{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ee7d77ff",
   "metadata": {},
   "source": [
    "# TP — Révisions sur la récursivité — Corrigé\n",
    "\n",
    "L'objectif de ce TP est de réviser la programmation récursive. On respectera les consignes suivantes :\n",
    "\n",
    "- on évitera autant que possible les boucles `for` et `while`, en leur préférant des fonctions récursives : une boucle `for` reste permise pour parcourir les **choix possibles** à une étape (les quatre quarts d'un échiquier, les valeurs possibles d'une case de Sudoku, les colonnes d'une ligne…), et quand l'énoncé l'autorise explicitement,\n",
    "- les listes en compréhension sont autorisées,\n",
    "- il est au contraire autorisé, et même conseillé, d'écrire des fonctions récursives auxiliaires,\n",
    "- sauf mention contraire, les fonctions ne doivent pas modifier les listes passées en argument,\n",
    "- on cherchera dès que possible à obtenir des complexités « raisonnables ».\n",
    "\n",
    "Après chaque fonction à écrire, une cellule de tests est fournie : une fois la fonction écrite, l'exécuter, elle ne doit afficher que des `True`.\n",
    "\n",
    "Python limite par défaut à 1000 le nombre d'appels imbriqués. La cellule suivante relève cette limite et importe le module `dessins.py` (à placer dans le même dossier que ce notebook) : l'exécuter avant toute chose. La plupart des fonctions `dessiner_…` de ce module dessinent vos résultats et les **vérifient** : le titre du dessin est vert si le résultat est correct, rouge sinon, et les erreurs sont marquées en rouge."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sommaire",
   "metadata": {
    "tags": [
     "sommaire"
    ]
   },
   "source": [
    "**Sommaire**\n",
    "\n",
    "- Un exemple\n",
    "- I\\. Récursivité et « diviser pour régner »\n",
    "    - 1\\. Quelques études de complexité classiques (Q1 à Q4)\n",
    "    - 2\\. Recherche dichotomique (Q5 et Q6)\n",
    "    - 3\\. Multiplication rapide de polynômes (Q7 à Q10)\n",
    "    - 4\\. Triangle de Pascal modulo 2 (Q11 et Q12)\n",
    "    - 5\\. Pavage par des triominos (bonus) (Q13 et Q14)\n",
    "    - 6\\. Tri rapide, sélection et médiane en temps linéaire (Q15 à Q19)\n",
    "- II\\. Mémoïsation\n",
    "    - 7\\. Échange de shokobons (Q20 et Q21)\n",
    "    - 8\\. La suite de Syracuse (Projet Euler 14) (Q22)\n",
    "    - 9\\. Chemins dans une grille à trous (Q23 et Q24)\n",
    "    - 10\\. Parenthésages et nombres de Catalan (Q25 à Q29)\n",
    "    - 11\\. Partitions d'un entier (Projet Euler 76) (Q30 et Q31)\n",
    "- III\\. Backtracking\n",
    "    - 12\\. Le problème des $n$ reines (Q32 à Q35)\n",
    "    - 13\\. Sudoku (Q36 à Q38)\n",
    "    - 14\\. Logimages (inspiré de X-ENS 2024) (Q39 à Q45)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ffa0c9ba",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-10-05T13:31:24.459349Z"
    }
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   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "sys.setrecursionlimit(10**4)   # au lieu de 1000 par défaut\n",
    "\n",
    "import numpy as np\n",
    "from dessins import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10896be4",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Un exemple\n",
    "\n",
    "Pour calculer la somme des valeurs d'une liste, comparons les quatre codes suivants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "25fcb9ce",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-10-05T13:31:24.464889Z"
    }
   },
   "outputs": [],
   "source": [
    "def somme_iterative(l):\n",
    "    S = 0\n",
    "    for i in range(len(l)):\n",
    "        S = S + l[i]\n",
    "    return S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d0914b5e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.468900Z",
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     "shell.execute_reply": "2026-10-05T13:31:24.472166Z"
    }
   },
   "outputs": [],
   "source": [
    "def somme_recursive_slicing(l):\n",
    "    if len(l) == 0:\n",
    "        return 0\n",
    "    else:\n",
    "        return l[0] + somme_recursive_slicing(l[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "67fba9b4",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-10-05T13:31:24.477056Z"
    }
   },
   "outputs": [],
   "source": [
    "def somme_recursive_modifie(l):\n",
    "    if len(l) == 0:\n",
    "        return 0\n",
    "    else:\n",
    "        x = l.pop()\n",
    "        return x + somme_recursive_modifie(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6b4b0f50",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-10-05T13:31:24.481992Z"
    }
   },
   "outputs": [],
   "source": [
    "def somme_recursive_aux(l, j):\n",
    "    if j == len(l):\n",
    "        return 0\n",
    "    else:\n",
    "        return l[j] + somme_recursive_aux(l, j + 1)\n",
    "\n",
    "def somme_recursive(l):\n",
    "    return somme_recursive_aux(l, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d57046a",
   "metadata": {},
   "source": [
    "- `somme_iterative` est itérative : elle ne respecte pas la consigne d'éviter les boucles,\n",
    "- `somme_recursive_slicing` est récursive, mais de complexité $O(n^2)$ : à chaque appel, `l[1:]` crée une nouvelle liste de taille $n-1$, $n-2$, …,\n",
    "- `somme_recursive_modifie` est récursive et de complexité $O(n)$ (`pop()` sans argument retire le dernier élément en $O(1)$), mais elle **vide** la liste passée en argument,\n",
    "- `somme_recursive` est récursive, de complexité $O(n)$, et ne modifie pas la liste : c'est la seule qui respecte toutes les consignes. L'indice `j` de la fonction auxiliaire joue le rôle du *slicing* sans en payer le coût."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a65be928",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## I. Récursivité et « diviser pour régner »\n",
    "\n",
    "**Rappel.** Une fonction récursive s'appelle elle-même avec d'autres arguments. Il faut :\n",
    "\n",
    "- un ou plusieurs **cas de base** (ou conditions d'arrêt), traités sans appel récursif,\n",
    "- des appels récursifs sur des arguments qui se rapprochent d'un cas de base, ce qu'on justifie par un **variant** : un entier positif qui décroît strictement à chaque appel (il garantit la **terminaison**),\n",
    "- pour la **complexité**, une relation de récurrence sur le coût $C(n)$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "091b97af",
   "metadata": {},
   "source": [
    "Pour la complexité, on rappelle qu'à partir de l'« équation maître » $C(n) = a C(n/b) + O(n^d)$, on peut en déduire les complexités suivantes (cf. cours de première année) :\n",
    "\n",
    "| relation | complexité |\n",
    "|---|---|\n",
    "| $C(n) = C(n-r) + O(1)$ | $O(n)$ |\n",
    "| $C(n) = C(n-r) + O(n)$ | $O(n^2)$ | \n",
    "| $C(n) = qC(n-1) + O(1)$ | $O(q^n)$ |\n",
    "| $C(n) = C(n-1) + C(n-2) + O(1)$ | $O(\\varphi^n)$, avec $\\varphi = \\frac{1+\\sqrt{5}}{2}$ |\n",
    "| $C(n) = C(n/b) + O(1)$ | $O(\\ln(n))$ | \n",
    "| $C(n) = bC(n/b) + O(n)$ | $O(n \\ln(n))$ |\n",
    "| $C(n) = aC(n/b) + O(n)$ avec $a > b$ | $O(n^{\\log_b a})$ |\n",
    "\n",
    "où $r \\geq 1$, $q \\geq 2$, $a$ et $b \\geq 2$ sont des constantes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ef5a71a",
   "metadata": {},
   "source": [
    "Par exemple pour l'écriture d'un entier $n \\geq 0$ en base $b$ (avec $b \\geq 2$) : le dernier chiffre est `n % b`, et les précédents sont ceux de `n // b`. On a donc le programme récursif suivant :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bf52e423",
   "metadata": {
    "execution": {
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     "iopub.status.idle": "2026-10-05T13:31:24.488219Z",
     "shell.execute_reply": "2026-10-05T13:31:24.487600Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 0, 2, 6] [1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0] [7, 14, 10] [0]\n"
     ]
    }
   ],
   "source": [
    "def ecriture(n, b):\n",
    "    if n < b:                             # cas de base : un seul chiffre\n",
    "        return [n]\n",
    "    else:                                 # appel sur n // b < n\n",
    "        l = ecriture(n // b, b)\n",
    "        l.append(n % b)\n",
    "        return l\n",
    "\n",
    "print(ecriture(2026, 10), ecriture(2026, 2), ecriture(2026, 16), ecriture(0, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83eb10c3",
   "metadata": {},
   "source": [
    "- *Variant* : l'entier naturel $n$, qui décroît strictement (`n // b < n` pour $n \\geq b$),\n",
    "- *Correction* : si `ecriture(n // b, b)` renvoie l'écriture de `n // b`, en lui ajoutant `n % b` on obtient celle de $n$, car $n = b \\cdot (n // b) + (n \\% b)$,\n",
    "- *Complexité* : en notant $C(n)$ le coût de `ecriture(n, b)`, on a l'équation $C(n) = C(n // b) + O(1)$, donc $C(n) = O(\\ln(n))$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd5342db",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 1. Quelques études de complexité classiques"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9b8eb27",
   "metadata": {},
   "source": [
    "**Question 1**. Quelles sont les complexités des fonctions suivantes ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a8dd3e36",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-10-05T13:31:24.492083Z"
    }
   },
   "outputs": [],
   "source": [
    "def fibo_affreux(n):\n",
    "    if n == 0:\n",
    "        return 0\n",
    "    elif n == 1:\n",
    "        return 1\n",
    "    else:\n",
    "        return fibo_affreux(n-1) + fibo_affreux(n-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "67b7080f",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-10-05T13:31:24.496396Z"
    }
   },
   "outputs": [],
   "source": [
    "def fibo_aux(n):\n",
    "    if n == 0:\n",
    "        return (0, 1)\n",
    "    else:\n",
    "        a, b = fibo_aux(n - 1)\n",
    "        return (b, a + b)\n",
    "\n",
    "def fibo(n):\n",
    "    return fibo_aux(n)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "33041679",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-10-05T13:31:24.500564Z"
    }
   },
   "outputs": [],
   "source": [
    "def fibo_argh(n):\n",
    "    if n == 0:\n",
    "        return (0, 1)\n",
    "    else:\n",
    "        return (fibo_argh(n - 1)[1], fibo_argh(n - 1)[0] + fibo_argh(n - 1)[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee6d53b9",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* On note $C(n)$ le nombre d'opérations élémentaires pour l'argument $n$ (additions en $O(1)$).\n",
    "\n",
    "- `fibo_affreux` : $C(n) = C(n-1) + C(n-2) + O(1)$. La suite $C$ se comporte comme la suite de Fibonacci elle-même : $C(n) = O(\\varphi^n)$ avec $\\varphi = \\frac{1+\\sqrt5}{2} \\approx 1{,}6$. Plus précisément, le nombre d'appels est $2F_{n+1} - 1$. Les mêmes valeurs sont recalculées un nombre exponentiel de fois.\n",
    "- `fibo` : `fibo_aux` fait **un seul** appel récursif, $C(n) = C(n-1) + O(1)$, d'où $C(n) = O(n)$ (et une profondeur de récursion $n$). Renvoyer le couple $(F_n, F_{n+1})$ évite de recalculer $F_{n-1}$.\n",
    "- `fibo_argh` : même idée que `fibo`, mais le couple est recalculé à chaque utilisation : **trois** appels à `fibo_argh(n-1)`, donc $C(n) = 3C(n-1) + O(1)$ et $C(n) = O(3^n)$, pire encore que `fibo_affreux` ! Il suffit de stocker le résultat dans une variable, comme dans `fibo_aux`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34f737a7",
   "metadata": {},
   "source": [
    "**Question 2**. En supposant que la multiplication de deux entiers est de complexité $O(1)$, et en remarquant que la suite de Fibonacci $(F_n)_{n \\in \\mathbb{N}}$ vérifie\n",
    "$$\n",
    "\\forall n \\in \\mathbb{N}, \\quad \\begin{pmatrix} F_{n+1} \\\\ F_{n+2} \\end{pmatrix} = \\begin{pmatrix} 0 & 1 \\\\ 1 & 1 \\end{pmatrix} \\begin{pmatrix} F_n \\\\ F_{n+1} \\end{pmatrix},\n",
    "$$\n",
    "écrire une fonction récursive `fibo_rapide(n)` qui prend en argument un entier naturel `n` et renvoie $F_n$, avec une complexité $O(\\ln n)$. On représentera les matrices par des listes de listes d'entiers Python, et non par des tableaux numpy : leurs entiers sur 64 bits débordent, et $F_{100}$ serait faux."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d3c6972",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* En notant $M = \\begin{pmatrix} 0 & 1 \\\\ 1 & 1 \\end{pmatrix}$, on a $\\begin{pmatrix} F_n \\\\ F_{n+1} \\end{pmatrix} = M^n \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}$, donc $F_n$ est le coefficient $(0, 1)$ de $M^n$. On calcule $M^n$ par **exponentiation rapide** : $M^n = \\left(M^{\\lfloor n/2 \\rfloor}\\right)^2$ si $n$ est pair, et $M^n = \\left(M^{\\lfloor n/2 \\rfloor}\\right)^2 M$ si $n$ est impair.\n",
    "\n",
    "L'hypothèse « multiplication en $O(1)$ » est discutable ici : $F_n$ s'écrit avec environ $0{,}7\\,n$ bits, et Python manipule des entiers de taille arbitraire. La complexité $O(\\ln n)$ compte des **opérations arithmétiques**, pas des opérations sur les bits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f0a8d964",
   "metadata": {
    "execution": {
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    },
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     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def produit(A, B):\n",
    "    \"\"\"Produit de deux matrices 2 x 2.\"\"\"\n",
    "    [[a, b], [c, d]] = A\n",
    "    [[e, f], [g, h]] = B\n",
    "    return [[a * e + b * g, a * f + b * h],\n",
    "            [c * e + d * g, c * f + d * h]]\n",
    "\n",
    "def puissance(A, n):\n",
    "    if n == 0:\n",
    "        return [[1, 0], [0, 1]]\n",
    "    B = puissance(A, n // 2)   # un SEUL appel récursif\n",
    "    C = produit(B, B)\n",
    "    if n % 2 == 1:\n",
    "        C = produit(C, A)\n",
    "    return C\n",
    "\n",
    "def fibo_rapide(n):\n",
    "    return puissance([[0, 1], [1, 1]], n)[0][1]\n",
    "\n",
    "# C(n) = C(n // 2) + O(1), d'où C(n) = O(ln n).\n",
    "# Écrire produit(puissance(A, n // 2), puissance(A, n // 2)) donnerait\n",
    "# C(n) = 2 C(n // 2) + O(1), soit O(n) : on perdrait tout le bénéfice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e5376190",
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(fibo_rapide(0) == 0, fibo_rapide(1) == 1, fibo_rapide(2) == 1)\n",
    "print([fibo_rapide(n) for n in range(20)] == [fibo(n) for n in range(20)])\n",
    "print(fibo_rapide(100) == 354224848179261915075)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37066fa6",
   "metadata": {},
   "source": [
    "**Question 3**. Écrire une fonction récursive `pgcd(a, b)` qui prend en arguments deux entiers naturels `a` et `b` non tous deux nuls et renvoie leur pgcd."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a59b2d86",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-10-05T13:31:24.516529Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def pgcd(a, b):\n",
    "    if b == 0:\n",
    "        return a\n",
    "    else:\n",
    "        return pgcd(b, a % b)   # Euclide : pgcd(a, b) = pgcd(b, a % b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cb05cd3d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.519169Z",
     "iopub.status.busy": "2026-10-05T13:31:24.518982Z",
     "iopub.status.idle": "2026-10-05T13:31:24.522464Z",
     "shell.execute_reply": "2026-10-05T13:31:24.521675Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True True\n",
      "True True True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(pgcd(12, 18) == 6, pgcd(18, 12) == 6, pgcd(17, 5) == 1)\n",
    "print(pgcd(7, 0) == 7, pgcd(0, 7) == 7, pgcd(9, 9) == 9)   # cas limites\n",
    "print(pgcd(2**10 * 3**5, 2**4 * 3**8 * 5) == 2**4 * 3**5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fdda2ba",
   "metadata": {},
   "source": [
    "**Question 4** *(bonus)*. Déterminer la complexité de votre fonction `pgcd(a, b)` en fonction de `b`, dans le cas où `a < b`.\n",
    "\n",
    "*Indication* : on pourra remarquer, et démontrer, que deux termes consécutifs de la suite de Fibonacci constituent le « pire des cas »."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08839c8f",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* Chaque appel coûte $O(1)$, il s'agit de compter les appels, c'est-à-dire les divisions euclidiennes effectuées. Si $a < b$, le premier appel échange les arguments : `pgcd(a, b)` appelle `pgcd(b, a)`. On étudie donc `pgcd(a, b)` avec $a > b \\geq 1$.\n",
    "\n",
    "**Lemme.** Si $a > b \\geq 1$ et si `pgcd(a, b)` effectue $k \\geq 1$ divisions, alors $a \\geq F_{k+2}$ et $b \\geq F_{k+1}$.\n",
    "\n",
    "*Démonstration*, par récurrence sur $k$.\n",
    "\n",
    "- $k = 1$ : $b \\geq 1 = F_2$ et $a > b \\geq 1$ donc $a \\geq 2 = F_3$.\n",
    "- Si `pgcd(a, b)` effectue $k+1 \\geq 2$ divisions, notons $a = qb + r$ la première. Comme une autre division suit, $r \\neq 0$, et `pgcd(b, r)` effectue $k$ divisions avec $b > r \\geq 1$. Par hypothèse de récurrence, $b \\geq F_{k+2}$ et $r \\geq F_{k+1}$. Comme $a > b$, on a $q \\geq 1$, donc $a \\geq b + r \\geq F_{k+2} + F_{k+1} = F_{k+3}$. $\\square$\n",
    "\n",
    "Par ailleurs, une récurrence immédiate donne $F_{k+1} \\geq \\varphi^{k-1}$ pour tout $k \\geq 0$ (car $\\varphi^2 = \\varphi + 1$). Donc $b \\geq \\varphi^{k-1}$, soit $k \\leq 1 + \\log_\\varphi b$.\n",
    "\n",
    "**Conclusion.** Pour $a < b$, l'appel `pgcd(a, b)` effectue au plus $1 + (1 + \\log_\\varphi a) \\leq 2 + \\log_\\varphi b$ divisions : la complexité est $O(\\ln b)$.\n",
    "\n",
    "Cette borne est atteinte à une constante près : pour $k \\geq 2$, $F_{k+2} = F_{k+1} + F_k$ avec $0 < F_k < F_{k+1}$, donc l'appel sur $(F_{k+2}, F_{k+1})$ se ramène à l'appel sur $(F_{k+1}, F_k)$ : de proche en proche, il faut exactement $k$ divisions, et deux termes consécutifs de la suite de Fibonacci réalisent bien le pire des cas."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99d5056c",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 2. Recherche dichotomique"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78d47cbf",
   "metadata": {},
   "source": [
    "**Question 5**. Écrire une fonction récursive `dicho(L, x)` qui prend en arguments une liste **triée** `L` et une valeur `x`, et renvoie `True` si `x` appartient à `L` et `False` sinon, en $O(\\ln n)$ où $n$ est la longueur de `L`. On n'utilisera pas de tranches : pourquoi ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9a38f098",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.524475Z",
     "iopub.status.busy": "2026-10-05T13:31:24.524318Z",
     "iopub.status.idle": "2026-10-05T13:31:24.528360Z",
     "shell.execute_reply": "2026-10-05T13:31:24.527578Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def dicho_aux(L, x, g, d):\n",
    "    \"\"\"x appartient-il à L[g], ..., L[d - 1] ?\"\"\"\n",
    "    if g >= d:\n",
    "        return False\n",
    "    m = (g + d) // 2\n",
    "    if L[m] == x:\n",
    "        return True\n",
    "    elif L[m] < x:\n",
    "        return dicho_aux(L, x, m + 1, d)\n",
    "    else:\n",
    "        return dicho_aux(L, x, g, m)\n",
    "\n",
    "def dicho(L, x):\n",
    "    return dicho_aux(L, x, 0, len(L))\n",
    "\n",
    "# d - g passe à au plus ceil((d - g) / 2) à chaque appel : O(ln n) appels en O(1).\n",
    "# Avec des tranches L[m + 1:], chaque appel copierait la moitié de la liste :\n",
    "# n/2 + n/4 + ... = O(n), et on perdrait l'intérêt de la dichotomie."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cf01d896",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.530112Z",
     "iopub.status.busy": "2026-10-05T13:31:24.529905Z",
     "iopub.status.idle": "2026-10-05T13:31:24.576171Z",
     "shell.execute_reply": "2026-10-05T13:31:24.575291Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True True True\n",
      "True True True True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "L = [1, 3, 3, 5, 8, 13, 21]\n",
    "print(dicho(L, 1), dicho(L, 3), dicho(L, 21), dicho(L, 8))\n",
    "print(not dicho(L, 0), not dicho(L, 4), not dicho(L, 22), not dicho([], 5))\n",
    "print(dicho(list(range(0, 10**6, 2)), 123456))\n",
    "print(not dicho(list(range(0, 10**6, 2)), 12345))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daca6234",
   "metadata": {},
   "source": [
    "**Question 6**. Écrire une fonction récursive `racine_entiere(n)` qui prend en argument un entier naturel `n` et renvoie la partie entière de $\\sqrt{n}$, par dichotomie et **sans calcul flottant**, en effectuant $O(\\ln n)$ opérations arithmétiques. Pourquoi éviter `int(n ** 0.5)` ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "98305236",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.578299Z",
     "iopub.status.busy": "2026-10-05T13:31:24.578093Z",
     "iopub.status.idle": "2026-10-05T13:31:24.582267Z",
     "shell.execute_reply": "2026-10-05T13:31:24.581304Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def racine_aux(n, g, d):\n",
    "    \"\"\"Partie entière de la racine de n, sachant que g * g <= n < d * d.\"\"\"\n",
    "    if d - g == 1:\n",
    "        return g\n",
    "    m = (g + d) // 2               # g < m < d\n",
    "    if m * m <= n:\n",
    "        return racine_aux(n, m, d)\n",
    "    else:\n",
    "        return racine_aux(n, g, m)\n",
    "\n",
    "def racine_entiere(n):\n",
    "    return racine_aux(n, 0, n + 1)   # 0 <= n < (n + 1)^2\n",
