{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ee7d77ff",
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   "source": [
    "# TP — Révisions sur la récursivité\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)"
   ]
  },
  {
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   "execution_count": null,
   "id": "ffa0c9ba",
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    "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": null,
   "id": "25fcb9ce",
   "metadata": {
    "execution": {
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     "iopub.status.busy": "2026-10-05T13:31:24.462235Z",
     "iopub.status.idle": "2026-10-05T13:31:24.466161Z",
     "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": null,
   "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": null,
   "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": null,
   "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": null,
   "id": "bf52e423",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.484754Z",
     "iopub.status.busy": "2026-10-05T13:31:24.484584Z",
     "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": null,
   "id": "a8dd3e36",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.490185Z",
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     "iopub.status.idle": "2026-10-05T13:31:24.492656Z",
     "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": null,
   "id": "67b7080f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.494274Z",
     "iopub.status.busy": "2026-10-05T13:31:24.494108Z",
     "iopub.status.idle": "2026-10-05T13:31:24.497049Z",
     "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": null,
   "id": "33041679",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.498620Z",
     "iopub.status.busy": "2026-10-05T13:31:24.498451Z",
     "iopub.status.idle": "2026-10-05T13:31:24.501146Z",
     "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": "reponse-texte-ee6d53b9",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "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": "code",
   "execution_count": null,
   "id": "reponse-code-f0a8d964",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-2d3c6972",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e5376190",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-05T13:31:24.509497Z",
     "iopub.status.busy": "2026-10-05T13:31:24.509347Z",
     "iopub.status.idle": "2026-10-05T13:31:24.512792Z",
     "shell.execute_reply": "2026-10-05T13:31:24.512098Z"
    }
   },
   "outputs": [],
   "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": null,
