnb = 10\nprint(nb, \"est-il un carre ? \", est_carre(nb))","execution_count":7,"outputs":[{"output_type":"stream","text":"9 est-il un carre ? True\n10 est-il un carre ? False\n","name":"stdout"}]},{"metadata":{},"cell_type":"markdown","source":"**(2)** 💻 Définir une fonction `liste_carres_entiers` qui prend en paramètre d'entrée un entier positif `n` et qui renvoie la liste décroissante des entiers compris entre 1 et `n` et qui sont des carrés d'entiers."},{"metadata":{"trusted":true},"cell_type":"code","source":"def liste_carres_entiers(n):\n L = []\n for k in reversed(range(1, n+1)):\n if est_carre(k):\n L.append(k)\n return L","execution_count":37,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# Test\nlistes_carres = liste_carres_entiers(100)\nprint(listes_carres) # doit afficher [100, 81, 64, 49, 36, 25, 16, 9, 4, 1]","execution_count":38,"outputs":[{"output_type":"stream","text":"[100, 81, 64, 49, 36, 25, 16, 9, 4, 1]\n","name":"stdout"}]},{"metadata":{"trusted":true},"cell_type":"code","source":"# Test\nlistes_carres = liste_carres_entiers(871)\nprint(listes_carres) # doit afficher [100, 81, 64, 49, 36, 25, 16, 9, 4, 1]","execution_count":39,"outputs":[{"output_type":"stream","text":"[841, 784, 729, 676, 625, 576, 529, 484, 441, 400, 361, 324, 289, 256, 225, 196, 169, 144, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1]\n","name":"stdout"}]},{"metadata":{},"cell_type":"markdown","source":"**(3)** 💻 Implémenter la fonction `decomposition_carres` qui prend en paramètre d'entrée un entier positif `n` et qui renvoie, sous forme de tableau de longueur inférieure ou égale à 4, une décomposition de `n` en somme de carrés d'entiers."},{"metadata":{"trusted":true},"cell_type":"code","source":"def decomposition_carres(n):\n if est_carre(n):\n return [n]\n else:\n listes_carres = liste_carres_entiers(n)\n for carre in listes_carres:\n decompo = decomposition_carres(n - carre) + [carre]\n if len(decompo) <= 4:\n return decompo","execution_count":35,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# Test\nnb = 1871\nprint(\"La décomposition de \",nb, \"est : \", decomposition_carres(nb))","execution_count":43,"outputs":[{"output_type":"stream","text":"La décomposition de 1871 est : [1, 25, 81, 1764]\n","name":"stdout"}]},{"metadata":{},"cell_type":"markdown","source":"**(4)** ✏️ Donner une décomposition en somme d'au plus quatre carrés pour les entiers $300$, $1789$, $2021$ et $12345$."},{"metadata":{"trusted":true},"cell_type":"code","source":"def print_decompoision(n, decompo):\n s = str(n)+ \" = \"\n for n in decompo:\n s = s + str(int(n**0.5))+\"² + \"\n s = s[:-3]\n print(s)","execution_count":45,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"nb = 1871\nprint_decompoision(nb, decomposition_carres(nb))\nnb = 300\nprint_decompoision(nb, decomposition_carres(nb))\nnb = 1789\nprint_decompoision(nb, decomposition_carres(nb))\nnb = 2021\nprint_decompoision(nb, decomposition_carres(nb))\nnb = 12345\nprint_decompoision(nb, decomposition_carres(nb))","execution_count":48,"outputs":[{"output_type":"stream","text":"1871 = 1² + 5² + 9² + 42²\n300 = 1² + 1² + 3² + 17²\n1789 = 5² + 42²\n2021 = 2² + 9² + 44²\n12345 = 2² + 2² + 4² + 111²\n","name":"stdout"}]},{"metadata":{},"cell_type":"markdown","source":"## Une version non récursive"},{"metadata":{"trusted":true},"cell_type":"code","source":"def decomposition_carres2(n):\n listes_carres = liste_carres_entiers(n)\n listes_carres = listes_carres + [0]\n for carre1 in listes_carres:\n for carre2 in listes_carres:\n for carre3 in listes_carres:\n for carre4 in listes_carres:\n if carre1 + carre2 +carre3 +carre4 ==n :\n return [carre1, carre2, carre3, carre4]","execution_count":50,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"nb = 1871\nprint_decompoision(nb, decomposition_carres2(nb))\nnb = 300\nprint_decompoision(nb, decomposition_carres2(nb))\nnb = 1789\nprint_decompoision(nb, decomposition_carres2(nb))\nnb = 2021\nprint_decompoision(nb, decomposition_carres2(nb))\nnb = 12345\nprint_decompoision(nb, decomposition_carres2(nb))","execution_count":51,"outputs":[{"output_type":"stream","text":"1871 = 43² + 3² + 3² + 2²\n300 = 17² + 3² + 1² + 1²\n1789 = 42² + 5² + 0² + 0²\n2021 = 44² + 9² + 2² + 0²\n12345 = 111² + 4² + 2² + 2²\n","name":"stdout"}]},{"metadata":{"trusted":true},"cell_type":"code","source":"","execution_count":null,"outputs":[]}],"metadata":{"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.8.5"}},"nbformat":4,"nbformat_minor":2}
\ No newline at end of file