    "\n",
    "# Variant : d - g, entier positif qui décroît strictement (g < m < d),\n",
    "# et qui passe à au plus ceil((d - g) / 2) à chaque appel : O(ln n) appels."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c7a9613",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* Les flottants n'ont que 53 bits de mantisse : pour de grands entiers, `n ** 0.5` est arrondi et `int(n ** 0.5)` peut être faux. Par exemple, pour $n = 10^{30} - 1$, on obtient $10^{15}$ au lieu de $10^{15} - 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f8b45c9d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.584411Z",
     "iopub.status.busy": "2026-10-05T13:31:24.584152Z",
     "iopub.status.idle": "2026-10-05T13:31:24.588761Z",
     "shell.execute_reply": "2026-10-05T13:31:24.588022Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print([racine_entiere(n) for n in range(10)] == [0, 1, 1, 1, 2, 2, 2, 2, 2, 3])\n",
    "print(racine_entiere(10**30) == 10**15)\n",
    "print(racine_entiere(10**30 - 1) == 10**15 - 1)\n",
    "print(racine_entiere(2**100 + 1) == 2**50)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "417cd1a2",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 3. Multiplication rapide de polynômes\n",
    "\n",
    "Un polynôme $P = a_0 + a_1 X + \\dots + a_{n-1} X^{n-1}$ est représenté par le **tableau numpy** `np.array([a0, a1, ..., a(n-1)])` de ses $n$ coefficients, du degré 0 au degré $n - 1$. Le produit d'un polynôme à $n$ coefficients par un polynôme à $p$ coefficients en a $n + p - 1$.\n",
    "\n",
    "Rappels sur numpy (module importé au début du notebook sous le nom `np`) :\n",
    "\n",
    "- `np.zeros(n)` crée un tableau de $n$ zéros,\n",
    "- pour deux tableaux `P` et `Q` de même longueur, `P + Q` et `P - Q` calculent la somme et la différence **coefficient par coefficient**, en $O(n)$,\n",
    "- la tranche `P[i:j]` est une **vue** sur les éléments `P[i]`, …, `P[j - 1]` : elle ne recopie rien et se crée en $O(1)$, mais modifier la vue modifie aussi `P`,\n",
    "- `R[i:j] += S` ajoute le tableau `S` (de longueur `j - i`) aux éléments `R[i]`, …, `R[j - 1]`,\n",
    "- `A == B` compare deux tableaux coefficient par coefficient et renvoie un tableau de booléens : pour savoir si deux tableaux sont égaux, on utilise `np.array_equal(A, B)`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d100bcd",
   "metadata": {},
   "source": [
    "**Question 7**. Écrire une fonction `produit_naif(P, Q)` qui prend en arguments deux polynômes `P` et `Q` de longueurs quelconques et renvoie leur produit, calculé avec deux boucles imbriquées. Quelle est sa complexité ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "9d8e8d55",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.590570Z",
     "iopub.status.busy": "2026-10-05T13:31:24.590364Z",
     "iopub.status.idle": "2026-10-05T13:31:24.594502Z",
     "shell.execute_reply": "2026-10-05T13:31:24.593671Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def produit_naif(P, Q):\n",
    "    R = np.zeros(len(P) + len(Q) - 1)\n",
    "    for i in range(len(P)):\n",
    "        for j in range(len(Q)):\n",
    "            R[i + j] = R[i + j] + P[i] * Q[j]\n",
    "    return R\n",
    "\n",
    "# len(P) * len(Q) multiplications et additions : O(n^2) pour deux\n",
    "# polynômes à n coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6c7702c5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.596492Z",
     "iopub.status.busy": "2026-10-05T13:31:24.596300Z",
     "iopub.status.idle": "2026-10-05T13:31:24.600930Z",
     "shell.execute_reply": "2026-10-05T13:31:24.600274Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "un, a, b = np.array([1, 1]), np.array([1, 2, 3]), np.array([4, 5])\n",
    "print(np.array_equal(produit_naif(un, un), [1, 2, 1]))\n",
    "print(np.array_equal(produit_naif(a, b), [4, 13, 22, 15]))\n",
    "print(np.array_equal(produit_naif(np.array([2]), np.array([3, 1])), [6, 2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad2c665b",
   "metadata": {},
   "source": [
    "Pour « diviser pour régner », on coupe un polynôme à $n$ coefficients en deux moitiés : $P = P_1 + X^m P_2$ avec $m = n / 2$, où $P_1$ est formé des $m$ premiers coefficients (`P[:m]`) et $P_2$ des suivants (`P[m:]`). Pour que les moitiés aient toujours la même longueur, on se ramène à deux polynômes de **même longueur $n$, puissance de 2**, en les complétant par des coefficients nuls avec la fonction fournie ci-dessous : le produit est inchangé, à des coefficients nuls près à la fin, qu'on ne cherchera pas à enlever. Le produit a alors $2n - 1$ coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a21ad052",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.602972Z",
     "iopub.status.busy": "2026-10-05T13:31:24.602715Z",
     "iopub.status.idle": "2026-10-05T13:31:24.607135Z",
     "shell.execute_reply": "2026-10-05T13:31:24.606447Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([1., 2., 3., 0.]), array([4., 5., 0., 0.]))\n"
     ]
    }
   ],
   "source": [
    "def completer(P, Q):\n",
    "    \"\"\"Complète P et Q par des zéros jusqu'à une même longueur 2^k.\"\"\"\n",
    "    N = 1\n",
    "    while N < len(P) or N < len(Q):\n",
    "        N = 2 * N\n",
    "    P2 = np.zeros(N)\n",
    "    P2[:len(P)] = P\n",
    "    Q2 = np.zeros(N)\n",
    "    Q2[:len(Q)] = Q\n",
    "    return (P2, Q2)\n",
    "\n",
    "print(completer(np.array([1, 2, 3]), np.array([4, 5])))"
   ]
  },
  {
   "attachments": {
    "fig_dpr.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "47d70f09",
   "metadata": {},
   "source": [
    "En écrivant $P = P_1 + X^m P_2$ et $Q = Q_1 + X^m Q_2$, on a $PQ = P_1 Q_1 + X^m (P_1 Q_2 + P_2 Q_1) + X^{2m} P_2 Q_2$ : quatre produits de polynômes de longueur $n/2$ (donc à $n - 1$ coefficients), ajoutés dans le résultat à partir des indices $0$, $m$ et $2m = n$.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_dpr.png)\n",
    "\n",
    "</div>\n",
    "**Question 8**. Écrire une fonction récursive `produit_dpr(P, Q)` qui prend en arguments deux polynômes de même longueur $n$, puissance de 2, et renvoie leur produit (à $2n - 1$ coefficients), en effectuant **quatre** appels récursifs sur des polynômes de longueur $n/2$. Établir une relation de récurrence sur sa complexité $C(n)$, et la résoudre. Qu'a-t-on gagné par rapport à `produit_naif` ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "28e72621",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.609452Z",
     "iopub.status.busy": "2026-10-05T13:31:24.609185Z",
     "iopub.status.idle": "2026-10-05T13:31:24.612720Z",
     "shell.execute_reply": "2026-10-05T13:31:24.612110Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def produit_dpr(P, Q):\n",
    "    n = len(P)\n",
    "    if n == 1:\n",
    "        return P * Q                  # tableau à un coefficient\n",
    "    m = n // 2\n",
    "    P1, P2, Q1, Q2 = P[:m], P[m:], Q[:m], Q[m:]     # vues : O(1)\n",
    "    R = np.zeros(2 * n - 1)\n",
    "    R[0:n - 1] += produit_dpr(P1, Q1)\n",
    "    R[m:m + n - 1] += produit_dpr(P1, Q2) + produit_dpr(P2, Q1)\n",
    "    R[n:2 * n - 1] += produit_dpr(P2, Q2)\n",
    "    return R"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abfeefea",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* Hors appels récursifs, on crée `R` et l'on fait des additions de tableaux de longueur $O(n)$ : $C(n) = 4C(n/2) + O(n)$ (les tranches, qui sont des vues, ne coûtent que $O(1)$). C'est le cas $a = 4 > b = 2$ du rappel : $C(n) = O(n^{\\log_2 4}) = O(n^2)$. Sur l'arbre des appels, le niveau $j$ compte $4^j$ appels de taille $n / 2^j$ et coûte $O(4^j \\cdot n/2^j) = O(2^j n)$ ; la somme est dominée par le dernier niveau ($j = \\log_2 n$), formé de $n^2$ multiplications de coefficients. On n'a **rien gagné** : diviser pour régner ne suffit pas, il faut faire moins de sous-problèmes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4ebee1b2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.614844Z",
     "iopub.status.busy": "2026-10-05T13:31:24.614620Z",
     "iopub.status.idle": "2026-10-05T13:31:24.673039Z",
     "shell.execute_reply": "2026-10-05T13:31:24.672052Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "a, b = np.array([1, 2]), np.array([3, 4])\n",
    "print(np.array_equal(produit_dpr(a, b), [3, 10, 8]))\n",
    "for n in [1, 2, 4, 8, 16, 64]:\n",
    "    P = np.random.randint(-9, 10, n)\n",
    "    Q = np.random.randint(-9, 10, n)\n",
    "    print(np.array_equal(produit_dpr(P, Q), produit_naif(P, Q)))\n",
    "P, Q = completer(np.array([1, 1, 1]), np.array([1, -1]))\n",
    "print(np.array_equal(produit_dpr(P, Q), [1, 0, 0, -1, 0, 0, 0]))"
   ]
  },
  {
   "attachments": {
    "fig_karatsuba.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "d2f551df",
   "metadata": {},
   "source": [
    "*Karatsuba (1960).* On pose $A = P_1 Q_1$ et $B = P_2 Q_2$. Comme $(P_1 + P_2)(Q_1 + Q_2) = A + P_1 Q_2 + P_2 Q_1 + B$, le terme du milieu s'obtient par $P_1 Q_2 + P_2 Q_1 = (P_1 + P_2)(Q_1 + Q_2) - A - B$ : **trois** produits de polynômes de longueur $n/2$ suffisent.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_karatsuba.png)\n",
    "\n",
    "</div>\n",
    "**Question 9**. Écrire une fonction récursive `karatsuba(P, Q)` qui prend en arguments deux polynômes de même longueur $n$, puissance de 2, et renvoie leur produit, en n'effectuant que **trois** appels récursifs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "03d5dc76",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.675738Z",
     "iopub.status.busy": "2026-10-05T13:31:24.675421Z",
     "iopub.status.idle": "2026-10-05T13:31:24.680651Z",
     "shell.execute_reply": "2026-10-05T13:31:24.679734Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def karatsuba(P, Q):\n",
    "    n = len(P)\n",
    "    if n == 1:\n",
    "        return P * Q\n",
    "    m = n // 2\n",
    "    P1, P2, Q1, Q2 = P[:m], P[m:], Q[:m], Q[m:]\n",
    "    A = karatsuba(P1, Q1)\n",
    "    B = karatsuba(P2, Q2)\n",
    "    S = karatsuba(P1 + P2, Q1 + Q2)       # trois appels seulement\n",
    "    R = np.zeros(2 * n - 1)\n",
    "    R[0:n - 1] += A\n",
    "    R[m:m + n - 1] += S - A - B           # P1 Q2 + P2 Q1\n",
    "    R[n:2 * n - 1] += B\n",
    "    return R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "dc828875",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.683572Z",
     "iopub.status.busy": "2026-10-05T13:31:24.683280Z",
     "iopub.status.idle": "2026-10-05T13:31:24.768009Z",
     "shell.execute_reply": "2026-10-05T13:31:24.767198Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "a, b = np.array([1, 2]), np.array([3, 4])\n",
    "print(np.array_equal(karatsuba(a, b), [3, 10, 8]))\n",
    "for n in [1, 2, 4, 8, 16, 64, 256]:\n",
    "    P = np.random.randint(-9, 10, n)\n",
    "    Q = np.random.randint(-9, 10, n)\n",
    "    print(np.array_equal(karatsuba(P, Q), produit_naif(P, Q)))\n",
    "P, Q = completer(np.array([1, 1, 1]), np.array([1, -1]))\n",
    "print(np.array_equal(karatsuba(P, Q), [1, 0, 0, -1, 0, 0, 0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "274699b4",
   "metadata": {},
   "source": [
    "**Question 10**.\n",
    "\n",
    "1. Établir une relation de récurrence sur la complexité $C(n)$ de `karatsuba`, et la résoudre.\n",
    "2. Si l'on ne compte que les **multiplications** de coefficients, combien `karatsuba` en effectue-t-elle pour $n = 2^k$ ? Le fait de compter aussi les additions change-t-il l'ordre de grandeur ?\n",
    "3. Exécuter la cellule suivante, qui trace les temps de calcul des trois fonctions pour $n = 2^k$ (environ 20 secondes), et commenter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "bd246a42",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.769960Z",
     "iopub.status.busy": "2026-10-05T13:31:24.769787Z",
     "iopub.status.idle": "2026-10-05T13:31:45.917995Z",
     "shell.execute_reply": "2026-10-05T13:31:45.917155Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def aleatoire_paire(n):\n",
    "    \"\"\"Deux polynômes aléatoires à n coefficients entre 0 et 9.\"\"\"\n",
    "    return (np.random.randint(0, 10, n), np.random.randint(0, 10, n))\n",
    "def naif(PQ):\n",
    "    return produit_naif(PQ[0], PQ[1])\n",
    "def dpr(PQ):\n",
    "    return produit_dpr(PQ[0], PQ[1])\n",
    "def kara(PQ):\n",
    "    return karatsuba(PQ[0], PQ[1])\n",
    "tracer_temps({\"produit_naif\": naif, \"produit_dpr\": dpr, \"karatsuba\": kara},\n",
    "             [2 ** k for k in range(4, 12)], aleatoire_paire)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5f73052",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.*\n",
    "\n",
    "1. Hors appels récursifs, les additions et différences de tableaux et la création de `R` coûtent $O(n)$ : $C(n) = 3C(n/2) + O(n)$. C'est le cas $a = 3 > b = 2$ du rappel : $C(n) = O(n^{\\log_2 3}) \\approx O(n^{1{,}59})$, au lieu de $O(n^2)$.\n",
    "2. Le nombre $M(n)$ de multiplications vérifie $M(1) = 1$ et $M(n) = 3M(n/2)$, donc $M(2^k) = 3^k = n^{\\log_2 3}$ : 59 049 multiplications au lieu de 1 048 576 pour $n = 1024$. Compter les autres opérations ne change pas l'ordre de grandeur : le niveau $j$ de l'arbre des appels compte $3^j$ appels de taille $n / 2^j$, et y coûte $O\\big(3^j \\cdot \\frac{n}{2^j}\\big) = O\\big(n (3/2)^j\\big)$ hors appels récursifs. Ces coûts croissent géométriquement avec $j$ (car $a = 3 > b = 2$), et leur somme est dominée par le dernier niveau, formé des $3^k$ multiplications : $O\\big(n (3/2)^{\\log_2 n}\\big) = O\\big(3^{\\log_2 n}\\big) = O(n^{\\log_2 3})$. Pour le tri fusion, au contraire ($a = b = 2$), tous les niveaux coûtent autant, d'où le facteur $\\ln n$.\n",
    "3. `karatsuba` devient plus rapide que `produit_naif` à partir de quelques centaines de coefficients (0,8 s contre 1,5 s pour $n = 2048$), et l'écart se creuse : en échelle logarithmique, les pentes valent $1{,}59$ et $2$. `produit_dpr` est de loin la plus lente (12 s pour $n = 2048$) : elle a la même complexité que `produit_naif`, avec le coût des appels et des tableaux en plus. En pratique, on arrête la récursion dès que $n$ est petit (par exemple $n \\le 32$) et l'on utilise alors un produit naïf.\n",
    "\n",
    "*Pour aller plus loin.* Un entier écrit en base 10 est la valeur en $X = 10$ du polynôme de ses chiffres : multiplier deux entiers, c'est multiplier deux polynômes, puis propager les retenues. Python utilise d'ailleurs Karatsuba pour multiplier les très grands entiers. La même idée appliquée aux matrices par blocs donne l'algorithme de Strassen (1969) : 7 produits de blocs au lieu de 8, d'où $O(n^{\\log_2 7}) \\approx O(n^{2{,}81})$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2b403d0",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 4. Triangle de Pascal modulo 2\n",
    "\n",
    "On s'intéresse à la parité des coefficients binomiaux $\\binom{n}{j}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76aeba72",
   "metadata": {},
   "source": [
    "**Question 11**. Écrire une fonction récursive `pascal_mod2(n)` qui prend en argument un entier naturel `n` et renvoie la liste des $n$ premières lignes du triangle de Pascal **modulo 2**, c'est-à-dire la liste de listes `[[1], [1, 1], [1, 0, 1], [1, 1, 1, 1], [1, 0, 0, 0, 1], ...]` : la ligne $i$ est la liste $\\left[\\binom{i}{0} \\% 2, \\dots, \\binom{i}{i} \\% 2\\right]$. Quelle est sa complexité ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "bc53983b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:45.920777Z",
     "iopub.status.busy": "2026-10-05T13:31:45.920597Z",
     "iopub.status.idle": "2026-10-05T13:31:45.924686Z",
     "shell.execute_reply": "2026-10-05T13:31:45.924070Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def ligne_suivante(L):\n",
    "    # Formule de Pascal, calculée modulo 2\n",
    "    return [1] + [(L[j] + L[j + 1]) % 2 for j in range(len(L) - 1)] + [1]\n",
    "\n",
    "def pascal_mod2(n):\n",
    "    if n == 0:\n",
    "        return []\n",
    "    elif n == 1:\n",
    "        return [[1]]\n",
    "    else:\n",
    "        lignes = pascal_mod2(n - 1)   # liste neuve : on peut la modifier\n",
    "        lignes.append(ligne_suivante(lignes[n - 2]))\n",
    "        return lignes\n",
    "\n",
    "# C(n) = C(n - 1) + O(n), d'où C(n) = O(n^2) : c'est la taille du résultat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "ff31a14c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:45.926912Z",
     "iopub.status.busy": "2026-10-05T13:31:45.926765Z",
     "iopub.status.idle": "2026-10-05T13:31:45.930382Z",
     "shell.execute_reply": "2026-10-05T13:31:45.929660Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(pascal_mod2(0) == [], pascal_mod2(1) == [[1]])\n",
    "print(pascal_mod2(5) == [[1], [1, 1], [1, 0, 1], [1, 1, 1, 1], [1, 0, 0, 0, 1]])\n",
    "print(pascal_mod2(20)[19]\n",
    "      == [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d89f83fa",
   "metadata": {},
   "source": [
    "**Question 12**. Écrire une fonction `afficher_pascal(n)` qui prend en argument un entier $n \\geq 1$ et **affiche** avec `print` les lignes $0$ à $n - 1$ du triangle de Pascal modulo 2, en représentant chaque coefficient impair par `▲` et chaque coefficient pair par une espace, les caractères d'une ligne étant séparés par une espace et la ligne $i$ étant précédée de $n - 1 - i$ espaces. Par exemple, `afficher_pascal(4)` affiche :\n",
    "\n",
    "```\n",
    "   ▲\n",
    "  ▲ ▲\n",
    " ▲   ▲\n",
    "▲ ▲ ▲ ▲\n",
    "```\n",
    "\n",
    "Afficher le triangle pour $n = 32$. Que remarque-t-on ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "59716255",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:45.932350Z",
     "iopub.status.busy": "2026-10-05T13:31:45.932186Z",
     "iopub.status.idle": "2026-10-05T13:31:45.937061Z",
     "shell.execute_reply": "2026-10-05T13:31:45.936260Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                               ▲\n",
      "                              ▲ ▲\n",
      "                             ▲   ▲\n",
      "                            ▲ ▲ ▲ ▲\n",
      "                           ▲       ▲\n",
      "                          ▲ ▲     ▲ ▲\n",
      "                         ▲   ▲   ▲   ▲\n",
      "                        ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲\n",
      "                       ▲               ▲\n",
      "                      ▲ ▲             ▲ ▲\n",
      "                     ▲   ▲           ▲   ▲\n",
      "                    ▲ ▲ ▲ ▲         ▲ ▲ ▲ ▲\n",
      "                   ▲       ▲       ▲       ▲\n",
      "                  ▲ ▲     ▲ ▲     ▲ ▲     ▲ ▲\n",
      "                 ▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲\n",
      "                ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲\n",
      "               ▲                               ▲\n",
      "              ▲ ▲                             ▲ ▲\n",
      "             ▲   ▲                           ▲   ▲\n",
      "            ▲ ▲ ▲ ▲                         ▲ ▲ ▲ ▲\n",
      "           ▲       ▲                       ▲       ▲\n",
      "          ▲ ▲     ▲ ▲                     ▲ ▲     ▲ ▲\n",
      "         ▲   ▲   ▲   ▲                   ▲   ▲   ▲   ▲\n",
      "        ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲                 ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲\n",
      "       ▲               ▲               ▲               ▲\n",
      "      ▲ ▲             ▲ ▲             ▲ ▲             ▲ ▲\n",
      "     ▲   ▲           ▲   ▲           ▲   ▲           ▲   ▲\n",
      "    ▲ ▲ ▲ ▲         ▲ ▲ ▲ ▲         ▲ ▲ ▲ ▲         ▲ ▲ ▲ ▲\n",
      "   ▲       ▲       ▲       ▲       ▲       ▲       ▲       ▲\n",
      "  ▲ ▲     ▲ ▲     ▲ ▲     ▲ ▲     ▲ ▲     ▲ ▲     ▲ ▲     ▲ ▲\n",
      " ▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲   ▲\n",
      "▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲\n"
     ]
    }
   ],
   "source": [
    "def motif(L, j):\n",
    "    \"\"\"Chaîne représentant L[j], ..., L[len(L) - 1], séparés par des espaces.\"\"\"\n",
    "    if L[j] == 1:\n",
    "        c = \"▲\"\n",
    "    else:\n",
    "        c = \" \"\n",
    "    if j == len(L) - 1:\n",
    "        return c\n",
    "    else:\n",
    "        return c + \" \" + motif(L, j + 1)\n",
    "\n",
    "def afficher_lignes(lignes, n, i):\n",
    "    \"\"\"Affiche les lignes i à n - 1 du triangle.\"\"\"\n",
    "    if i < n:\n",
    "        print(\" \" * (n - 1 - i) + motif(lignes[i], 0))\n",
    "        afficher_lignes(lignes, n, i + 1)\n",
    "\n",
    "def afficher_pascal(n):\n",
    "    afficher_lignes(pascal_mod2(n), n, 0)\n",
    "\n",
    "afficher_pascal(32)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d70323c7",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* On voit apparaître le **triangle de Sierpiński** : les lignes $0$ à $2^{k+1} - 1$ sont formées d'une copie des lignes $0$ à $2^k - 1$, au-dessus de deux copies côte à côte. Explication : dans $(\\mathbb{Z}/2\\mathbb{Z})[X]$, $(1+X)^2 = 1 + 2X + X^2 = 1 + X^2$, et par récurrence $(1+X)^{2^k} = 1 + X^{2^k}$. Pour $0 \\le i < 2^k$, on a donc $(1+X)^{2^k + i} = (1+X)^i + X^{2^k}(1+X)^i$, où le premier terme est de degré $i < 2^k$ : les deux termes ne se chevauchent pas. La ligne $2^k + i$ modulo 2 est formée de la ligne $i$, de $2^k - 1 - i$ zéros, puis de nouveau de la ligne $i$."