   "id": "reponse-code-a59b2d86",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-a59b2d86",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": "reponse-texte-08839c8f",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "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": null,
   "id": "reponse-code-9a38f098",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-9a38f098",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-98305236",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-98305236",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-9d8e8d55",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-9d8e8d55",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "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": [],
   "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": {
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NzQ01atTQSGoAoFatWupk8MKFC3lyvjm1fft2jBw5EgcPHsS4cePS7f/666/Rr18//Pjjj4iIiCjQ2NIKDw9H+/btoVAocOPGDY2kBgAMDAywe/dueHh4qHs/8trRo0exY8eOz65HKpVi9uzZAJDuev/111+wsrLC5cuX1UkNAAQGBmLUqFF48eIFKleujMmTJ0MikSA2Nha+vr747bffYGJigqioKCiVSkgkGffYe3l5oW3btmjYsCFOnDiRbkn/EiVKYP369bh06RKOHz/+2eeaG6ofHr70xwwcP34cPXv21EjOx48fjyVLlmDhwoXo2bMnDhw4gCFDhmD8+PG4ceOGutzw4cPx3XffQakUbx4sExsiIgKQ+jBVQ0NDNG7cON2+kJAQAMCbN28KOqx0nJ2dAQBfffVVhvtDQkIgk8ng7+//We3ExcXh1atXn1WHiqGhIUaPHo2UlBRs374dQOrN8ogRI7Bz506UKlVKo7yFhQXatWsHZ2dnDBo0CGZmZgAAFxcX2NraokOHDgAAT09P+Pv7o3Xr1lm2//DhQ8TGxmb5ngEFe33/+ecfTJo0CbNnz0a7du0yLdeoUSOEh4fj8uXLBRZbWoIgoGfPnggJCcGePXsy7YmoVq0aTExMcPjw4XyJIyAgAB8+fMiTurp164by5cvj+vXr8PDwAABcvXoVJ0+exPbt29MlJu3bt4epqSlu3bqF77//Xr399u3b+Oabb9RD1y5duoSWLVtm2OsXGxuLjh07onjx4li7dm26/Sqq4a759T5m5MOHDzh06FChGvIolkOHDmkMQ0tISMA///yDVatWaZQbMmQIBEHQWMHU2toaOjo66u84MTCxISIixMTEwN3dHc2aNctwGI2TkxOA9L05YnB2doZUKkWrVq3S7fPz84Ovry9sbW1Ru3ZtEaLL3IQJEyCVStW9SUOHDsX69etRrly5TI9xcnLSuOl3dnZGjx491Deex44dQ7t27WBhYYEDBw5kWk9WyaAgCLh58yYkEkmBXV+ZTIapU6fC2toaixYtyrJs+fLlAUB9A17QduzYgbt372LBggWwtbXNtJxEIoGDgwO8vb0L/eRziUSCiRMnAgA2b96Me/fuYdOmTdi7d2+mw7Dc3d2RkpKi8Xyxmzdvonfv3urXx48fx6BBg/DgwQM8ffpU4/glS5bAz88Pa9asUSdCGSlTpgz09PQK9HqvW7cu0x91FIr0z75QPUQ6LZmscAybzije5OTkHB377t07+Pn5oU2bNhrbjYyMcPfuXY2e4ZIlS0IikeDBgwcaZdu3b49FixaJtqAGExsiIoKLiwuUSmWGN77h4eH45ZdfULduXdEXaElJSYGrqyvq1q2bbpK2IAiYNWsWTE1NC3wYS06UK1cO3bt3R2BgIFq3bo2lS5eiRo0amZb38/PDu3fvNG4ynJ2d0bZtW/XrV69eoXPnzti8eXO2CZJUKs2wZ2fbtm14/fo1Vq5cqTH8KD9t3boVb9++xbBhw7KdJK7qTUpJSSmI0DTIZDIsWLAAhoaGGDp0aLblQ0JCoFQqC31iA0A96X///v1YunQpDh8+nGXC4eTkhGbNmqmv1/PnzxETE4MWLVoAAORyOby9vdGqVSts3boVVapUUR/r7++PTZs2wcHBAR07dswyrsjISKSkpBTo9T58+DCaNm0KHR0dje1TpkzBwIEDMWPGDCiVSixZsgRz5szB+PHj0aJFC4SEhMDd3R0//PADFixYgAYNGmDv3r0FFvfH1qxZg3HjxqFr166QyWTYuXMnZs+ejVmzZqFhw4bZ9kAfPnwYgwYN0thmbGyM169f4+nTpxo9effu3YMgCOohsSotW7ZEWFgY/vzzz7w7sVzg4gFERKTukSldurT6l9KAgAA8fPgQf/zxB/r06YMVK1bAwsIiy3p27NiBJ0+e5KrtUaNGoX79+jkq6+bmhsTERFStWlUdZ0xMDF69eoVNmzbBzMwMN27cyHF9BW3SpEk4d+4czMzM0KhRoyzLSiQSrF27Vr2CGQAMHDgQPXr0UL9esmQJ9u3bh6ZNm2bYgwWkrkB1+/ZtODg4ICQkRD1U782bNzh16hTu37+PAwcOYPDgwXlzkjlw8OBBAMhRsuDp6QkA6W6gPnb06FG4uLjkKo7+/fun+3U6rUuXLiEsLAx9+/bN9rMfGRmJ8PBwVKhQQbTV5XLDwsICgwcPxs6dO9GhQ4ds55ZUqFBBo3fN0NAQGzZsgLGxMQBAV1cXR44cwYEDB/Dzzz9rJEnHjh2DTCbD4MGDM51/o+Ll5QUg++udV8LCwhAcHJzuR4ZLly6hbt26qFu3Lho3bgwvLy+sWrUK1apVA5D6Q8W4ceNQr149rF69GkDqnLEZM2Zg2LBh6ZKktBISEvDzzz/nKgE2NTXFkiVLMk0+/fz88PbtW+zatQv6+vpo27Yt5s2bhzFjxgBIna+2fPly9d+9jBw8eDDDH4Uy6qk8ffo0jIyMNBafAP67bidOnMBPP/2U09PLM0xsiIgIzs7O0NHRgY+Pj3qZbUNDQ1SuXBn3799PN+E8M/Xq1YOlpWWu2ra2ts5xWVUCplQqcfToUQCpk6EdHBywc+dO1KlTJ1dtF7SjR4+iePHiuHfvHh4/foy6detmWtbe3h5Tp07V2LZw4UKN1xUrVsSyZcuybPPhw4eIiYlBtWrV1O8ZkHqzMmbMGOzfvz/Lm7C8Fhsbi0ePHsHc3DxHwwUvXboEANmWrVmzZq5XdMvuc62aGJ1Z0piWag5QYRsCmZnAwED1s8L+/PNPzJgxI8vyX3/9tcbrihUromLFihrbevbsmeE8ldy8jzm93nlF9R58nEgdOnQImzZtUs8hGTdunDqpAVKHd4WGhmoke3K5HDExMYiPj0exYsUybdPQ0FC9zHtO6erqZvn5PnHiBAYOHAgPDw8oFAq0a9cO3bp1U+9PSUnJ8qGbjx49goGBQZa9yCqHDx9WL/DwcXlbW1tYWlri8ePH2Z9UPmBikwfefAjB5PVHsy9YADaevAFT48y7kvNbaGSs+s9ivyeJstQvjIt3X8Dd6/MmEeeVw5duwthQvOsTGROn/vOKvX+JFgcAJP//+rg89sAr37yZEPu5xL4+YVExorQbGxsLd3d31K1bV2OZ50/RsGHDfH3WjWquyKpVq9JNuP9Unp6emD59erqVfJKSkuDv748uXbqkO8be3j7XK1RNnz4drVu3Rs2aNfHDDz9g8+bNebLKVXZU79n48eNFXzIZgHpRh5z8Iu/p6YnXr1+jdevW2SatNWvWRM2aNfMkRpX379+r686O6gb442Q0t3bv3p3hr+bv3r2DXC7H3bt30+0bPHgwhg8fnuM2IiIi8N133+HAgQMYOnQo7t27hytXruTbHKvcvI9nz56FgYEBxo8fny+xfOzFixcAgMqVK2ts//XXX2Fubo6bN2/C3t4evXr1Uu979+4dQkJC0g3NvX37NhwdHbNMaoDUH2PSzk3KCwMHDkTp0qXVS6ZPmjRJvU+pVOLu3btZPt/r40UDMuPn54fp06fjzz//1FhiXhAEdW9c5cqV82zhldxiYpMHYhOS8cizcNw4e74PETsEtcLyngSGRyMwvHA8FfpdUKjYIah5+L4XOwQAQGhUDEJFuqH/WGG6PgXJxcUFCoUiyyE5hYFcLoerqysqVKiQbVLz+vVrODs7Z7iE8MfKlSuHBQsWpFsyOTg4GLNmzUrXSwIg10vCLl68GOXLl8d3332HqKgoLFiwAEeOHMGqVauyHeL0uVSJTVbX19PTE4cPH0ZCQgKaNm2KPn36ZDtk6FOpeuhy8iBLVaL9uQn3pypevDiA7GN9+fIlTp06hfbt22c4j+mvv/5CyZIlNSbeZ6Zbt26oWrVquu1Hjx5FXFycemhRWg4ODtnWqxIfH4+hQ4di7dq1cHR0xKRJk3Dv3j1s3rw53xKbnL6P586dg7u7OyZOnIiyZcuqt0dGRmLPnj14//49qlSpgqFDh+bZssxBQUEAUoekpWVvbw8gtZe4ffv2GvtUQx7TzkmUy+W4fPlygQ7pTEv1sEwnJydUr15dY0ny27dvIyoqKsMfaYDUxOf48eO4f/9+lm1ERUWhT58+2Lp1a7ql8NN+X4SGhqZLFAsKE5vP8FVNewDZf0kVBOfnqUlEnfI2sDAR7xfnqPgkPPFJvTlsU9NetDgA4LFPCKLjk+FgUwzlbMR9ICivT3q8Ppkr6PcjJze+OTV9+nSN5xrkxPLly3O0zKqbmxsSEhKyXNr4+vXr2LlzJ/z9/aFQKHKU2Ojr66NZs2bptvv7+8PIyChHN6NZ2bBhAyQSCaZNmwbgv