   ]
  },
  {
   "attachments": {
    "fig_triominos_16.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "84c2e600",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 5. Pavage par des triominos (bonus)\n",
    "\n",
    "Un **triomino** est une pièce en forme de L formée de trois cases. On veut paver par des triominos un échiquier $2^n \\times 2^n$ privé d'une case quelconque. Voici par exemple un pavage d'un échiquier $16 \\times 16$ privé d'une case (en noir).\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_triominos_16.png)\n",
    "\n",
    "</div>"
   ]
  },
  {
   "attachments": {
    "fig_triominos.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "c97d3c31",
   "metadata": {},
   "source": [
    "**Question 13**. Montrer par récurrence sur $n$ qu'un tel pavage existe toujours, quelle que soit la case retirée. Combien de triominos utilise-t-il ?\n",
    "\n",
    "*Indication* : on pourra regarder le schéma suivant.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_triominos.png)\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "627062da",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* Pour $n = 0$, l'échiquier privé de sa seule case est vide. Pour $n \\geq 1$, on découpe l'échiquier en quatre quarts $2^{n-1} \\times 2^{n-1}$, la case retirée est dans l'un d'eux. On pose un triomino sur les trois cases centrales qui appartiennent aux trois **autres** quarts (figure). Chaque quart est alors un échiquier $2^{n-1} \\times 2^{n-1}$ privé d'une case, que l'on pave par hypothèse de récurrence. Le pavage couvre $4^n - 1$ cases, donc il utilise $\\frac{4^n - 1}{3}$ triominos (et $4^n - 1$ est bien divisible par 3, car $4 \\equiv 1 \\pmod 3$). La preuve est un algorithme récursif."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "795cc85e",
   "metadata": {},
   "source": [
    "**Question 14**. Écrire une fonction `pavage(n, i, j)` qui prend en arguments un entier naturel `n` et les coordonnées `(i, j)` d'une case, et renvoie un pavage de l'échiquier $2^n \\times 2^n$ privé de la case $(i, j)$, sous forme d'une liste de listes `G` : `G[i][j]` vaut $-1$, et chaque autre case contient le numéro (à partir de 1) du triomino qui la couvre. Quelle est sa complexité ?\n",
    "\n",
    "*Indication* : on pourra écrire une fonction récursive auxiliaire `pavage_aux(G, x, y, t, ti, tj, num)` qui pave le carré de coin supérieur gauche $(x, y)$ (ligne $x$, colonne $y$) et de côté $t$ privé de la case $(t_i, t_j)$ (déjà couverte, et repérée par ses coordonnées dans la grille `G` entière), en numérotant les triominos à partir de `num`, et qui renvoie le premier numéro non utilisé."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "7f572962",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:45.939530Z",
     "iopub.status.busy": "2026-10-05T13:31:45.939152Z",
     "iopub.status.idle": "2026-10-05T13:31:45.945095Z",
     "shell.execute_reply": "2026-10-05T13:31:45.944198Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def pavage_aux(G, x, y, t, ti, tj, num):\n",
    "    if t == 1:\n",
    "        return num          # la seule case est déjà couverte\n",
    "    m = t // 2\n",
    "    coins = [(x, y), (x, y + m), (x + m, y), (x + m, y + m)]\n",
    "    centres = [(x + m - 1, y + m - 1), (x + m - 1, y + m),\n",
    "               (x + m, y + m - 1), (x + m, y + m)]\n",
    "    # numéro du quart contenant la case déjà couverte\n",
    "    k = 0\n",
    "    if ti >= x + m:\n",
    "        k = k + 2\n",
    "    if tj >= y + m:\n",
    "        k = k + 1\n",
    "    trous = []\n",
    "    for q in range(4):\n",
    "        if q == k:\n",
    "            trous.append((ti, tj))\n",
    "        else:                           # le triomino central couvre ce centre\n",
    "            G[centres[q][0]][centres[q][1]] = num\n",
    "            trous.append(centres[q])\n",
    "    num = num + 1\n",
    "    for q in range(4):\n",
    "        (a, b), (u, v) = coins[q], trous[q]\n",
    "        num = pavage_aux(G, a, b, m, u, v, num)\n",
    "    return num\n",
    "\n",
    "def pavage(n, i, j):\n",
    "    t = 2 ** n\n",
    "    G = [[0 for b in range(t)] for a in range(t)]\n",
    "    G[i][j] = -1\n",
    "    pavage_aux(G, 0, 0, t, i, j, 1)\n",
    "    return G\n",
    "\n",
    "# C(t) = 4 C(t / 2) + O(1) : C(t) = O(t^2), linéaire en le nombre de cases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "60049ed4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:45.947241Z",
     "iopub.status.busy": "2026-10-05T13:31:45.947051Z",
     "iopub.status.idle": "2026-10-05T13:31:45.962049Z",
     "shell.execute_reply": "2026-10-05T13:31:45.961087Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "def est_pavage(G, i, j):\n",
    "    t = len(G)\n",
    "    cases = {}\n",
    "    for x in range(t):\n",
    "        for y in range(t):\n",
    "            cases.setdefault(G[x][y], []).append((x, y))\n",
    "    if cases.get(-1) != [(i, j)]:\n",
    "        return False\n",
    "    for v, L in cases.items():\n",
    "        if v != -1:\n",
    "            xs, ys = [x for x, y in L], [y for x, y in L]\n",
    "            if len(L) != 3 or max(xs) - min(xs) != 1 or max(ys) - min(ys) != 1:\n",
    "                return False\n",
    "    return len(cases) - 1 == (t * t - 1) // 3\n",
    "print(pavage(0, 0, 0) == [[-1]], est_pavage(pavage(1, 0, 1), 0, 1))\n",
    "print(all(est_pavage(pavage(3, i, j), i, j)\n",
    "          for i in range(8) for j in range(8)))\n",
    "print(est_pavage(pavage(6, 37, 12), 37, 12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "6864daa1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:45.964260Z",
     "iopub.status.busy": "2026-10-05T13:31:45.964075Z",
     "iopub.status.idle": "2026-10-05T13:31:47.418560Z",
     "shell.execute_reply": "2026-10-05T13:31:47.417513Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 380x380 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualisation : titre vert si le résultat est correct, rouge sinon.\n",
    "dessiner_triominos(pavage(3, 1, 6))\n",
    "dessiner_triominos(pavage(5, 20, 9))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6285fead",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 6. Tri rapide, sélection et médiane en temps linéaire\n",
    "\n",
    "Dans cette partie, on s'autorise des boucles `for` dans la fonction `partition` et dans le calcul des médianes des blocs."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abb869f4",
   "metadata": {},
   "source": [
    "**Question 15**. Écrire une fonction `partition(L, p)` qui prend en arguments une liste `L` et une valeur `p`, et renvoie le triplet `(Li, Le, Ls)` des listes des éléments de `L` respectivement strictement inférieurs, égaux et strictement supérieurs à `p`, dans l'ordre où ils apparaissent dans `L`, en $O(n)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "0f39b4ea",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:47.420899Z",
     "iopub.status.busy": "2026-10-05T13:31:47.420739Z",
     "iopub.status.idle": "2026-10-05T13:31:47.424551Z",
     "shell.execute_reply": "2026-10-05T13:31:47.423621Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def partition(L, p):\n",
    "    Li, Le, Ls = [], [], []\n",
    "    for x in L:\n",
    "        if x < p:\n",
    "            Li.append(x)\n",
    "        elif x == p:\n",
    "            Le.append(x)\n",
    "        else:\n",
    "            Ls.append(x)\n",
    "    return Li, Le, Ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "24649f6a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:47.426666Z",
     "iopub.status.busy": "2026-10-05T13:31:47.426446Z",
     "iopub.status.idle": "2026-10-05T13:31:47.430430Z",
     "shell.execute_reply": "2026-10-05T13:31:47.429575Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(partition([4, 3, 2, 1, 5], 3) == ([2, 1], [3], [4, 5]))\n",
    "print(partition([4, 3, 2, 1, 5], 6) == ([4, 3, 2, 1, 5], [], []))\n",
    "print(partition([2, 7, 2, 1, 2], 2) == ([1], [2, 2, 2], [7]))\n",
    "print(partition([], 0) == ([], [], []))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b0ef446",
   "metadata": {},
   "source": [
    "**Question 16**. Le **tri rapide** d'une liste `L` de longueur au moins 2 choisit un **pivot** `p` (ici le premier élément de `L`), partitionne `L` autour de `p`, trie récursivement `Li` et `Ls`, puis renvoie leur concaténation avec `Le` intercalée.\n",
    "\n",
    "1. Écrire une fonction récursive `tri_rapide(L)` qui prend en argument une liste `L` et renvoie une **nouvelle** liste, triée, formée des éléments de `L`. Justifier sa terminaison.\n",
    "2. Montrer que sa complexité est $O(n^2)$, et donner une liste pour laquelle elle est effectivement de l'ordre de $n^2$. Quelle est la profondeur de récursion de `tri_rapide(list(range(n)))` ? Que se passe-t-il quand $n$ dépasse la limite de récursion ?\n",
    "3. Quelle serait sa complexité si le pivot était toujours une médiane de la liste, calculée en $O(n)$ ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "aad54456",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:47.432812Z",
     "iopub.status.busy": "2026-10-05T13:31:47.432642Z",
     "iopub.status.idle": "2026-10-05T13:31:47.436002Z",
     "shell.execute_reply": "2026-10-05T13:31:47.435169Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def tri_rapide(L):\n",
    "    if len(L) <= 1:\n",
    "        return L.copy()     # nouvelle liste, pas L elle-même\n",
    "    else:\n",
    "        Li, Le, Ls = partition(L, L[0])\n",
    "        return tri_rapide(Li) + Le + tri_rapide(Ls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "2b6af1de",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:47.437764Z",
     "iopub.status.busy": "2026-10-05T13:31:47.437609Z",
     "iopub.status.idle": "2026-10-05T13:31:47.453967Z",
     "shell.execute_reply": "2026-10-05T13:31:47.453173Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(tri_rapide([]) == [])\n",
    "print(tri_rapide([3]) == [3])\n",
    "print(tri_rapide([3, 1, 2]) == [1, 2, 3])\n",
    "L = [5, 3, 8, 3, 1, 9, 2, 8, 8, 0]\n",
    "print(tri_rapide(L) == [0, 1, 2, 3, 3, 5, 8, 8, 8, 9])\n",
    "print(L == [5, 3, 8, 3, 1, 9, 2, 8, 8, 0])     # L n'est pas modifiée\n",
    "from random import randint\n",
    "R = [randint(0, 1000) for i in range(10**4)]\n",
    "print(tri_rapide(R) == sorted(R))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b159886b",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.*\n",
    "\n",
    "1. Le pivot appartient à `L`, donc `Le` n'est pas vide : `Li` et `Ls` sont strictement plus courtes que `L`, et la longueur est un variant.\n",
    "2. Partitionner et concaténer coûte $O(n)$, et `Li`, `Ls` sont de longueurs $k$ et $\\ell$ avec $k + \\ell \\le n - 1$. En notant $C(n)$ le coût maximal pour une liste de longueur au plus $n$, on obtient par récurrence $C(n) \\le \\beta(n + (n-1) + \\dots + 1) = O(n^2)$, où $\\beta$ est une constante : chaque niveau de l'arbre des appels coûte $O(n)$, et il y a au plus $n$ niveaux. Pour une liste **triée sans doublons**, `Li` est toujours vide et `Ls` de longueur $n - 1$ : le coût est $\\beta(n + (n - 1) + \\dots + 1)$, de l'ordre de $n^2$. Pour `list(range(n))`, la profondeur de récursion est $n$ : au-delà de la limite (ici $10^4$), on obtient une `RecursionError`, après un calcul déjà quadratique.\n",
    "3. On aurait, pour une constante $\\alpha$, $C(n) \\le 2C(\\lfloor n/2 \\rfloor) + \\alpha n$, d'où $C(n) = O(n \\ln n)$ (comme le tri fusion)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81eaac81",
   "metadata": {},
   "source": [
    "**Question 17**. Pour $0 \\le k < n$, le **$k$-ième plus petit élément** de `L` est l'élément d'indice $k$ de la liste `L` triée. Pour $k = \\lfloor n/2 \\rfloor$, c'est la **médiane** de `L`. Écrire une fonction récursive `selection(L, k)` qui prend en arguments une liste `L` de longueur $n$ et un entier $k \\in [\\![0, n[\\![$, et renvoie le $k$-ième plus petit élément de `L`. Elle procédera comme le tri rapide (pivot `L[0]`), mais avec **un seul** appel récursif. Quelle est sa complexité dans le pire cas ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "2266da39",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:47.455758Z",
     "iopub.status.busy": "2026-10-05T13:31:47.455596Z",
     "iopub.status.idle": "2026-10-05T13:31:47.459353Z",
     "shell.execute_reply": "2026-10-05T13:31:47.458512Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def selection(L, k):\n",
    "    Li, Le, Ls = partition(L, L[0])\n",
    "    if k < len(Li):\n",
    "        return selection(Li, k)\n",
    "    elif k < len(Li) + len(Le):\n",
    "        return L[0]\n",
    "    else:\n",
    "        return selection(Ls, k - len(Li) - len(Le))\n",
    "\n",
    "# Pire cas (liste triée sans doublons, k = n - 1) : n + (n - 1) + ... = O(n^2),\n",
    "# et une profondeur de récursion n. En moyenne sur les permutations,\n",
    "# on peut montrer que la complexité est O(n), mais ce n'est pas garanti."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "f05f460e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:47.461167Z",
     "iopub.status.busy": "2026-10-05T13:31:47.460987Z",
     "iopub.status.idle": "2026-10-05T13:31:47.480747Z",
     "shell.execute_reply": "2026-10-05T13:31:47.479708Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "from random import randint\n",
    "L = [5, 3, 8, 3, 1, 9, 2, 8, 8, 0]\n",
    "R = [randint(0, 1000) for i in range(10**4)]\n",
    "print([selection(L, k) for k in range(10)] == [0, 1, 2, 3, 3, 5, 8, 8, 8, 9])\n",
    "print(all(selection(R, k) == sorted(R)[k] for k in [0, 1, 5000, 9998, 9999]))"
   ]
  },
  {
   "attachments": {
    "fig_mom.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "8256dd08",
   "metadata": {},
   "source": [
    "#### Médiane en temps linéaire (bonus)\n",
    "\n",
    "**Objectif : calculer la médiane d'une liste en temps linéaire**, sans la trier. Avec `selection`, le calcul de la médiane est quadratique dans le pire cas, car le pivot `L[0]` peut être proche d'une extrémité. Il faut donc un pivot qui ne soit jamais trop proche des extrémités. L'algorithme de la **médiane des médianes** (Blum, Floyd, Pratt, Rivest et Tarjan, 1973) choisit le pivot ainsi, pour un entier $B \\geq 2$ fixé :\n",
    "\n",
    "- on découpe `L` en $\\lceil n/B \\rceil$ blocs consécutifs de $B$ éléments (le dernier pouvant être plus court),\n",
    "- on calcule la médiane de chaque bloc, en le triant,\n",
    "- le pivot est la médiane de la liste de ces médianes, calculée **récursivement** par le même algorithme.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_mom.png)\n",
    "\n",
    "</div>\n",
    "L'appel récursif sur `Li` ou `Ls` ne cherche pas une médiane : il faut savoir calculer le $k$-ième plus petit élément pour tout $k$.\n",
    "\n",
    "**Question 18**. Écrire une fonction `selection_mom(L, k, B)` qui prend en arguments une liste `L` de longueur $n$, un entier $k \\in [\\![0, n[\\![$ et un entier $B \\geq 2$, et renvoie le $k$-ième plus petit élément de `L`. Elle procédera comme `selection`, mais avec ce choix de pivot, calculé par une fonction auxiliaire `pivot_mom(L, B)` qui prend en arguments une liste `L` et l'entier $B$ et renvoie la médiane des médianes de ses blocs. Les listes d'au plus $B$ éléments seront triées directement avec `tri_rapide`. En déduire une fonction `mediane(L)` qui prend en argument une liste non vide `L` et renvoie sa médiane, avec $B = 5$. Pourquoi a-t-on autorisé une boucle pour calculer les médianes des blocs ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "e2765334",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:47.482551Z",
     "iopub.status.busy": "2026-10-05T13:31:47.482385Z",
     "iopub.status.idle": "2026-10-05T13:31:47.487094Z",
     "shell.execute_reply": "2026-10-05T13:31:47.486376Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def pivot_mom(L, B):\n",
    "    medianes = []\n",
    "    for j in range((len(L) + B - 1) // B):     # ceil(n / B) blocs\n",
    "        bloc = tri_rapide(L[B * j : B * j + B])\n",
    "        medianes.append(bloc[len(bloc) // 2])\n",
    "    return selection_mom(medianes, len(medianes) // 2, B)\n",
    "\n",
    "def selection_mom(L, k, B):\n",
    "    if len(L) <= B:\n",
    "        return tri_rapide(L)[k]\n",
    "    p = pivot_mom(L, B)\n",
    "    Li, Le, Ls = partition(L, p)\n",
    "    if k < len(Li):\n",
    "        return selection_mom(Li, k, B)\n",
    "    elif k < len(Li) + len(Le):\n",
    "        return p\n",
    "    else:\n",
    "        return selection_mom(Ls, k - len(Li) - len(Le), B)\n",
    "\n",
    "def mediane(L):\n",
    "    return selection_mom(L, len(L) // 2, 5)\n",
    "\n",
    "# Une fonction récursive parcourant les blocs aurait une profondeur n / B,\n",
    "# trop grande dès que n / B dépasse la limite de récursion.\n",
    "# Ici, la profondeur est O(ln n) pour tout B >= 2 (question suivante) :\n",
    "# list(range(10**5)) ne pose plus de problème."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "f013986f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:47.488622Z",
     "iopub.status.busy": "2026-10-05T13:31:47.488482Z",
     "iopub.status.idle": "2026-10-05T13:31:48.647341Z",
     "shell.execute_reply": "2026-10-05T13:31:48.646383Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True True\n",
      "True\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "from random import randint\n",
    "L = [5, 3, 8, 3, 1, 9, 2, 8, 8, 0]\n",
    "R = [randint(0, 1000) for i in range(10**4)]\n",
    "print(mediane(L) == 5, mediane([7]) == 7, mediane(R) == sorted(R)[5000])\n",
    "print([selection_mom(L, k, 5) for k in range(10)]\n",
    "      == [0, 1, 2, 3, 3, 5, 8, 8, 8, 9])\n",
    "print(all(selection_mom(R, k, B) == sorted(R)[k]\n",
    "          for k in [0, 1, 5000, 9998, 9999] for B in [2, 3, 5, 7, 31]))\n",
    "print(selection_mom(list(range(10**5)), 12345, 5) == 12345)\n",
    "print(selection_mom(list(range(10**5, 0, -1)), 99999, 5) == 10**5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "9cfdafb5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:48.649295Z",
     "iopub.status.busy": "2026-10-05T13:31:48.649104Z",
     "iopub.status.idle": "2026-10-05T13:31:48.823176Z",
     "shell.execute_reply": "2026-10-05T13:31:48.822045Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 505x305 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Illustration de la question suivante (pas de vérification ici).\n",
    "from random import randint\n",
    "dessiner_blocs([randint(0, 99) for i in range(45)], 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "026c5645",
   "metadata": {},
   "source": [
    "**Question 19**. On note $m$ le pivot choisi par `pivot_mom` pour une liste de longueur $n > B$.\n",
    "\n",
    "1. Montrer qu'au moins $\\lceil B/2 \\rceil \\left(\\left\\lceil \\lceil n/B \\rceil / 2 \\right\\rceil - 1\\right)$ éléments de `L` sont inférieurs ou égaux à $m$, et de même pour les éléments supérieurs ou égaux. En déduire que `Li` et `Ls` ont au plus $\\left(1 - \\frac{\\lceil B/2 \\rceil}{2B}\\right) n + \\lceil B/2 \\rceil$ éléments.\n",
    "2. On note $T(n)$ le coût maximal de `selection_mom` pour une liste de longueur au plus $n$. Justifier qu'il existe une constante $\\gamma_B > 0$ telle que, pour $n > B$,\n",
    "$$T(n) \\le T\\left(\\left\\lceil \\frac{n}{B} \\right\\rceil\\right) + T\\left(n - \\left\\lceil \\frac{B}{2} \\right\\rceil \\left(\\left\\lceil \\frac{\\lceil n/B \\rceil}{2} \\right\\rceil - 1\\right)\\right) + \\gamma_B n.$$\n",
    "3. On admet qu'on peut négliger les parties entières et les constantes additives, c'est-à-dire remplacer cette inégalité par $T(n) \\le T\\left(\\frac{n}{B}\\right) + T(\\beta_B n) + \\gamma_B n$, avec $\\beta_B = 1 - \\frac{\\lceil B/2 \\rceil}{2B}$. Montrer que si $\\frac{1}{B} + \\beta_B < 1$, alors $T(n) = O(n)$.\n",
    "4. Pour quelles valeurs de $B$ cette condition est-elle satisfaite ?\n",
    "5. Comparer les temps d'exécution de `selection` et `selection_mom` (avec $B = 5$) sur une liste aléatoire et sur `list(range(800))`, puis ceux de `selection_mom` pour différentes valeurs de $B$. Commenter. On pourra utiliser `tracer_temps`, comme pour la multiplication de polynômes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "242cd7ab",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.*\n",
    "\n",
    "1. La médiane d'un bloc trié de longueur $b$ est l'élément d'indice $\\lfloor b/2 \\rfloor$ : elle est supérieure ou égale à $\\lfloor b/2 \\rfloor + 1$ éléments du bloc et inférieure ou égale à $b - \\lfloor b/2 \\rfloor = \\lceil b/2 \\rceil$ d'entre eux, soit au moins $\\lceil B/2 \\rceil$ dans les deux cas pour un bloc complet. De même, $m$ est supérieur ou égal à au moins $\\left\\lceil \\lceil n/B \\rceil / 2 \\right\\rceil$ médianes de blocs, et inférieur ou égal à au moins $\\left\\lceil \\lceil n/B \\rceil / 2 \\right\\rceil$ d'entre elles. En écartant le dernier bloc, peut-être incomplet, au moins $\\lceil B/2 \\rceil(\\left\\lceil \\lceil n/B \\rceil / 2 \\right\\rceil - 1)$ éléments sont inférieurs ou égaux à $m$ : ils ne sont pas dans `Ls`. Comme $\\left\\lceil \\lceil n/B \\rceil / 2 \\right\\rceil \\ge \\frac{n}{2B}$, `Ls` a au plus $n - \\lceil B/2 \\rceil \\left(\\frac{n}{2B} - 1\\right) = \\beta_B n + \\lceil B/2 \\rceil$ éléments. Le raisonnement est symétrique pour `Li`.\n",
    "2. Trier les $\\lceil n/B \\rceil$ blocs coûte $O(B^2)$ par bloc, soit $O(Bn)$, et la partition coûte $O(n)$ : en tout $\\gamma_B n$. S'y ajoutent l'appel récursif sur les $\\lceil n/B \\rceil$ médianes, puis au plus un appel sur `Li` ou `Ls`, de longueur majorée au point 1.\n",
    "3. Montrons par récurrence forte que $T(n) \\le \\lambda n$, avec $\\lambda = \\max\\left(T(1), \\dots, T(B), \\frac{\\gamma_B}{1 - 1/B - \\beta_B}\\right)$. C'est vrai pour $n \\le B$, pour $n > B$,\n",
    "$$T(n) \\le \\lambda \\frac{n}{B} + \\lambda \\beta_B n + \\gamma_B n = \\left(\\left(\\tfrac{1}{B} + \\beta_B\\right)\\lambda + \\gamma_B\\right) n \\le \\lambda n,$$\n",
    "par le choix de $\\lambda$. Les deux appels portent sur des tailles de somme $\\left(\\frac{1}{B} + \\beta_B\\right) n < n$ : le coût de chaque niveau de l'arbre des appels décroît géométriquement.\n",
    "4. $\\frac{1}{B} + \\beta_B < 1 \\iff \\frac{\\lceil B/2 \\rceil}{2B} > \\frac{1}{B} \\iff \\lceil B/2 \\rceil > 2 \\iff B \\geq 5$. Pour $B = 5$, $\\frac{1}{5} + \\frac{7}{10} = \\frac{9}{10}$. Pour $B = 3$ ou $B = 4$, la somme vaut exactement 1 : chaque niveau de l'arbre des appels coûte $O(n)$, et on obtient seulement $O(n \\ln n)$. Pour $B = 2$, la somme vaut $\\frac{1}{2} + \\frac{3}{4} > 1$ : on n'obtient aucune borne linéaire.\n",
    "5. Sur une liste aléatoire, `selection` est environ 10 fois plus rapide : la constante cachée dans le $O(n)$ de `selection_mom` est grande. Sur une liste triée, `selection` est quadratique (et lève une `RecursionError` dès que $n$ dépasse la limite de récursion), alors que `selection_mom` reste linéaire. Pour $B \\geq 5$, les temps varient peu, $B = 3$ est un peu plus lent (de l'ordre de 1,5 fois), ce qui illustre le point 4. Avec $10^4$ éléments, les temps sont de l'ordre de 10 ms et donc bruités : mieux vaut mesurer sur $10^5$ éléments. En pratique, on choisit plutôt un pivot **aléatoire**, ce qui donne une complexité linéaire **en moyenne** quelle que soit la liste."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "dced3bc8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:48.825393Z",
     "iopub.status.busy": "2026-10-05T13:31:48.825216Z",
     "iopub.status.idle": "2026-10-05T13:31:49.804347Z",
     "shell.execute_reply": "2026-10-05T13:31:49.803468Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 éléments : 0.009896278381347656 s contre 0.1492297649383545 s\n",
      "800 éléments : 0.010574817657470703 s contre 0.0014204978942871094 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = 3 : 0.23727154731750488 s\n",
      "B = 5 : 0.14792156219482422 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = 7 : 0.12425017356872559 s\n",
      "B = 15 : 0.1188809871673584 s\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B = 31 : 0.12149286270141602 s\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "from random import randint\n",
    "R = [randint(0, 10**9) for i in range(10**5)]   # valeurs distinctes\n",
    "\n",
    "for liste in [R, list(range(800))]:\n",
    "    n = len(liste)\n",
    "    debut = time.time()\n",
    "    selection(liste, n // 2)\n",
    "    milieu = time.time()\n",
    "    selection_mom(liste, n // 2, 5)\n",
    "    fin = time.time()\n",
    "    print(n, \"éléments :\", milieu - debut, \"s contre\", fin - milieu, \"s\")\n",
    "\n",
    "for B in [3, 5, 7, 15, 31]:\n",
    "    debut = time.time()\n",
    "    selection_mom(R, len(R) // 2, B)\n",
    "    print(\"B =\", B, \":\", time.time() - debut, \"s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb0ec8dc",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Remarque* : pourquoi ne pas écrire une version **en place**, qui permute les éléments d'une seule liste au lieu de créer `Li`, `Le`, `Ls` et les blocs ?\n",
    "\n",
    "- La complexité temporelle est la même, $O(n)$ : créer ces listes ne coûte pas plus que les parcourir pour partitionner.\n",
    "- La mémoire supplémentaire reste $O(n)$ dans les deux cas : la version avec listes utilise $n + \\beta_B n + \\beta_B^2 n + \\dots = O(n)$, et une version en place doit d'abord **copier** `L` pour ne pas la modifier. On a mesuré un pic de mémoire de 16 Mo pour la version avec listes contre 8 Mo pour la version en place, pour $n = 10^6$.\n",
    "- En Python, la version en place est environ **5 fois plus lente** (11 s contre 2,3 s pour $n = 10^6$). Les `append` sont exécutés par l'interpréteur en C, alors que la gestion des indices et des échanges est écrite en Python.\n",
    "- Le code en place est nettement plus délicat : il faut une partition en trois zones par échanges, et ranger les médianes des blocs au début de la liste.\n",
    "\n",
    "La version **en place** prend son intérêt dans un langage compilé, ou quand la mémoire est vraiment limitée."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9674fe20",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## II. Mémoïsation\n",
    "\n",
    "**Rappel.** Quand une fonction récursive est appelée de nombreuses fois avec les mêmes arguments, on range chaque résultat calculé et on le relit au lieu de le recalculer : c'est la **mémoïsation**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ab74d18",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 7. Échange de shokobons\n",
    "\n",
    "Un professeur d'ITC propose à ses élèves l'échange suivant. Un élève qui possède un paquet de $n$ shokobons peut l'échanger contre **trois** paquets de $\\lfloor n/2 \\rfloor$, $\\lfloor n/3 \\rfloor$ et $\\lfloor n/4 \\rfloor$ shokobons, qu'il peut à leur tour échanger, ou bien garder ses $n$ shokobons. Par exemple, un paquet de 12 shokobons s'échange contre des paquets de 6, 4 et 3 shokobons, soit 13 shokobons. Le nombre maximal de shokobons qu'on peut obtenir à partir d'un paquet de $n$ shokobons vérifie\n",
    "$$f(0) = 0 \\quad \\text{et} \\quad f(n) = \\max\\big(n,\\ f(\\lfloor n/2 \\rfloor) + f(\\lfloor n/3 \\rfloor) + f(\\lfloor n/4 \\rfloor)\\big) \\text{ pour } n \\geq 1.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71c6d792",
   "metadata": {},
   "source": [
    "**Question 20**. Écrire une fonction récursive `shokobons_naif(n)` qui prend en argument un entier naturel `n` et renvoie $f(n)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "65ae195d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:49.806617Z",
     "iopub.status.busy": "2026-10-05T13:31:49.806438Z",
     "iopub.status.idle": "2026-10-05T13:31:49.810008Z",
     "shell.execute_reply": "2026-10-05T13:31:49.809389Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def shokobons_naif(n):\n",
    "    if n == 0:\n",
    "        return 0\n",
    "    echange = (shokobons_naif(n // 2) + shokobons_naif(n // 3)\n",
    "               + shokobons_naif(n // 4))\n",
    "    if echange > n:\n",
    "        return echange\n",
    "    return n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "98ef716e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:49.811817Z",
     "iopub.status.busy": "2026-10-05T13:31:49.811657Z",
     "iopub.status.idle": "2026-10-05T13:31:49.818498Z",
     "shell.execute_reply": "2026-10-05T13:31:49.817979Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(shokobons_naif(0) == 0)\n",
    "print(shokobons_naif(11) == 11)\n",
    "print(shokobons_naif(12) == 13)\n",
    "print(shokobons_naif(100) == 120, shokobons_naif(10**4) == 16615)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f8a02da",
   "metadata": {},
   "source": [
    "Exécuter la cellule suivante, qui trace le temps de calcul de `shokobons_naif(n)` pour $n$ allant de 10 à $10^6$ (quelques secondes)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "0ec3ce46",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:49.820706Z",
     "iopub.status.busy": "2026-10-05T13:31:49.820541Z",
     "iopub.status.idle": "2026-10-05T13:31:50.887637Z",
     "shell.execute_reply": "2026-10-05T13:31:50.886690Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def identite(n):\n",
    "    return n\n",
    "\n",
    "tailles = [10 ** k for k in range(1, 7)]\n",
    "tracer_temps({\"shokobons_naif\": shokobons_naif}, tailles, identite)"
   ]
  },
  {
   "attachments": {
    "fig_arbre_shokobons.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "7f0d82cf",
   "metadata": {},
   "source": [
    "En échelle logarithmique, la courbe est presque une droite, de pente $\\alpha \\approx 1{,}08$ : le temps de calcul est de l'ordre de $n^\\alpha$, où $\\alpha$ est la solution de $2^{-\\alpha} + 3^{-\\alpha} + 4^{-\\alpha} = 1$ (le nombre d'appels $A(n)$ vérifie $A(n) = 1 + A(\\lfloor n/2 \\rfloor) + A(\\lfloor n/3 \\rfloor) + A(\\lfloor n/4 \\rfloor)$). Pour $n = 10^9$, il faudrait une vingtaine de minutes. Pour comprendre pourquoi, voici l'arbre des appels de `shokobons_naif(12)` :\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_arbre_shokobons.png)\n",
    "\n",
    "</div>\n",
    "Les mêmes valeurs sont calculées plusieurs fois : $f(3)$ deux fois, $f(2)$ deux fois, $f(1)$ neuf fois. Pour $n = 10^6$, la fonction fait près de 10 millions d'appels. Pourtant, elle n'est appelée que sur les entiers de la forme $\\lfloor n / (2^i 3^j) \\rfloor$, qui sont peu nombreux. On mémorise donc chaque valeur $f(k)$ calculée dans un dictionnaire `memo` dont les clés sont les entiers $k$ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "c7034a18",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:50.889751Z",
     "iopub.status.busy": "2026-10-05T13:31:50.889562Z",
     "iopub.status.idle": "2026-10-05T13:31:50.893895Z",
     "shell.execute_reply": "2026-10-05T13:31:50.893168Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13 2566393 4243218150\n"
     ]
    }
   ],
   "source": [
    "def shokobons_memo(n, memo):\n",
    "    if n not in memo:\n",
    "        if n == 0:\n",
    "            memo[n] = 0\n",
    "        else:\n",
    "            echange = (shokobons_memo(n // 2, memo)\n",
    "                       + shokobons_memo(n // 3, memo)\n",
    "                       + shokobons_memo(n // 4, memo))\n",
    "            if echange > n:\n",
    "                memo[n] = echange\n",
    "            else:\n",
    "                memo[n] = n\n",
    "    return memo[n]\n",
    "\n",
    "def shokobons(n):\n",
    "    return shokobons_memo(n, {})\n",
    "\n",
    "print(shokobons(12), shokobons(10**6), shokobons(10**9))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aaf57f17",
   "metadata": {},
   "source": [
    "**Question 21**. Commenter le code de `shokobons_memo` : que contient le dictionnaire `memo` ? À quoi sert le test `if n not in memo` ? Pourquoi `shokobons` crée-t-elle un dictionnaire vide, et pourquoi le passe-t-on en argument au lieu de le recréer à chaque appel ? Combien d'appels à `shokobons_memo` (appel initial compris) fait `shokobons(12)`, et combien d'entre eux font un calcul plutôt qu'une lecture dans `memo` ?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c449ad2",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* `memo` associe à chaque entier $k$ déjà rencontré la valeur $f(k)$. Le test `if n not in memo` détecte un argument jamais vu : on calcule alors $f(n)$, une seule fois, et on le range. Sinon, on relit directement la valeur rangée, sans aucun appel récursif. Le dictionnaire doit être **partagé** par tous les appels issus d'un même calcul : c'est pourquoi on le passe en argument (un dictionnaire recréé à chaque appel serait toujours vide). `shokobons` le crée vide au départ. Pour $n = 12$, seules les valeurs 12, 6, 4, 3, 2, 1 et 0 sont calculées : 19 appels en tout, dont 12 qui relisent `memo`, au lieu de 49. Pour $n = 10^9$, `memo` ne contient que 242 clés, et il y a 724 appels, au lieu de plus de $10^{10}$ pour la version naïve."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c7f0bb2",
   "metadata": {},
   "source": [
    "Ici, les arguments sont quelques entiers dispersés entre 0 et $n$ : on les range dans un **dictionnaire** (une liste de longueur $n + 1$ serait impossible à créer pour $n = 10^9$). Quand les arguments sont au contraire **tous** les entiers de $0$ à $n$, une **liste** de longueur $n + 1$ initialisée à `None` (« pas encore calculé ») suffit, et l'on teste `if memo[k] is None`. Quand il y a deux arguments entiers $(i, j)$, on utilise de même une **grille** (une liste de listes) `memo[i][j]`, ou un dictionnaire dont les clés sont des tuples (une liste ne peut pas être une clé) : `if (i, j) not in memo`.\n",
    "\n",
    "Toute la difficulté est de choisir **ce qu'il faut mettre dans la clé** : tous les arguments dont dépend le résultat, et seulement eux. Le prochain TP, de programmation dynamique, prolongera ces idées."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87ebf4ca",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 8. La suite de Syracuse (Projet Euler 14)\n",
    "\n",
    "Pour un entier $n \\geq 1$, la **suite de Syracuse** issue de $n$ est définie par $u_0 = n$ et\n",
    "$$\n",
    "u_{k+1} = \\begin{cases} u_k / 2 & \\text{si } u_k \\text{ est pair,} \\\\ 3u_k + 1 & \\text{sinon.} \\end{cases}\n",
    "$$\n",
    "Par exemple, la suite issue de 13 est $13, 40, 20, 10, 5, 16, 8, 4, 2, 1$ : elle compte 10 termes jusqu'au premier 1 inclus. La **conjecture de Syracuse** affirme que la suite atteint 1 quel que soit $n$. Elle a été vérifiée jusqu'à plus de $10^{20}$, mais personne ne sait la démontrer."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79df3913",
   "metadata": {},
   "source": [
    "**Question 22**. Écrire une fonction `plus_longue(N)` qui prend en argument un entier $N \\geq 2$ et renvoie l'entier $n \\in [\\![1, N-1]\\!]$ dont la suite de Syracuse est la plus longue (le plus petit en cas d'égalité). Elle doit répondre en quelques secondes pour $N = 10^6$ : quel est alors le résultat ? On justifiera les choix faits (récursivité, mémoïsation, boucle éventuelle)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "91995a4e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:50.896117Z",
     "iopub.status.busy": "2026-10-05T13:31:50.895942Z",
     "iopub.status.idle": "2026-10-05T13:31:52.115482Z",
     "shell.execute_reply": "2026-10-05T13:31:52.114457Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "837799\n",
      "1.2145118713378906 secondes\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "\n",
    "def longueur_memo(n, memo):\n",
    "    \"\"\"Nombre de termes de la suite issue de n (memo contient {1: 1}).\"\"\"\n",
    "    if n not in memo:\n",
    "        if n % 2 == 0:\n",
    "            memo[n] = 1 + longueur_memo(n // 2, memo)\n",
    "        else:\n",
    "            memo[n] = 1 + longueur_memo(3 * n + 1, memo)\n",
    "    return memo[n]\n",
    "\n",
    "def plus_longue(N):\n",
    "    memo = {1: 1}       # le cas de base est dans le dictionnaire\n",
    "    meilleur = 1\n",
    "    record = 1\n",
    "    for n in range(2, N):\n",
    "        l = longueur_memo(n, memo)\n",
    "        if l > record:\n",
    "            meilleur = n\n",
    "            record = l\n",
    "    return meilleur\n",
    "\n",
    "debut = time.time()\n",
    "print(plus_longue(10**6))\n",
    "print(time.time() - debut, \"secondes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83b7707d",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* On calcule la longueur de la suite issue de $n$ par une fonction récursive : 1 si $n = 1$, et 1 de plus que la longueur de la suite issue du terme suivant sinon. Sa terminaison pour tout $n$ **est** la conjecture de Syracuse : il n'y a pas de variant évident, puisque $3n + 1 > n$.\n",
    "\n",
    "- **Mémoïsation** : la suite issue de 13 passe par 10, dont la longueur a déjà été calculée. On range les longueurs dans un dictionnaire (les termes rencontrés sont des entiers dispersés, jusqu'à environ $5{,}7 \\times 10^{10}$ pour $N = 10^6$ : une liste serait impossible). Sans mémoïsation, le calcul pour $N = 10^6$ prend une dizaine de secondes, avec mémoïsation, environ une seconde, et le dictionnaire contient plus de deux millions de clés.\n",
    "- **Boucle** : on parcourt les entiers de 2 à $N - 1$ avec une boucle. Une récursion sur $n$ aurait une profondeur de $10^6$, bien au-delà de la limite de récursion (ici $10^4$).\n",
    "- **Résultat** : 837 799, dont la suite compte 525 termes.\n",
    "\n",
    "Le gain de la mémoïsation est moins spectaculaire que pour les shokobons : la fonction ne fait qu'**un** appel récursif, et la mémoïsation évite seulement de reparcourir les fins de suites déjà rencontrées."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "b9a19b62",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.117526Z",
     "iopub.status.busy": "2026-10-05T13:31:52.117352Z",
     "iopub.status.idle": "2026-10-05T13:31:52.200031Z",
     "shell.execute_reply": "2026-10-05T13:31:52.199295Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(plus_longue(2) == 1, plus_longue(10) == 9, plus_longue(100) == 97)\n",
    "print(plus_longue(20) == 18)       # 18 et 19 : 21 termes chacun\n",
    "print(plus_longue(10**5) == 77031)"
   ]
  },
  {
   "attachments": {
    "fig_trous.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "bb384acd",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 9. Chemins dans une grille à trous\n",
    "\n",
    "Une grille de $n$ lignes et $p$ colonnes est donnée par une liste de $n$ listes de $p$ booléens : `G[i][j]` vaut `True` si la case $(i, j)$ est un **trou**, et `False` si elle est libre. Un **chemin** part de la case $(0, 0)$ en haut à gauche, ne se déplace que d'une case vers la **droite** ou vers le **bas**, et ne passe par aucun trou. Voici un exemple de grille et de chemin.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_trous.png)\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "d4759f0e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.202233Z",
     "iopub.status.busy": "2026-10-05T13:31:52.201949Z",
     "iopub.status.idle": "2026-10-05T13:31:52.274021Z",
     "shell.execute_reply": "2026-10-05T13:31:52.273230Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F, T = False, True     # T : trou\n",
    "P = [[F, F, F, F, T],\n",
    "     [F, T, F, F, F],\n",
    "     [F, F, F, T, F],\n",
    "     [T, F, F, F, F],\n",
    "     [F, F, T, F, F]]\n",
    "dessiner_grille_trouee(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79e99450",
   "metadata": {},
   "source": [
    "**Question 23**. Écrire une fonction récursive `nb_chemins_naif(G, i, j)` qui prend en arguments une grille `G` et les coordonnées $(i, j)$ d'une case, et renvoie le nombre de chemins de $(0, 0)$ à $(i, j)$ dans `G`. Mesurer son temps de calcul sur une grille de $13 \\times 13$ cases sans trou, et expliquer pourquoi il est si long."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "120b80d7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.276542Z",
     "iopub.status.busy": "2026-10-05T13:31:52.276347Z",
     "iopub.status.idle": "2026-10-05T13:31:52.280384Z",
     "shell.execute_reply": "2026-10-05T13:31:52.279622Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def nb_chemins_naif(G, i, j):\n",
    "    if G[i][j]:                       # un trou\n",
    "        return 0\n",
    "    elif i == 0 and j == 0:\n",
    "        return 1\n",
    "    else:\n",
    "        total = 0\n",
    "        if i > 0:\n",
    "            # on arrive par le haut\n",
    "            total = total + nb_chemins_naif(G, i - 1, j)\n",
    "        if j > 0:\n",
    "            # on arrive par la gauche\n",
    "            total = total + nb_chemins_naif(G, i, j - 1)\n",
    "        return total"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d8df0a7",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* La fonction obtient son résultat en additionnant des 1 : elle fait au moins autant d'appels qu'il y a de chemins. Sans trou, il y a $\\binom{24}{12} = 2\\,704\\,156$ chemins de $(0, 0)$ à $(12, 12)$ (choisir les 12 déplacements vers le bas parmi 24), soit plusieurs millions d'appels et environ une seconde. Les mêmes cases sont recalculées un très grand nombre de fois."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "9ca703e4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.282008Z",
     "iopub.status.busy": "2026-10-05T13:31:52.281836Z",
     "iopub.status.idle": "2026-10-05T13:31:52.286485Z",
     "shell.execute_reply": "2026-10-05T13:31:52.285633Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "F, T = False, True     # T : trou\n",
    "P = [[F, F, F, F, T],\n",
    "     [F, T, F, F, F],\n",
    "     [F, F, F, T, F],\n",
    "     [T, F, F, F, F],\n",
    "     [F, F, T, F, F]]\n",
    "print(nb_chemins_naif(P, 4, 4) == 8)\n",
    "print(nb_chemins_naif(P, 0, 4) == 0)\n",
    "print(nb_chemins_naif(P, 2, 2) == 2)\n",
    "print(nb_chemins_naif([[F, F], [F, F]], 1, 1) == 2)\n",
    "print(nb_chemins_naif([[F, T], [T, F]], 1, 1) == 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da8a29ea",
   "metadata": {},
   "source": [
    "**Question 24**. Écrire une fonction `nb_chemins(G)` qui prend en argument une grille `G` et renvoie le nombre de chemins de $(0, 0)$ jusqu'à la case en bas à droite, en mémoïsant les résultats. Quelle est sa complexité ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "b7ce82db",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.288163Z",
     "iopub.status.busy": "2026-10-05T13:31:52.287943Z",
     "iopub.status.idle": "2026-10-05T13:31:52.292509Z",
     "shell.execute_reply": "2026-10-05T13:31:52.291679Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def nb_chemins_memo(G, i, j, memo):\n",
    "    \"\"\"memo[i][j] : nombre de chemins jusqu'à (i, j), ou None.\"\"\"\n",
    "    if memo[i][j] is None:\n",
    "        if G[i][j]:                   # un trou\n",
    "            memo[i][j] = 0\n",
    "        elif i == 0 and j == 0:\n",
    "            memo[i][j] = 1\n",
    "        else:\n",
    "            total = 0\n",
    "            if i > 0:\n",
    "                total = total + nb_chemins_memo(G, i - 1, j, memo)\n",
    "            if j > 0:\n",
    "                total = total + nb_chemins_memo(G, i, j - 1, memo)\n",
    "            memo[i][j] = total\n",
    "    return memo[i][j]\n",
    "\n",
    "def nb_chemins(G):\n",
    "    n, p = len(G), len(G[0])\n",
    "    memo = [[None for j in range(p)] for i in range(n)]\n",
    "    return nb_chemins_memo(G, n - 1, p - 1, memo)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66046e54",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* Les arguments qui varient sont les coordonnées $(i, j)$, toutes dans $[\\![0, n[\\![ \\times [\\![0, p[\\![$ : on mémorise dans une **grille** `memo` de même taille que `G`, initialisée à `None`. Un dictionnaire de clés $(i, j)$ conviendrait aussi, mais la grille est plus simple et plus rapide. Chaque case est calculée une fois, en $O(1)$ hors appels récursifs : $O(np)$ pour une grille $n \\times p$. La grille `memo` ne dépend que de `G` : `nb_chemins` en crée une neuve à chaque appel, car des valeurs calculées pour une grille seraient fausses pour une autre."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "337b257a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.294123Z",
     "iopub.status.busy": "2026-10-05T13:31:52.293892Z",
     "iopub.status.idle": "2026-10-05T13:31:52.300891Z",
     "shell.execute_reply": "2026-10-05T13:31:52.299956Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "F, T = False, True     # T : trou\n",
    "P = [[F, F, F, F, T],\n",
    "     [F, T, F, F, F],\n",
    "     [F, F, F, T, F],\n",
    "     [T, F, F, F, F],\n",
    "     [F, F, T, F, F]]\n",
    "VIDE13 = [[False for j in range(13)] for i in range(13)]\n",
    "VIDE30 = [[False for j in range(30)] for i in range(30)]\n",
    "G30 = [[(7 * i + 3 * j) % 11 == 0 and 0 < i + j < 58 for j in range(30)]\n",
    "       for i in range(30)]\n",
    "print(nb_chemins(P) == 8, nb_chemins([[True]]) == 0)\n",
    "print(nb_chemins(VIDE13) == 2704156)\n",
    "print(nb_chemins(VIDE30) == 30067266499541040)\n",
    "print(nb_chemins(G30) == 11856863193075)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "de4661ee",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.303049Z",
     "iopub.status.busy": "2026-10-05T13:31:52.302770Z",
     "iopub.status.idle": "2026-10-05T13:31:52.417029Z",
     "shell.execute_reply": "2026-10-05T13:31:52.416244Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualisation : titre vert si le résultat est correct, rouge sinon.\n",
    "F, T = False, True     # T : trou\n",
    "P = [[F, F, F, F, T],\n",
    "     [F, T, F, F, F],\n",
    "     [F, F, F, T, F],\n",
    "     [T, F, F, F, F],\n",
    "     [F, F, T, F, F]]\n",
    "def f(i, j):\n",
    "    # chemins jusqu'à (i, j) = chemins dans la sous-grille des lignes 0..i\n",
    "    # et des colonnes 0..j\n",
    "    return nb_chemins([ligne[:j + 1] for ligne in P[:i + 1]])\n",
    "dessiner_grille_trouee(P, f)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7409a20",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 10. Parenthésages et nombres de Catalan\n",
    "\n",
    "Un **mot de parenthèses** est une chaîne formée des caractères `(` et `)`. Il est **bien parenthésé** s'il est vide, ou s'il s'écrit `\"(\" + u + \")\" + v` avec `u` et `v` bien parenthésés. Par exemple, `\"(())()\"` est bien parenthésé, mais ni `\")(\"`, ni `\"(()\"`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8889791f",
   "metadata": {},
   "source": [
    "**Question 25**. Écrire une fonction `est_bien_parenthese(s)` qui prend en argument un mot de parenthèses `s` et renvoie `True` s'il est bien parenthésé et `False` sinon, en $O(n)$ où $n$ est la longueur de `s`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "342832ff",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.419171Z",
     "iopub.status.busy": "2026-10-05T13:31:52.419008Z",
     "iopub.status.idle": "2026-10-05T13:31:52.422708Z",
     "shell.execute_reply": "2026-10-05T13:31:52.421883Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def est_bien_parenthese_aux(s, i, h):\n",
    "    if h < 0:\n",
    "        return False\n",
    "    elif i == len(s):\n",
    "        return h == 0\n",
    "    elif s[i] == \"(\":\n",
    "        return est_bien_parenthese_aux(s, i + 1, h + 1)\n",
    "    else:\n",
    "        return est_bien_parenthese_aux(s, i + 1, h - 1)\n",
    "\n",
    "def est_bien_parenthese(s):\n",
    "    return est_bien_parenthese_aux(s, 0, 0)"
   ]
  },
  {
   "attachments": {
    "fig_dyck.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "e74c44e3",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* Principe : on lit le mot de gauche à droite en tenant à jour sa **hauteur**, le nombre de `(` lues moins le nombre de `)` lues. Un mot est bien parenthésé si et seulement si sa hauteur reste positive ou nulle et vaut 0 à la fin : c'est un chemin qui monte à chaque `(`, descend à chaque `)`, ne passe jamais sous 0 et revient à 0. La décomposition `\"(\" + u + \")\" + v` correspond au premier retour du chemin à la hauteur 0. La fonction auxiliaire reçoit l'indice `i` et la hauteur `h` après lecture des `i` premiers caractères : un seul appel par caractère, d'où $O(n)$.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_dyck.png)\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "cd4137f9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.424833Z",
     "iopub.status.busy": "2026-10-05T13:31:52.424580Z",
     "iopub.status.idle": "2026-10-05T13:31:52.428224Z",
     "shell.execute_reply": "2026-10-05T13:31:52.427510Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(est_bien_parenthese(\"\"))\n",
    "print(est_bien_parenthese(\"()\"))\n",
    "print(est_bien_parenthese(\"(())()\"))\n",
    "print(not est_bien_parenthese(\")(\"))\n",
    "print(not est_bien_parenthese(\"(()\"))\n",
    "print(not est_bien_parenthese(\"())(()\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b9e35f4",
   "metadata": {},
   "source": [
    "**Question 26**. Écrire une fonction `parenthesages(n)` qui prend en argument un entier naturel `n` et renvoie la liste de tous les mots bien parenthésés contenant $n$ parenthèses ouvrantes et $n$ fermantes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "950793a2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.430661Z",
     "iopub.status.busy": "2026-10-05T13:31:52.430492Z",
     "iopub.status.idle": "2026-10-05T13:31:52.434455Z",
     "shell.execute_reply": "2026-10-05T13:31:52.433605Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def parenthesages_aux(debut, o, f, liste):\n",
    "    if o == 0 and f == 0:\n",
    "        liste.append(debut)\n",
    "    if o > 0:\n",
    "        parenthesages_aux(debut + \"(\", o - 1, f, liste)\n",
    "    if f > o:   # on peut fermer si la hauteur f - o est strictement positive\n",
    "        parenthesages_aux(debut + \")\", o, f - 1, liste)\n",
    "\n",
    "def parenthesages(n):\n",
    "    liste = []\n",
    "    parenthesages_aux(\"\", n, n, liste)\n",
    "    return liste\n",
    "\n",
    "# Aucune impasse : chaque appel produit au moins un mot.\n",
    "# Chaque mot est construit en 2n appels : complexité O(n^2 C_n)\n",
    "# en comptant le coût des concaténations (C_n mots, cf. question suivante)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "aed40e2a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.436541Z",
     "iopub.status.busy": "2026-10-05T13:31:52.436352Z",
     "iopub.status.idle": "2026-10-05T13:31:52.441112Z",
     "shell.execute_reply": "2026-10-05T13:31:52.440510Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(parenthesages(0) == [\"\"], parenthesages(1) == [\"()\"])\n",
    "print(sorted(parenthesages(3))\n",
    "      == [\"((()))\", \"(()())\", \"(())()\", \"()(())\", \"()()()\"])\n",
    "print([len(parenthesages(n)) for n in range(9)]\n",
    "      == [1, 1, 2, 5, 14, 42, 132, 429, 1430])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "098c4c89",
   "metadata": {},
   "source": [
    "**Question 27**. On note $C_n$ le nombre de mots bien parenthésés à $n$ paires de parenthèses (le $n$-ième **nombre de Catalan**). Justifier que\n",
    "$$\n",
    "C_0 = 1 \\quad \\text{et} \\quad \\forall n \\in \\mathbb{N}, \\quad C_{n+1} = \\sum_{k=0}^{n} C_k \\, C_{n-k}.\n",
    "$$\n",
    "Écrire une fonction `catalan(n)` qui prend en argument un entier naturel `n` et renvoie $C_n$, avec $O(n^2)$ opérations arithmétiques."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f188ab69",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* Un mot bien parenthésé non vide s'écrit de manière **unique** `\"(\" + u + \")\" + v`, où `\"(\" + u + \")\"` est le plus court préfixe non vide de hauteur nulle. Si le mot a $n+1$ paires, `u` en a $k \\in [\\![0, n]\\!]$ et `v` en a $n - k$. Inversement, tout tel couple $(u, v)$ donne un mot bien parenthésé à $n+1$ paires. D'où la formule.\n",
    "\n",
    "Calculée naïvement par récursion, la formule recalcule les mêmes $C_k$ un nombre exponentiel de fois : on mémoïse. Chaque $C_m$ est alors calculé une seule fois, en $O(m)$ opérations, soit $O(n^2)$ au total."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "c201bdff",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.443339Z",
     "iopub.status.busy": "2026-10-05T13:31:52.443183Z",
     "iopub.status.idle": "2026-10-05T13:31:52.446876Z",
     "shell.execute_reply": "2026-10-05T13:31:52.446085Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def catalan_memo(n, memo):\n",
    "    if memo[n] is None:\n",
    "        s = 0\n",
    "        for k in range(n):\n",
    "            s = s + catalan_memo(k, memo) * catalan_memo(n - 1 - k, memo)\n",
    "        memo[n] = s\n",
    "    return memo[n]\n",
    "\n",
    "def catalan(n):\n",
    "    memo = [None for k in range(n + 1)]   # arguments de 0 à n : une liste\n",
    "    memo[0] = 1\n",
    "    return catalan_memo(n, memo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "280697c4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.448766Z",
     "iopub.status.busy": "2026-10-05T13:31:52.448480Z",
     "iopub.status.idle": "2026-10-05T13:31:52.452013Z",
     "shell.execute_reply": "2026-10-05T13:31:52.451409Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print([catalan(n) for n in range(10)]\n",
    "      == [1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862])\n",
    "print(catalan(30) == 3814986502092304)\n",
    "print(catalan(50) == 1978261657756160653623774456)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fd5a01a",
   "metadata": {},
   "source": [
    "**Question 28**. On utilise maintenant deux types de parenthèses, `( )` et `[ ]`. Un mot est bien parenthésé s'il est vide, ou s'il s'écrit `\"(\" + u + \")\" + v` ou `\"[\" + u + \"]\" + v` avec `u` et `v` bien parenthésés. Ainsi `\"([])[]\"` est bien parenthésé, mais pas `\"([)]\"`. Écrire une fonction `est_bien_parenthese2(s)` qui prend en argument un tel mot `s` et renvoie `True` s'il est bien parenthésé et `False` sinon, en $O(n)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "9b54bfb2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.453816Z",
     "iopub.status.busy": "2026-10-05T13:31:52.453654Z",
     "iopub.status.idle": "2026-10-05T13:31:52.457297Z",
     "shell.execute_reply": "2026-10-05T13:31:52.456689Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def fermante(c):\n",
    "    if c == \"(\":\n",
    "        return \")\"\n",
    "    else:\n",
    "        return \"]\"\n",
    "\n",
    "def lire(s, i):\n",
    "    if i == len(s) or s[i] == \")\" or s[i] == \"]\":\n",
    "        return i                          # mot vide\n",
    "    j = lire(s, i + 1)                    # le mot u, après l'ouvrante s[i]\n",
    "    if j == -1 or j == len(s) or s[j] != fermante(s[i]):\n",
    "        return -1\n",
    "    return lire(s, j + 1)                 # le mot v, après la fermante s[j]\n",
    "\n",
    "def est_bien_parenthese2(s):\n",
    "    return lire(s, 0) == len(s)\n",
    "\n",
    "# Chaque caractère est lu une fois : O(n). La pile d'appels joue le rôle\n",
    "# de la pile des ouvrantes en attente de leur fermante."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "2078783b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.458994Z",
     "iopub.status.busy": "2026-10-05T13:31:52.458840Z",
     "iopub.status.idle": "2026-10-05T13:31:52.462050Z",
     "shell.execute_reply": "2026-10-05T13:31:52.461539Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(est_bien_parenthese2(\"\"))\n",
    "print(est_bien_parenthese2(\"()[]\"))\n",
    "print(est_bien_parenthese2(\"([])[()()]\"))\n",
    "print(not est_bien_parenthese2(\"(]\"))\n",
    "print(not est_bien_parenthese2(\"([)]\"))\n",
    "print(not est_bien_parenthese2(\"((\"))\n",
    "print(not est_bien_parenthese2(\"])\"))\n",
    "print(not est_bien_parenthese2(\"()]\"))\n",
    "print(not est_bien_parenthese2(\"[(])\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "075ac765",
   "metadata": {},
   "source": [
    "**Question 29**. Combien y a-t-il de mots bien parenthésés à $n$ paires avec deux types de parenthèses ? Écrire une fonction `parenthesages2(n)` qui prend en argument un entier naturel `n` et renvoie la liste de tous ces mots, et vérifier."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "074eced3",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* $2^n C_n$ : en oubliant les types, on obtient un mot bien parenthésé à une seule sorte de parenthèses, et chacune des $n$ paires peut ensuite prendre l'un des deux types, indépendamment des autres. (On peut aussi adapter la question sur les nombres de Catalan : $E_{n+1} = 2 \\sum_{k=0}^{n} E_k E_{n-k}$.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "cc5e9072",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.464103Z",
     "iopub.status.busy": "2026-10-05T13:31:52.463847Z",
     "iopub.status.idle": "2026-10-05T13:31:52.467644Z",
     "shell.execute_reply": "2026-10-05T13:31:52.467006Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def parenthesages2_aux(debut, o, ouvertes, liste):\n",
    "    if o == 0 and len(ouvertes) == 0:\n",
    "        liste.append(debut)\n",
    "    if o > 0:\n",
    "        parenthesages2_aux(debut + \"(\", o - 1, ouvertes + \"(\", liste)\n",
    "        parenthesages2_aux(debut + \"[\", o - 1, ouvertes + \"[\", liste)\n",
    "    if len(ouvertes) > 0:\n",
    "        # la dernière ouvrante ouverte est la première fermée\n",
    "        k = len(ouvertes) - 1\n",
    "        fin = debut + fermante(ouvertes[k])\n",
    "        parenthesages2_aux(fin, o, ouvertes[:k], liste)\n",
    "\n",
    "def parenthesages2(n):\n",
    "    liste = []\n",
    "    parenthesages2_aux(\"\", n, \"\", liste)\n",
    "    return liste"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "618c36a0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.469535Z",
     "iopub.status.busy": "2026-10-05T13:31:52.469370Z",
     "iopub.status.idle": "2026-10-05T13:31:52.544900Z",
     "shell.execute_reply": "2026-10-05T13:31:52.544237Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(sorted(parenthesages2(1)) == [\"()\", \"[]\"])\n",
    "print([len(parenthesages2(n)) for n in range(8)]\n",
    "      == [1, 2, 8, 40, 224, 1344, 8448, 54912])\n",
    "print(all(est_bien_parenthese2(s) for s in parenthesages2(5)))"
   ]
  },
  {
   "attachments": {
    "fig_partitions.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "81f55437",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 11. Partitions d'un entier (Projet Euler 76)\n",
    "\n",
    "Une **partition** d'un entier $n \\geq 0$ est une écriture de $n$ comme somme d'entiers strictement positifs, sans tenir compte de l'ordre des termes (les **parts**). On la représente par la liste décroissante de ses parts. Par exemple, $4$ a cinq partitions : `[4]`, `[3, 1]`, `[2, 2]`, `[2, 1, 1]` et `[1, 1, 1, 1]`. L'entier 0 a une seule partition, la liste vide. On note $p(n)$ le nombre de partitions de $n$. On représente souvent une partition par un **tableau de Young** : une ligne de cases par part, de longueur la valeur de la part. Voici les cinq partitions de 4.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_partitions.png)\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa591b88",
   "metadata": {},
   "source": [
    "**Question 30**. On note $p(n, m)$ le nombre de partitions de $n$ dont toutes les parts sont inférieures ou égales à $m$. Justifier que, pour $1 \\le m \\le n$,\n",
    "$$p(n, m) = p(n, m - 1) + p(n - m, m),$$\n",
    "et préciser les cas de base. Écrire une fonction récursive `nb_partitions_naif(n)` qui prend en argument un entier naturel `n` et renvoie $p(n) = p(n, n)$, et mesurer son temps de calcul pour $n = 50$ et $n = 60$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3164af9",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* Une partition de $n$ en parts au plus égales à $m$ ou bien ne contient pas la part $m$ (c'est une partition en parts au plus égales à $m - 1$), ou bien la contient : en retirant une part $m$, on obtient une partition de $n - m$ en parts au plus égales à $m$, et réciproquement. Cas de base : $p(0, m) = 1$ (la partition vide), $p(n, 0) = 0$ pour $n > 0$, et $p(n, m) = p(n, n)$ si $m > n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "83e2e144",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.547187Z",
     "iopub.status.busy": "2026-10-05T13:31:52.546977Z",
     "iopub.status.idle": "2026-10-05T13:31:52.551849Z",
     "shell.execute_reply": "2026-10-05T13:31:52.551187Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def p_naif(n, m):\n",
    "    \"\"\"Nombre de partitions de n en parts au plus égales à m.\"\"\"\n",
    "    if n == 0:\n",
    "        return 1\n",
    "    elif m == 0:\n",
    "        return 0\n",
    "    elif m > n:\n",
    "        return p_naif(n, n)\n",
    "    else:\n",
    "        return p_naif(n, m - 1) + p_naif(n - m, m)\n",
    "\n",
    "def nb_partitions_naif(n):\n",
    "    return p_naif(n, n)\n",
    "\n",
    "# Le nombre d'appels est au moins p(n) : environ 0,1 s pour n = 50,\n",
    "# 0,5 s pour n = 60, et il est multiplié par 5 tous les 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "5b50e8a7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.553952Z",
     "iopub.status.busy": "2026-10-05T13:31:52.553802Z",
     "iopub.status.idle": "2026-10-05T13:31:52.560831Z",
     "shell.execute_reply": "2026-10-05T13:31:52.560281Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print([nb_partitions_naif(n) for n in range(11)]\n",
    "      == [1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42])\n",
    "print(nb_partitions_naif(30) == 5604)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4e94ff6",
   "metadata": {},
   "source": [
    "**Question 31**. Écrire une fonction `nb_partitions(n)` qui prend en argument un entier naturel `n` et renvoie $p(n)$, en mémoïsant les valeurs $p(n', m')$. Quelle est sa complexité ? Le problème 76 du Projet Euler demande le nombre de façons d'écrire 100 comme somme d'au moins deux entiers strictement positifs : que vaut-il ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "aaabbf21",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.563264Z",
     "iopub.status.busy": "2026-10-05T13:31:52.563065Z",
     "iopub.status.idle": "2026-10-05T13:31:52.567271Z",
     "shell.execute_reply": "2026-10-05T13:31:52.566606Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def p_memo(n, m, memo):\n",
    "    \"\"\"memo[n][m] : nombre de partitions de n en parts <= m, ou None.\"\"\"\n",
    "    if memo[n][m] is None:\n",
    "        if n == 0:\n",
    "            memo[n][m] = 1\n",
    "        elif m == 0:\n",
    "            memo[n][m] = 0\n",
    "        elif m > n:\n",
    "            memo[n][m] = p_memo(n, n, memo)\n",
    "        else:\n",
    "            memo[n][m] = p_memo(n, m - 1, memo) + p_memo(n - m, m, memo)\n",
    "    return memo[n][m]\n",
    "\n",
    "def nb_partitions(n):\n",
    "    # les arguments (n', m') vérifient n' <= n et m' <= n : une grille suffit\n",
    "    memo = [[None for j in range(n + 1)] for i in range(n + 1)]\n",
    "    return p_memo(n, n, memo)\n",
    "\n",
    "# Au plus (n + 1)^2 couples (n', m'), chacun calculé une fois en O(1)\n",
    "# hors appels récursifs : O(n^2)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "cead6f72",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:52.569687Z",
     "iopub.status.busy": "2026-10-05T13:31:52.569526Z",
     "iopub.status.idle": "2026-10-05T13:31:57.315741Z",
     "shell.execute_reply": "2026-10-05T13:31:57.314539Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print([nb_partitions(n) for n in range(61)]\n",
    "      == [nb_partitions_naif(n) for n in range(61)])\n",
    "print(nb_partitions(200) == 3972999029388)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "269710b8",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* $p(100) - 1 = 190\\,569\\,291$ : on retire la partition `[100]`, qui n'a qu'une part."
   ]
  },
  {
   "attachments": {
    "fig_arbre_reines.png": {
     "image/png": 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"
    },
    "fig_arbre_reines_plateaux.png": {
     "image/png": 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    }
   },
   "cell_type": "markdown",
   "id": "627db8ee",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## III. Backtracking\n",
    "\n",
    "**Rappel.** On construit une solution par une suite de choix. Une fonction récursive reçoit une solution partielle :\n",
    "\n",
    "- si elle est complète, on l'enregistre (ou on s'arrête, si une seule solution suffit),\n",
    "- sinon, pour chaque choix **compatible** avec elle, on fait ce choix, on appelle récursivement la fonction, puis on **annule** le choix avant d'essayer le suivant (c'est inutile si l'on a transmis une copie modifiée, comme `pos + [c]`).\n",
    "\n",
    "Quand aucun choix ne convient, la fonction se termine sans rien trouver et l'on revient au choix précédent : c'est le **backtracking**. On parcourt ainsi en profondeur l'arbre des choix, sans jamais prolonger une solution partielle incompatible : on **élague** les branches qui ne mènent à aucune solution.\n",
    "\n",
    "Exemple : placer $n$ reines sur un échiquier $n \\times n$ sans que deux d'entre elles soient sur une même ligne, une même colonne ou une même diagonale. Il y a exactement une reine par ligne : on place la reine de la ligne 0, puis celle de la ligne 1, et ainsi de suite, en n'essayant à chaque ligne que les colonnes où la nouvelle reine n'est en prise avec aucune des précédentes. Si aucune colonne ne convient, on revient à la ligne précédente pour y essayer la colonne suivante. Voici l'arbre des choix pour $n = 4$ : chaque nœud est l'état de l'échiquier, une croix marquant une impasse.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_arbre_reines_plateaux.png)\n",
    "\n",
    "</div>\n",
    "Pour programmer cette recherche, il est inutile de stocker tout l'échiquier : puisqu'il y a une reine par ligne, un placement des reines sur les $k$ premières lignes est entièrement décrit par la liste `pos` de longueur $k$, où `pos[i]` est la colonne de la reine de la ligne $i$. Le même arbre, avec cette représentation :\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_arbre_reines.png)\n",
    "\n",
    "</div>\n",
    "Pour compter les appels d'une fonction récursive, on pourra utiliser une liste `cpt = [0]` définie en dehors de la fonction, et l'incrémenter au début de chaque appel par `cpt[0] = cpt[0] + 1`."
   ]
  },
  {
   "attachments": {
    "fig_reines.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "68bbae3a",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 12. Le problème des $n$ reines\n",
    "\n",
    "La fonction `dessiner_echiquier(pos, n)` du module `dessins` dessine un placement sur un échiquier $n \\times n$, et relie en rouge les reines en prise.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_reines.png)\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40c0fd09",
   "metadata": {},
   "source": [
    "**Question 32**. Écrire une fonction `compatible(pos, c)` qui prend en arguments un placement `pos` de $k$ reines et une colonne `c`, et renvoie `True` si l'on peut placer une reine en colonne `c` sur la ligne $k$ sans qu'elle soit en prise avec les reines déjà placées, et `False` sinon, en $O(k)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "2c798842",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:57.318263Z",
     "iopub.status.busy": "2026-10-05T13:31:57.318048Z",
     "iopub.status.idle": "2026-10-05T13:31:57.322673Z",
     "shell.execute_reply": "2026-10-05T13:31:57.321447Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def compatible_aux(pos, c, i):\n",
    "    \"\"\"La reine (k, c) est-elle compatible avec celles des lignes i à k - 1 ?\"\"\"\n",
    "    k = len(pos)\n",
    "    if i == k:\n",
    "        return True\n",
    "    elif pos[i] == c or pos[i] - c == k - i or c - pos[i] == k - i:\n",
    "        return False                       # même colonne ou même diagonale\n",
    "    else:\n",
    "        return compatible_aux(pos, c, i + 1)\n",
    "\n",
    "def compatible(pos, c):\n",
    "    return compatible_aux(pos, c, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "db19e00d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:57.324966Z",
     "iopub.status.busy": "2026-10-05T13:31:57.324614Z",
     "iopub.status.idle": "2026-10-05T13:31:57.329646Z",
     "shell.execute_reply": "2026-10-05T13:31:57.328648Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True True\n",
      "True\n",
      "True\n",
      "True\n",
      "True True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(compatible([], 0), compatible([0], 2), compatible([1, 3], 0))\n",
    "print(not compatible([0], 0))\n",
    "print(not compatible([0], 1))\n",
    "print(not compatible([1, 3], 2))\n",
    "print(not compatible([1, 3, 0], 1), not compatible([2], 1))\n",
    "print(compatible([0, 2], 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85ae3e45",
   "metadata": {},
   "source": [
    "**Question 33**. Écrire une fonction `nb_solutions(n)` qui prend en argument un entier $n \\geq 1$ et renvoie le nombre de façons de placer $n$ reines sur un échiquier $n \\times n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "f4f99b3c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:57.332075Z",
     "iopub.status.busy": "2026-10-05T13:31:57.331765Z",
     "iopub.status.idle": "2026-10-05T13:31:57.337193Z",
     "shell.execute_reply": "2026-10-05T13:31:57.336164Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def nb_solutions_aux(pos, n):\n",
    "    if len(pos) == n:\n",
    "        return 1\n",
    "    s = 0\n",
    "    for c in range(n):\n",
    "        # élagage : on ne prolonge que les placements valides\n",
    "        if compatible(pos, c):\n",
    "            s = s + nb_solutions_aux(pos + [c], n)\n",
    "    return s\n",
    "\n",
    "def nb_solutions(n):\n",
    "    return nb_solutions_aux([], n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "1dbbc633",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:57.339589Z",
     "iopub.status.busy": "2026-10-05T13:31:57.339314Z",
     "iopub.status.idle": "2026-10-05T13:31:57.632577Z",
     "shell.execute_reply": "2026-10-05T13:31:57.631366Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print([nb_solutions(n) for n in range(1, 11)]\n",
    "      == [1, 0, 0, 2, 10, 4, 40, 92, 352, 724])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c86e776",
   "metadata": {},
   "source": [
    "**Question 34**. Écrire une fonction `nb_solutions_appels(pos, n)` qui prend en arguments un placement `pos` et un entier `n`, et renvoie le couple (nombre de solutions qui prolongent `pos`, nombre d'appels), où le nombre d'appels compte **tous** les appels de la fonction, appel initial compris : c'est le nombre de nœuds de l'arbre des choix (17 pour $n = 4$, voir la figure du rappel). Pour $n = 8$, comparer ce nombre au nombre $8^8$ de placements d'une reine par ligne, et au nombre $8!$ de placements d'une reine par ligne et par colonne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "4de04f3b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:57.634757Z",
     "iopub.status.busy": "2026-10-05T13:31:57.634548Z",
     "iopub.status.idle": "2026-10-05T13:31:57.639006Z",
     "shell.execute_reply": "2026-10-05T13:31:57.637945Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def nb_solutions_appels(pos, n):\n",
    "    \"\"\"Renvoie le couple (nombre de solutions, nombre d'appels).\"\"\"\n",
    "    if len(pos) == n:\n",
    "        return (1, 1)\n",
    "    s, a = 0, 1\n",
    "    for c in range(n):\n",
    "        if compatible(pos, c):\n",
    "            x, y = nb_solutions_appels(pos + [c], n)\n",
    "            s, a = s + x, a + y\n",
    "    return (s, a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "4800baef",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:57.641036Z",
     "iopub.status.busy": "2026-10-05T13:31:57.640774Z",
     "iopub.status.idle": "2026-10-05T13:31:57.655664Z",
     "shell.execute_reply": "2026-10-05T13:31:57.654988Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(nb_solutions_appels([], 4) == (2, 17))\n",
    "print(nb_solutions_appels([], 8) == (92, 2057))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bead3755",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* 2057 appels, contre $8! = 40\\,320$ permutations et $8^8 = 16\\,777\\,216$ placements d'une reine par ligne. L'élagage abandonne un placement partiel dès qu'il est invalide, et coupe ainsi des sous-arbres entiers de l'arbre des placements. La complexité reste au moins exponentielle (on sait que le nombre de solutions croît plus vite que toute exponentielle), mais le gain est considérable : environ 0,7 s pour $n = 11$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fa18699",
   "metadata": {},
   "source": [
    "**Question 35**. Écrire une fonction `une_solution(n)` qui prend en argument un entier $n \\geq 1$ et renvoie **une** solution (la liste `pos`), ou `None` s'il n'y en a pas. Elle doit s'arrêter **dès qu'une solution est trouvée**, sans explorer le reste de l'arbre. Dessiner une solution pour $n = 8$ et pour $n = 20$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "9b6d214d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:57.658259Z",
     "iopub.status.busy": "2026-10-05T13:31:57.658014Z",
     "iopub.status.idle": "2026-10-05T13:31:57.662525Z",
     "shell.execute_reply": "2026-10-05T13:31:57.661555Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def une_solution_aux(pos, n):\n",
    "    if len(pos) == n:\n",
    "        return pos\n",
    "    for c in range(n):\n",
    "        if compatible(pos, c):\n",
    "            s = une_solution_aux(pos + [c], n)\n",
    "            if s is not None:\n",
    "                return s           # on remonte la solution sans continuer\n",
    "    return None    # aucune colonne ne convient : retour en arrière\n",
    "\n",
    "def une_solution(n):\n",
    "    return une_solution_aux([], n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "28880c3b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:57.664784Z",
     "iopub.status.busy": "2026-10-05T13:31:57.664602Z",
     "iopub.status.idle": "2026-10-05T13:31:57.706987Z",
     "shell.execute_reply": "2026-10-05T13:31:57.706188Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "def valide(s, n):\n",
    "    return (len(s) == n and sorted(s) == list(range(n))\n",
    "            and all(s[j] - s[i] != j - i and s[i] - s[j] != j - i\n",
    "                    for i in range(n) for j in range(i + 1, n)))\n",
    "print(une_solution(2) is None)\n",
    "print(une_solution(3) is None)\n",
    "print(une_solution(1) == [0])\n",
    "print(all(valide(une_solution(n), n) for n in range(4, 16)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "999a4ed6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:57.708923Z",
     "iopub.status.busy": "2026-10-05T13:31:57.708726Z",
     "iopub.status.idle": "2026-10-05T13:32:01.636258Z",
     "shell.execute_reply": "2026-10-05T13:32:01.635403Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 380x380 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualisation : titre vert si le résultat est correct, rouge sinon.\n",
    "dessiner_echiquier(une_solution(8))\n",
    "dessiner_echiquier(une_solution(20))      # quelques secondes"
   ]
  },
  {
   "attachments": {
    "fig_sudoku.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "ccd9b5a0",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 13. Sudoku\n",
    "\n",
    "Une grille de Sudoku est représentée par une liste de 9 listes de 9 entiers, la valeur 0 indiquant une case vide. Il faut la compléter avec des chiffres de 1 à 9 de sorte que chaque ligne, chaque colonne et chacun des 9 carrés $3 \\times 3$ contienne une seule fois chaque chiffre. La fonction `dessiner_sudoku(G, initiale)` du module `dessins` dessine la grille `G`, avec en gras les chiffres de la grille `initiale`, et marque en rouge les chiffres en conflit.\n",
    "\n",
    "Dans cette partie, on s'autorise les boucles pour parcourir la grille : la récursivité sert au backtracking. Les fonctions de résolution **modifient** la grille qu'on leur passe.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_sudoku.png)\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "4a89f645",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:01.638879Z",
     "iopub.status.busy": "2026-10-05T13:32:01.638712Z",
     "iopub.status.idle": "2026-10-05T13:32:01.797612Z",
     "shell.execute_reply": "2026-10-05T13:32:01.796815Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 420x420 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "FACILE = [[5, 3, 0, 0, 7, 0, 0, 0, 0],\n",
    "          [6, 0, 0, 1, 9, 5, 0, 0, 0],\n",
    "          [0, 9, 8, 0, 0, 0, 0, 6, 0],\n",
    "          [8, 0, 0, 0, 6, 0, 0, 0, 3],\n",
    "          [4, 0, 0, 8, 0, 3, 0, 0, 1],\n",
    "          [7, 0, 0, 0, 2, 0, 0, 0, 6],\n",
    "          [0, 6, 0, 0, 0, 0, 2, 8, 0],\n",
    "          [0, 0, 0, 4, 1, 9, 0, 0, 5],\n",
    "          [0, 0, 0, 0, 8, 0, 0, 7, 9]]\n",
    "\n",
    "DIFFICILE = [[8, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "             [0, 0, 3, 6, 0, 0, 0, 0, 0],\n",
    "             [0, 7, 0, 0, 9, 0, 2, 0, 0],\n",
    "             [0, 5, 0, 0, 0, 7, 0, 0, 0],\n",
    "             [0, 0, 0, 0, 4, 5, 7, 0, 0],\n",
    "             [0, 0, 0, 1, 0, 0, 0, 3, 0],\n",
    "             [0, 0, 1, 0, 0, 0, 0, 6, 8],\n",
    "             [0, 0, 8, 5, 0, 0, 0, 1, 0],\n",
    "             [0, 9, 0, 0, 0, 0, 4, 0, 0]]\n",
    "\n",
    "dessiner_sudoku(FACILE)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43594f3a",
   "metadata": {},
   "source": [
    "**Question 36**. Écrire une fonction `possible(G, i, j, v)` qui prend en arguments une grille `G`, les coordonnées $(i, j)$ d'une case et un chiffre `v`, et renvoie `True` si l'on peut écrire `v` dans la case $(i, j)$, c'est-à-dire si `v` n'apparaît ni dans la ligne $i$, ni dans la colonne $j$, ni dans le carré $3 \\times 3$ contenant la case, et `False` sinon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "f2d57e44",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:01.800177Z",
     "iopub.status.busy": "2026-10-05T13:32:01.799939Z",
     "iopub.status.idle": "2026-10-05T13:32:01.803654Z",
     "shell.execute_reply": "2026-10-05T13:32:01.803015Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def possible(G, i, j, v):\n",
    "    for k in range(9):\n",
    "        if G[i][k] == v or G[k][j] == v:\n",
    "            return False\n",
    "    a, b = 3 * (i // 3), 3 * (j // 3)        # coin du carré 3 x 3\n",
    "    for x in range(a, a + 3):\n",
    "        for y in range(b, b + 3):\n",
    "            if G[x][y] == v:\n",
    "                return False\n",
    "    return True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "c9ba4c01",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:01.805793Z",
     "iopub.status.busy": "2026-10-05T13:32:01.805646Z",
     "iopub.status.idle": "2026-10-05T13:32:01.810934Z",
     "shell.execute_reply": "2026-10-05T13:32:01.810196Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "FACILE = [[5, 3, 0, 0, 7, 0, 0, 0, 0],\n",
    "          [6, 0, 0, 1, 9, 5, 0, 0, 0],\n",
    "          [0, 9, 8, 0, 0, 0, 0, 6, 0],\n",
    "          [8, 0, 0, 0, 6, 0, 0, 0, 3],\n",
    "          [4, 0, 0, 8, 0, 3, 0, 0, 1],\n",
    "          [7, 0, 0, 0, 2, 0, 0, 0, 6],\n",
    "          [0, 6, 0, 0, 0, 0, 2, 8, 0],\n",
    "          [0, 0, 0, 4, 1, 9, 0, 0, 5],\n",
    "          [0, 0, 0, 0, 8, 0, 0, 7, 9]]\n",
    "G = FACILE\n",
    "print(possible(G, 0, 2, 1), possible(G, 0, 2, 4), possible(G, 4, 4, 5))\n",
    "print(not possible(G, 0, 2, 5))\n",
    "print(not possible(G, 0, 2, 8))\n",
    "print(not possible(G, 0, 2, 9))\n",
    "print(not possible(G, 0, 2, 7))   # 7 : seulement dans la ligne\n",
    "print(not possible(G, 4, 4, 7))   # 7 : seulement dans la colonne"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa93bc27",
   "metadata": {},
   "source": [
    "**Question 37**. Écrire une fonction `resoudre(G)` qui prend en argument une grille `G`, la complète (en la modifiant) et renvoie `True` si c'est possible, et qui renvoie `False` sinon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "d9d17d68",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:01.812859Z",
     "iopub.status.busy": "2026-10-05T13:32:01.812686Z",
     "iopub.status.idle": "2026-10-05T13:32:01.816691Z",
     "shell.execute_reply": "2026-10-05T13:32:01.815938Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def resoudre_aux(G, c):\n",
    "    if c == 81:\n",
    "        return True\n",
    "    i, j = c // 9, c % 9\n",
    "    if G[i][j] != 0:                             # case donnée par l'énoncé\n",
    "        return resoudre_aux(G, c + 1)\n",
    "    for v in range(1, 10):\n",
    "        if possible(G, i, j, v):\n",
    "            G[i][j] = v\n",
    "            if resoudre_aux(G, c + 1):\n",
    "                return True\n",
    "    G[i][j] = 0     # on efface avant de revenir en arrière : sinon la case\n",
    "    return False    # garderait une valeur qui fausserait les tests possible\n",
    "\n",
    "def resoudre(G):\n",
    "    return resoudre_aux(G, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "50bc2db5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:01.818859Z",
     "iopub.status.busy": "2026-10-05T13:32:01.818653Z",
     "iopub.status.idle": "2026-10-05T13:32:02.021073Z",
     "shell.execute_reply": "2026-10-05T13:32:02.019854Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "FACILE = [[5, 3, 0, 0, 7, 0, 0, 0, 0],\n",
    "          [6, 0, 0, 1, 9, 5, 0, 0, 0],\n",
    "          [0, 9, 8, 0, 0, 0, 0, 6, 0],\n",
    "          [8, 0, 0, 0, 6, 0, 0, 0, 3],\n",
    "          [4, 0, 0, 8, 0, 3, 0, 0, 1],\n",
    "          [7, 0, 0, 0, 2, 0, 0, 0, 6],\n",
    "          [0, 6, 0, 0, 0, 0, 2, 8, 0],\n",
    "          [0, 0, 0, 4, 1, 9, 0, 0, 5],\n",
    "          [0, 0, 0, 0, 8, 0, 0, 7, 9]]\n",
    "DIFFICILE = [[8, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "             [0, 0, 3, 6, 0, 0, 0, 0, 0],\n",
    "             [0, 7, 0, 0, 9, 0, 2, 0, 0],\n",
    "             [0, 5, 0, 0, 0, 7, 0, 0, 0],\n",
    "             [0, 0, 0, 0, 4, 5, 7, 0, 0],\n",
    "             [0, 0, 0, 1, 0, 0, 0, 3, 0],\n",
    "             [0, 0, 1, 0, 0, 0, 0, 6, 8],\n",
    "             [0, 0, 8, 5, 0, 0, 0, 1, 0],\n",
    "             [0, 9, 0, 0, 0, 0, 4, 0, 0]]\n",
    "def est_solution(G, initiale):\n",
    "    \"\"\"G est-elle complète, valide, et conforme aux chiffres de initiale ?\"\"\"\n",
    "    for i in range(9):\n",
    "        for j in range(9):\n",
    "            if initiale[i][j] != 0 and G[i][j] != initiale[i][j]:\n",
    "                return False\n",
    "    lignes = [G[i] for i in range(9)]\n",
    "    colonnes = [[G[i][j] for i in range(9)] for j in range(9)]\n",
    "    carres = [[G[3 * a + x][3 * b + y] for x in range(3) for y in range(3)]\n",
    "              for a in range(3) for b in range(3)]\n",
    "    return all(sorted(z) == list(range(1, 10))\n",
    "               for z in lignes + colonnes + carres)\n",
    "for initiale in [FACILE, DIFFICILE]:\n",
    "    G = [ligne.copy() for ligne in initiale]\n",
    "    print(resoudre(G) and est_solution(G, initiale))\n",
    "# la case (0, 8) ne peut recevoir aucun chiffre\n",
    "G = [[1, 2, 3, 4, 5, 6, 7, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 9]]\n",
    "G = G + [[0 for j in range(9)] for i in range(7)]\n",
    "print(not resoudre(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "c06e9dfb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:02.023226Z",
     "iopub.status.busy": "2026-10-05T13:32:02.023042Z",
     "iopub.status.idle": "2026-10-05T13:32:02.375848Z",
     "shell.execute_reply": "2026-10-05T13:32:02.374636Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 420x420 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualisation : titre vert si le résultat est correct, rouge sinon.\n",
    "DIFFICILE = [[8, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "             [0, 0, 3, 6, 0, 0, 0, 0, 0],\n",
    "             [0, 7, 0, 0, 9, 0, 2, 0, 0],\n",
    "             [0, 5, 0, 0, 0, 7, 0, 0, 0],\n",
    "             [0, 0, 0, 0, 4, 5, 7, 0, 0],\n",
    "             [0, 0, 0, 1, 0, 0, 0, 3, 0],\n",
    "             [0, 0, 1, 0, 0, 0, 0, 6, 8],\n",
    "             [0, 0, 8, 5, 0, 0, 0, 1, 0],\n",
    "             [0, 9, 0, 0, 0, 0, 4, 0, 0]]\n",
    "G = [ligne.copy() for ligne in DIFFICILE]\n",
    "resoudre(G)\n",
    "dessiner_sudoku(G, DIFFICILE)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22e84e87",
   "metadata": {},
   "source": [
    "**Question 38**. Plutôt que de traiter les cases dans l'ordre, on peut choisir à chaque étape la case vide qui a le **moins de chiffres possibles**, et revenir en arrière dès qu'une case vide n'en a aucun. Écrire une fonction `resoudre_mieux(G)`, de même argument et de même résultat que `resoudre`, qui suit cette stratégie. Comparer, pour la grille `DIFFICILE`, le nombre d'appels récursifs **et** le temps de calcul des deux méthodes : le résultat peut surprendre, l'expliquer.\n",
    "\n",
    "La grille `ANTI` ci-dessous a été conçue pour piéger la première méthode : ne pas lancer `resoudre` dessus (plusieurs minutes), mais seulement `resoudre_mieux`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "a47345f7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:02.378000Z",
     "iopub.status.busy": "2026-10-05T13:32:02.377834Z",
     "iopub.status.idle": "2026-10-05T13:32:02.381731Z",
     "shell.execute_reply": "2026-10-05T13:32:02.380889Z"
    }
   },
   "outputs": [],
   "source": [
    "ANTI = [[0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 0, 3, 0, 8, 5],\n",
    "        [0, 0, 1, 0, 2, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 5, 0, 7, 0, 0, 0],\n",
    "        [0, 0, 4, 0, 0, 0, 1, 0, 0],\n",
    "        [0, 9, 0, 0, 0, 0, 0, 0, 0],\n",
    "        [5, 0, 0, 0, 0, 0, 0, 7, 3],\n",
    "        [0, 0, 2, 0, 1, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 4, 0, 0, 0, 9]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "9a85df0b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:02.383819Z",
     "iopub.status.busy": "2026-10-05T13:32:02.383647Z",
     "iopub.status.idle": "2026-10-05T13:32:02.388319Z",
     "shell.execute_reply": "2026-10-05T13:32:02.387554Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def candidats(G, i, j):\n",
    "    liste = []\n",
    "    for v in range(1, 10):\n",
    "        if possible(G, i, j, v):\n",
    "            liste.append(v)\n",
    "    return liste\n",
    "\n",
    "def resoudre_mieux(G):\n",
    "    # recherche de la case vide ayant le moins de candidats\n",
    "    meilleure = None\n",
    "    for i in range(9):\n",
    "        for j in range(9):\n",
    "            if G[i][j] == 0:\n",
    "                c = candidats(G, i, j)\n",
    "                if meilleure is None or len(c) < len(meilleure[2]):\n",
    "                    meilleure = (i, j, c)\n",
    "    if meilleure is None:            # plus de case vide : grille complète\n",
    "        return True\n",
    "    i, j, c = meilleure\n",
    "    for v in c:           # si c est vide, retour en arrière immédiat\n",
    "        G[i][j] = v\n",
    "        if resoudre_mieux(G):\n",
    "            return True\n",
    "    G[i][j] = 0\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "3defaed0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:02.390255Z",
     "iopub.status.busy": "2026-10-05T13:32:02.390106Z",
     "iopub.status.idle": "2026-10-05T13:32:13.739952Z",
     "shell.execute_reply": "2026-10-05T13:32:13.739122Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "FACILE = [[5, 3, 0, 0, 7, 0, 0, 0, 0],\n",
    "          [6, 0, 0, 1, 9, 5, 0, 0, 0],\n",
    "          [0, 9, 8, 0, 0, 0, 0, 6, 0],\n",
    "          [8, 0, 0, 0, 6, 0, 0, 0, 3],\n",
    "          [4, 0, 0, 8, 0, 3, 0, 0, 1],\n",
    "          [7, 0, 0, 0, 2, 0, 0, 0, 6],\n",
    "          [0, 6, 0, 0, 0, 0, 2, 8, 0],\n",
    "          [0, 0, 0, 4, 1, 9, 0, 0, 5],\n",
    "          [0, 0, 0, 0, 8, 0, 0, 7, 9]]\n",
    "DIFFICILE = [[8, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "             [0, 0, 3, 6, 0, 0, 0, 0, 0],\n",
    "             [0, 7, 0, 0, 9, 0, 2, 0, 0],\n",
    "             [0, 5, 0, 0, 0, 7, 0, 0, 0],\n",
    "             [0, 0, 0, 0, 4, 5, 7, 0, 0],\n",
    "             [0, 0, 0, 1, 0, 0, 0, 3, 0],\n",
    "             [0, 0, 1, 0, 0, 0, 0, 6, 8],\n",
    "             [0, 0, 8, 5, 0, 0, 0, 1, 0],\n",
    "             [0, 9, 0, 0, 0, 0, 4, 0, 0]]\n",
    "ANTI = [[0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 0, 3, 0, 8, 5],\n",
    "        [0, 0, 1, 0, 2, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 5, 0, 7, 0, 0, 0],\n",
    "        [0, 0, 4, 0, 0, 0, 1, 0, 0],\n",
    "        [0, 9, 0, 0, 0, 0, 0, 0, 0],\n",
    "        [5, 0, 0, 0, 0, 0, 0, 7, 3],\n",
    "        [0, 0, 2, 0, 1, 0, 0, 0, 0],\n",
    "        [0, 0, 0, 0, 4, 0, 0, 0, 9]]\n",
    "def est_solution(G, initiale):\n",
    "    \"\"\"G est-elle complète, valide, et conforme aux chiffres de initiale ?\"\"\"\n",
    "    for i in range(9):\n",
    "        for j in range(9):\n",
    "            if initiale[i][j] != 0 and G[i][j] != initiale[i][j]:\n",
    "                return False\n",
    "    lignes = [G[i] for i in range(9)]\n",
    "    colonnes = [[G[i][j] for i in range(9)] for j in range(9)]\n",
    "    carres = [[G[3 * a + x][3 * b + y] for x in range(3) for y in range(3)]\n",
    "              for a in range(3) for b in range(3)]\n",
    "    return all(sorted(z) == list(range(1, 10))\n",
    "               for z in lignes + colonnes + carres)\n",
    "for initiale in [FACILE, DIFFICILE, ANTI]:\n",
    "    G = [ligne.copy() for ligne in initiale]\n",
    "    print(resoudre_mieux(G) and est_solution(G, initiale))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d586c952",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* Pour `DIFFICILE`, `resoudre` fait environ 72 000 appels et `resoudre_mieux` 10 000 : 7 fois moins. Mais chaque appel de `resoudre_mieux` recalcule les candidats de toutes les cases vides, et son temps total est **plus long** : environ 2 s, contre 0,2 s pour `resoudre`. Le choix de la case ne paie que si l'arbre naïf est vraiment grand : pour `ANTI`, `resoudre` fait 88 millions d'appels (4 min), contre 45 000 appels (8 s) pour `resoudre_mieux`. On gagnerait encore en tenant à jour les chiffres déjà utilisés dans chaque ligne, colonne et carré, comme pour les reines dans les compléments du TP."
   ]
  },
  {
   "attachments": {
    "fig_logimage.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "74301fb7",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 14. Logimages (inspiré de X-ENS 2024)\n",
    "\n",
    "Un **logimage** est une grille de $n_l$ lignes et $n_c$ colonnes dont il faut noircir certaines cases. Pour chaque ligne et chaque colonne, on donne la liste des longueurs des **blocs** de cases noires consécutives, dans l'ordre. Une grille est représentée par une liste de listes de 0 (case blanche) et de 1 (case noire), et les indications par deux listes de listes `il` (lignes) et `ic` (colonnes). La fonction `dessiner_logimage(G, il, ic)` du module `dessins` dessine une grille avec ses indications, en rouge celles qui ne sont pas respectées.\n",
    "\n",
    "On s'autorise les boucles pour parcourir les lignes et les colonnes.\n",
    "\n",
    "<div align=\"center\">\n",
    "\n",
    "![Figure](attachment:fig_logimage.png)\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c81756bc",
   "metadata": {},
   "source": [
    "**Question 39**. Écrire une fonction `blocs(L)` qui prend en argument une liste `L` de 0 et de 1 et renvoie la liste des longueurs des blocs de 1 consécutifs de `L`. Par exemple, `blocs([1, 1, 0, 1, 0, 0, 1, 1, 1])` renvoie `[2, 1, 3]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "30a70c50",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:13.742042Z",
     "iopub.status.busy": "2026-10-05T13:32:13.741871Z",
     "iopub.status.idle": "2026-10-05T13:32:13.745134Z",
     "shell.execute_reply": "2026-10-05T13:32:13.744512Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def blocs(L):\n",
    "    resultat = []\n",
    "    courant = 0                    # longueur du bloc en cours\n",
    "    for x in L:\n",
    "        if x == 1:\n",
    "            courant = courant + 1\n",
    "        elif courant > 0:\n",
    "            resultat.append(courant)\n",
    "            courant = 0\n",
    "    if courant > 0:\n",
    "        resultat.append(courant)\n",
    "    return resultat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "d6e8490e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:13.747029Z",
     "iopub.status.busy": "2026-10-05T13:32:13.746861Z",
     "iopub.status.idle": "2026-10-05T13:32:13.750857Z",
     "shell.execute_reply": "2026-10-05T13:32:13.750205Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(blocs([1, 1, 0, 1, 0, 0, 1, 1, 1]) == [2, 1, 3])\n",
    "print(blocs([]) == [])\n",
    "print(blocs([0, 0]) == [])\n",
    "print(blocs([1]) == [1])\n",
    "print(blocs([0, 1, 1, 0]) == [2])\n",
    "print(blocs([1, 0, 1]) == [1, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "472b07ce",
   "metadata": {},
   "source": [
    "**Question 40**. Écrire une fonction `verifie(G, il, ic)` qui prend en arguments une grille `G` et des indications `il` et `ic`, et renvoie `True` si `G` respecte les indications et `False` sinon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "0c3be223",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:13.753639Z",
     "iopub.status.busy": "2026-10-05T13:32:13.753413Z",
     "iopub.status.idle": "2026-10-05T13:32:13.756888Z",
     "shell.execute_reply": "2026-10-05T13:32:13.756306Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def verifie(G, il, ic):\n",
    "    for i in range(len(il)):\n",
    "        if blocs(G[i]) != il[i]:\n",
    "            return False\n",
    "    for j in range(len(ic)):\n",
    "        if blocs([G[i][j] for i in range(len(il))]) != ic[j]:\n",
    "            return False\n",
    "    return True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "f10a2fb7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:13.758956Z",
     "iopub.status.busy": "2026-10-05T13:32:13.758782Z",
     "iopub.status.idle": "2026-10-05T13:32:13.762743Z",
     "shell.execute_reply": "2026-10-05T13:32:13.762175Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "G = [[1, 1, 0], [0, 1, 1], [1, 0, 1]]\n",
    "print(verifie(G, [[2], [2], [1, 1]], [[1, 1], [2], [2]]))\n",
    "print(not verifie(G, [[2], [2], [1, 1]], [[1, 1], [2], [1]]))\n",
    "print(not verifie(G, [[2], [1], [1, 1]], [[1, 1], [2], [2]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdfb15d0",
   "metadata": {},
   "source": [
    "**Question 41**. Écrire une fonction `solutions_naif(il, ic)` qui prend en arguments des indications `il` et `ic` et renvoie la liste de toutes les grilles qui les respectent, en énumérant **toutes** les grilles possibles case par case : la case numéro $k$ est $(k\\ //\\ n_c, k\\ \\%\\ n_c)$. Quelle est sa complexité ? Peut-on l'utiliser pour une grille $10 \\times 10$ ?\n",
    "\n",
    "*Indication* : on pourra écrire une fonction récursive auxiliaire `solutions_naif_aux(k, grille, il, ic, liste)` qui essaie les deux valeurs possibles de la case numéro $k$ dans `grille`, et ajoute à `liste` les solutions trouvées. Attention à ce qu'on ajoute à `liste`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "bd75bb7e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:13.764881Z",
     "iopub.status.busy": "2026-10-05T13:32:13.764716Z",
     "iopub.status.idle": "2026-10-05T13:32:13.769702Z",
     "shell.execute_reply": "2026-10-05T13:32:13.769062Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def solutions_naif_aux(k, grille, il, ic, liste):\n",
    "    nl, nc = len(il), len(ic)\n",
    "    if k == nl * nc:\n",
    "        if verifie(grille, il, ic):\n",
    "            # copie complète : grille va encore être modifiée\n",
    "            liste.append([ligne.copy() for ligne in grille])\n",
    "    else:\n",
    "        i, j = k // nc, k % nc\n",
    "        for x in range(2):\n",
    "            grille[i][j] = x\n",
    "            solutions_naif_aux(k + 1, grille, il, ic, liste)\n",
    "\n",
    "def solutions_naif(il, ic):\n",
    "    grille = [[0 for j in range(len(ic))] for i in range(len(il))]\n",
    "    liste = []\n",
    "    solutions_naif_aux(0, grille, il, ic, liste)\n",
    "    return liste\n",
    "\n",
    "# 2^(nl nc) grilles, chacune vérifiée en O(nl nc) : O(nl nc 2^(nl nc)).\n",
    "# Pour 10 x 10, 2^100 ~ 10^30 grilles : hors de portée.\n",
    "# Erreurs relevées par le jury d'X-ENS 2024 : ajouter grille sans copie\n",
    "# (ou avec une copie superficielle grille.copy()), oublier le facteur nl nc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "191b52ed",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:13.771236Z",
     "iopub.status.busy": "2026-10-05T13:32:13.771045Z",
     "iopub.status.idle": "2026-10-05T13:32:13.840870Z",
     "shell.execute_reply": "2026-10-05T13:32:13.839966Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "il, ic = [[2], [1, 1], [3], [1]], [[3], [1, 1], [3], []]\n",
    "S = solutions_naif(il, ic)          # ce logimage a deux solutions\n",
    "print(sorted(S) == [[[0, 1, 1, 0], [1, 0, 1, 0], [1, 1, 1, 0], [1, 0, 0, 0]],\n",
    "                    [[1, 1, 0, 0], [1, 0, 1, 0], [1, 1, 1, 0], [0, 0, 1, 0]]])\n",
    "print(len(solutions_naif([[1], [1]], [[1], [1]])) == 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "b9aa7d11",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:13.842984Z",
     "iopub.status.busy": "2026-10-05T13:32:13.842809Z",
     "iopub.status.idle": "2026-10-05T13:32:14.022614Z",
     "shell.execute_reply": "2026-10-05T13:32:14.021725Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 236x222 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 236x222 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualisation : titre vert si le résultat est correct, rouge sinon.\n",
    "il, ic = [[2], [1, 1], [3], [1]], [[3], [1, 1], [3], []]\n",
    "for G in solutions_naif(il, ic):\n",
    "    dessiner_logimage(G, il, ic)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c44c5f0",
   "metadata": {},
   "source": [
    "On procède maintenant **ligne par ligne** : on n'essaie pour chaque ligne que les listes compatibles avec son indication, et on revient en arrière dès que le début d'une colonne contredit l'indication de cette colonne.\n",
    "\n",
    "**Question 42**. Écrire une fonction récursive `lignes_possibles(ind, nc)` qui prend en arguments une indication `ind` et un entier `nc`, et renvoie la liste de toutes les listes de longueur `nc` dont les blocs sont donnés par `ind`. Par exemple, `lignes_possibles([2, 1], 5)` renvoie (dans un ordre quelconque) `[1, 1, 0, 1, 0]`, `[1, 1, 0, 0, 1]` et `[0, 1, 1, 0, 1]`.\n",
    "\n",
    "*Indication* : choisir le nombre de 0 placés avant le premier bloc, puis placer les blocs suivants récursivement. On pourra calculer d'abord la longueur minimale d'une liste contenant les blocs `ind`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "9b858b8d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:14.024797Z",
     "iopub.status.busy": "2026-10-05T13:32:14.024588Z",
     "iopub.status.idle": "2026-10-05T13:32:14.029577Z",
     "shell.execute_reply": "2026-10-05T13:32:14.028930Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def place_min(ind):\n",
    "    \"\"\"Longueur minimale d'une liste dont les blocs sont ind.\"\"\"\n",
    "    if len(ind) == 0:\n",
    "        return 0\n",
    "    elif len(ind) == 1:\n",
    "        return ind[0]\n",
    "    else:\n",
    "        return ind[0] + 1 + place_min(ind[1:])\n",
    "\n",
    "def lignes_possibles(ind, nc):\n",
    "    if len(ind) == 0:\n",
    "        return [[0 for k in range(nc)]]\n",
    "    resultat = []\n",
    "    for s in range(nc - place_min(ind) + 1):\n",
    "        debut = [0 for k in range(s)] + [1 for k in range(ind[0])]\n",
    "        if len(ind) > 1:\n",
    "            debut = debut + [0]            # séparateur obligatoire\n",
    "        for fin in lignes_possibles(ind[1:], nc - len(debut)):\n",
    "            resultat.append(debut + fin)\n",
    "    return resultat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "6fcbb977",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:14.031905Z",
     "iopub.status.busy": "2026-10-05T13:32:14.031751Z",
     "iopub.status.idle": "2026-10-05T13:32:14.036470Z",
     "shell.execute_reply": "2026-10-05T13:32:14.035735Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(sorted(lignes_possibles([2, 1], 5))\n",
    "      == [[0, 1, 1, 0, 1], [1, 1, 0, 0, 1], [1, 1, 0, 1, 0]])\n",
    "print(lignes_possibles([], 3) == [[0, 0, 0]])\n",
    "print(lignes_possibles([3], 3) == [[1, 1, 1]])\n",
    "print(len(lignes_possibles([1], 6)) == 6)\n",
    "print(len(lignes_possibles([1, 1, 1], 7)) == 10)\n",
    "print(all(blocs(l) == [2, 1, 3] and len(l) == 12\n",
    "          for l in lignes_possibles([2, 1, 3], 12)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d2a7fd4",
   "metadata": {},
   "source": [
    "**Question 43**. Écrire une fonction `prefixe_compatible(p, ind)` qui prend en arguments une liste `p` de 0 et de 1 et une indication `ind`, et renvoie `True` si `p` peut être le **début** d'une liste dont les blocs sont donnés par `ind`, et `False` sinon. Autrement dit, les blocs **terminés** de `p` doivent être exactement les premiers blocs de `ind`, et un éventuel bloc **en cours** (si `p` finit par 1) ne doit pas dépasser le bloc correspondant de `ind`. Par exemple, `[1, 0, 1, 1]` est compatible avec `[1, 3]` mais pas avec `[1, 1]`, et `[1, 1, 0]` n'est pas compatible avec `[3]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "0c12468b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:14.038399Z",
     "iopub.status.busy": "2026-10-05T13:32:14.038217Z",
     "iopub.status.idle": "2026-10-05T13:32:14.041306Z",
     "shell.execute_reply": "2026-10-05T13:32:14.040805Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def prefixe_compatible(p, ind):\n",
    "    b = blocs(p)\n",
    "    if len(b) > len(ind):\n",
    "        return False\n",
    "    if len(p) > 0 and p[len(p) - 1] == 1:\n",
    "        # le dernier bloc n'est peut-être pas terminé\n",
    "        k = len(b) - 1\n",
    "        return b[:k] == ind[:k] and b[k] <= ind[k]\n",
    "    else:\n",
    "        return b == ind[:len(b)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "54ba0ba0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:14.043125Z",
     "iopub.status.busy": "2026-10-05T13:32:14.042940Z",
     "iopub.status.idle": "2026-10-05T13:32:14.047231Z",
     "shell.execute_reply": "2026-10-05T13:32:14.046572Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "print(prefixe_compatible([1, 0, 1, 1], [1, 3]))\n",
    "print(not prefixe_compatible([1, 0, 1, 1], [1, 1]))\n",
    "print(not prefixe_compatible([1, 1, 0], [3]))\n",
    "print(prefixe_compatible([], [2]))\n",
    "print(prefixe_compatible([0, 0], [2]))\n",
    "print(prefixe_compatible([1, 1], [3, 1]))\n",
    "print(not prefixe_compatible([1, 0, 1], [1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49e5040f",
   "metadata": {},
   "source": [
    "**Question 44**. Écrire une fonction `resoudre_logimage(il, ic)` qui prend en arguments des indications `il` et `ic` et renvoie la liste de toutes les solutions, par backtracking ligne par ligne. Résoudre le logimage $10 \\times 10$ dont les indications `IL` et `IC` sont données dans la cellule de tests, et compter le nombre d'appels récursifs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "14281d26",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:14.049056Z",
     "iopub.status.busy": "2026-10-05T13:32:14.048886Z",
     "iopub.status.idle": "2026-10-05T13:32:14.053200Z",
     "shell.execute_reply": "2026-10-05T13:32:14.052586Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [],
   "source": [
    "def resoudre_logimage_aux(grille, possibles, il, ic, liste):\n",
    "    i = len(grille)                     # nombre de lignes déjà placées\n",
    "    for j in range(len(ic)):            # élagage sur les débuts de colonnes\n",
    "        if not prefixe_compatible([grille[k][j] for k in range(i)], ic[j]):\n",
    "            return\n",
    "    if i == len(il):\n",
    "        # les débuts de colonnes ne suffisent plus : un bloc peut manquer\n",
    "        if verifie(grille, il, ic):\n",
    "            # grille + [ligne] est une liste neuve, mais ses lignes sont\n",
    "            # partagées avec possibles : il ne faut pas les modifier ensuite.\n",
    "            liste.append(grille)\n",
    "        return\n",
    "    for ligne in possibles[i]:\n",
    "        resoudre_logimage_aux(grille + [ligne], possibles, il, ic, liste)\n",
    "\n",
    "def resoudre_logimage(il, ic):\n",
    "    possibles = [lignes_possibles(ind, len(ic)) for ind in il]\n",
    "    liste = []\n",
    "    resoudre_logimage_aux([], possibles, il, ic, liste)\n",
    "    return liste"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74fd967d",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* En comptant les appels (par exemple avec une liste `cpt` à un élément), on trouve 10 499 appels pour ce logimage $10 \\times 10$, contre $2^{100} \\approx 10^{30}$ grilles pour la méthode naïve. Les logimages de la question suivante, plus difficiles, demandent quelques centaines de milliers d'appels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "d2b6692d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:14.054824Z",
     "iopub.status.busy": "2026-10-05T13:32:14.054665Z",
     "iopub.status.idle": "2026-10-05T13:32:14.144631Z",
     "shell.execute_reply": "2026-10-05T13:32:14.143960Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Tests : chaque ligne doit afficher True.\n",
    "IL = [[], [4], [1, 1], [1, 1, 1, 1], [1, 1],\n",
    "      [1, 1, 1, 1], [1, 2, 1], [1, 1], [4], []]\n",
    "IC = [[], [4], [1, 1], [1, 1, 1, 1], [1, 1, 1],\n",
    "      [1, 1, 1], [1, 1, 1, 1], [1, 1], [4], []]\n",
    "S = resoudre_logimage(IL, IC)\n",
    "print(len(S) == 1, verifie(S[0], IL, IC))\n",
    "il, ic = [[2], [1, 1], [3], [1]], [[3], [1, 1], [3], []]\n",
    "print(sorted(resoudre_logimage(il, ic)) == sorted(solutions_naif(il, ic)))\n",
    "print(resoudre_logimage([[1]], [[1], [1]]) == [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "9eb2ab11",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:14.146869Z",
     "iopub.status.busy": "2026-10-05T13:32:14.146707Z",
     "iopub.status.idle": "2026-10-05T13:32:14.402008Z",
     "shell.execute_reply": "2026-10-05T13:32:14.401338Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 502x474 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualisation : titre vert si le résultat est correct, rouge sinon.\n",
    "IL = [[], [4], [1, 1], [1, 1, 1, 1], [1, 1],\n",
    "      [1, 1, 1, 1], [1, 2, 1], [1, 1], [4], []]\n",
    "IC = [[], [4], [1, 1], [1, 1, 1, 1], [1, 1, 1],\n",
    "      [1, 1, 1], [1, 1, 1, 1], [1, 1], [4], []]\n",
    "for G in resoudre_logimage(IL, IC):\n",
    "    dessiner_logimage(G, IL, IC)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2b868b6",
   "metadata": {},
   "source": [
    "**Question 45** *(bonus)*. Les indications de trois logimages mystères sont données ci-dessous. Les résoudre avec `resoudre_logimage`, vérifier que chacun a une seule solution, et dessiner les solutions avec `dessiner_logimage`. Quels animaux reconnaît-on ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "fb02e5f7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:14.404594Z",
     "iopub.status.busy": "2026-10-05T13:32:14.404415Z",
     "iopub.status.idle": "2026-10-05T13:32:14.411866Z",
     "shell.execute_reply": "2026-10-05T13:32:14.411297Z"
    }
   },
   "outputs": [],
   "source": [
    "# Trois animaux mystères (19 x 18, 19 x 19 et 16 x 21)\n",
    "IL_1 = [[1], [2], [2], [3, 1], [2, 2], [2, 3], [5, 3], [6, 5], [3, 4, 2, 2],\n",
    "        [10, 2, 2], [12, 2, 1], [14, 2], [3, 10, 3], [2, 10, 2], [9, 1],\n",
    "        [7, 2], [6, 1], [5, 2], [5, 1]]\n",
    "IC_1 = [[2], [2, 4], [3, 5], [3, 4], [3, 6], [9], [2, 6], [10], [12], [14],\n",
    "        [11], [2, 10], [3, 9], [4, 8], [1, 2, 6], [2, 3], [2, 8],\n",
    "        [2, 2, 1, 1]]\n",
    "\n",
    "IL_2 = [[1, 1, 1], [1, 1, 1], [9], [13], [3, 3, 3], [3, 1, 3],\n",
    "        [2, 2, 1, 2, 2], [3, 2, 1, 2, 3], [3, 3, 3], [4, 5, 4], [7, 7],\n",
    "        [6, 5, 6], [6, 5, 6], [2, 4, 4, 2], [3, 11, 3], [4, 4], [4, 4],\n",
    "        [5, 5], [11]]\n",
    "IC_2 = [[9], [12], [9, 4], [3, 5, 3], [2, 5, 3], [1, 2, 5, 2],\n",
    "        [3, 2, 1, 2, 2], [2, 2, 1, 2, 1, 1], [3, 2, 2, 1, 1], [10, 2, 1, 1],\n",
    "        [3, 2, 2, 1, 1], [2, 2, 1, 2, 1, 1], [3, 2, 1, 2, 2], [1, 2, 5, 2],\n",
    "        [2, 5, 3], [3, 5, 3], [9, 4], [12], [9]]\n",
    "\n",
    "IL_3 = [[1, 1], [2, 2], [3, 3], [3, 3], [6], [1, 4, 2], [7, 4], [7, 5],\n",
    "        [4, 7], [14], [13], [8], [1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1],\n",
    "        [2, 2, 2, 2]]\n",
    "IC_3 = [[1], [2], [4, 2], [7], [3, 3], [7, 1], [16], [6, 4], [4, 7], [3, 1],\n",
    "        [3], [3, 1], [7], [4], [3, 4], [3, 1], [4], [5], [4], [4], [3]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "0b9c3f28",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:32:14.413978Z",
     "iopub.status.busy": "2026-10-05T13:32:14.413832Z",
     "iopub.status.idle": "2026-10-05T13:32:25.406328Z",
     "shell.execute_reply": "2026-10-05T13:32:25.405671Z"
    },
    "tags": [
     "corrige"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 solution(s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 782x789 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 solution(s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 845x831 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 solution(s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 887x642 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for il, ic in [(IL_1, IC_1), (IL_2, IC_2), (IL_3, IC_3)]:\n",
    "    S = resoudre_logimage(il, ic)\n",
    "    print(len(S), \"solution(s)\")\n",
    "    for G in S:\n",
    "        dessiner_logimage(G, il, ic)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bed21486",
   "metadata": {
    "tags": [
     "corrige"
    ]
   },
   "source": [
    "*Réponse.* Une licorne (vue de profil : corne, oreille, crinière), la Petite Taupe (vue de face : trois poils, grands yeux, gros nez, bouche ouverte) et le renard du Petit Prince (grandes oreilles, queue touffue). Chaque résolution prend quelques secondes, les indications ont été calculées et l'unicité vérifiée par le script `logimage_inverse.py`."
   ]
  }
 ],
 "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}