7kNu3btwu7duzFz5szPqj8rSqUSLi4usLe3z3RxAWdnZxw5cgTz5s1DXFwcxo4di3379uH06dP58qBCGxsb2NraagyLEQQBDx48gL29vfqG7OHDhzh69CjGjRuXoyFMy5Ytw8mTJ3MVy8yZM7PsxVL1EgUEBKBBgwYAUhcI8PHxQaNGjdTvz+zZs2Fubo6NGzdqHL9ixQq8fPkSN27cwKxZs3L0WbKzs0v3nBwAuHv3LmJiYj7r8yiTyTBkyBAsWrRI3XvSv39/zJo1CxcvXoSvr2+Wi1B8qjp16sDJyQkBAQHqRQV8fX0RFRWlHo6pUCgwZ84cVKpUCYsXL1YfGxwcjIkTJ2LhwoWwsbHBsmXLsGrVKri6usLGxuazY1MlSC9fvkSfPn009qlWWfx4URXV3ynVin1A6hC6yMhIDBw4EEDqXKFKlSpl2GZMTAzatm2bqzk2JiYmuHLlCkxNTbMs5+TkhP79+2tsO3LkCKytrdG2bVuEhITAwMBAI8m8du0aqlWrluXQTJlMhkGDBuG3335TLzcPADNmzMC6devUr5OSkuDr6yveD2UCERF90Zo2bSro6uoKkZGRn11XQkKCEBwcnKv/5HJ5jupesWKFIJVKhf3792dbdsOGDUKzZs0+61z8/PyE6tWrf1Yd69evFyZOnJhu++PHjwWpVCpUrFjxs+rPzoMHDwSJRCIMGzYs0zK9evUSfv31V/VrNzc3QSqVCs7Ozhrl4uLi8iyu2bNnC0ZGRkJAQICQkpIiDBkyRPjjjz+Efv36Ce/fvxe8vb2FKlWqCP369ROUSmWO6kxKSsr1Z08mk2VZZ0BAgFCsWDFh+vTpgiAIwtmzZ4XRo0cLa9euFRYtWiQIgiAsWbJEMDMzE+7evZtpPa1atRLWrl2bszcnE2vWrFG3+SliYmKEXr16CVevXk23b968eYJUKhV++umnz4gwc25uboKurq6wZcsWQRBS/37++OOPwvz584Vdu3YJKSkpwogRI4TSpUsLPj4+GseuWbNG6Ny5s/q1QqEQzM3NhaVLl+ZJbK9fvxakUqkwZMiQdPv27dsnSKXSdDFVqVJFGD58uMa2UaNGCeXLlxcEIfVzsmvXrizbDQ8Pz9VnNTw8PNtz8fDwEKRSqXDs2DGN7ba2turvoQkTJgiBgYEa+4cPHy7s3bs303qVSqUwcuRI4caNGxrbP3z4IIwcOVJjm7u7uyCVSoV169ZlG29+YI8NEdEXKiUlBTdv3sSDBw9QpkyZPPl13sjICEZGRnkQ3X+USiXCwsKwa9cuAKnPNVEqlfnSm5AXUlJScOfOHWzatAmnTp1Sr+qVlrGxMWxsbPD27Vvs3LkTw4cPz/D5QZ8jISFB/SDESpUqQSaTZdhGly5dNN5L1QpI4eHh6m07d+7EpEmTsGPHjlzN5cjMwoULcebMGUyZMgUjRoxAt27dMHjwYNSuXRvz58/HtWvX8O233+LXX3/N8ZA4AwODPPkFP62SJUti5cqV+OGHH9C/f3+cOXMGu3fvBgD069cPo0aNwsOHD3H58mU0adIkT9vOK+Hh4fj3338xf/582NjYpPslXRAE9SIA27dvx9ixY1G+fPk8/fvVsGFDTJkyBcuXL0e7du3w+PFj9fvYvXt3HD16FHK5HDdu3EjXY9S4cWO8fftW/VoqlcLa2jrd0LFPVblyZbRq1QqPHj1Kt8/Z2Rlly5bViCkgIABeXl6YM2eORtnIyEh07twZCoUCx48fz3b+XNrVDvOKqvc9ba+2TCZDYmIiOnfuDG9vb+jq6mr0CCYkJODy5cvYvHlzpvXOmjULR44cwblz59TbFAoF4uLisHz5co2yqvcxu4cG5xeJIHw0qJiIiIq8d+/eYcyYMdDT04Oenh6USiWSk5MxdOjQPLlxzUvfffcdgoOD1TflKSkpKFu2rHqSbEY2btyIo0ePwtXV9ZPbVS0coJpcnFOzZ8/G8+fPoaenB5lMBmtra42HZ4aEhGDo0KHQ1dWFnp6eemWkw4cP59l8mz/++APnz5+Hvr4+pFIp5HI5FAoFDh06pJ7vkJmNGzdixYoV8PT0hJmZGYDUhzNOmjQJlpaWuHDhQp7EGB8fj7lz5+LChQvqif/Xr19HZGQkzp49qx6ydPXq1WyffZLf/v33X8ybNw8BAQEYO3YsvLy8cO7cOfz444+YM2cOpFIpXr16BVNTU5QpUybd8a1bt0afPn2yXXksK2vXrkVMTIzGMK3sREVFYdCgQerVtJKTkzFgwACNeTp//fUXtm3bpv6syGQy1KlTB7/99tsnx5qZQ4cOYf369YiMjMSIESPw9OlT/P3339i3bx++/fZbAKnzQerXr5/pDySPHz9Go0aNcOvWLTRt2jRP4nr06BGaNGmCd+/eaczf+/bbb1G9enWNlc8ePnyIQYMG4eHDh+q/H0Dqc11+//132NjY4Pvvv89yxcP8smrVKty8eVMjAQFSnxt169YtFC9eHL/99pt6iW4A6oTl8OHDGdaZmJiIHj16pFtcRWXp0qUaQ0WHDBmCwMBAXL9+PQ/O6BOI0k9ERESUjwrLUDRt4+HhIVSsWFFwd3dPt8/X11f4/vvv86Vdb29vwcvLS/j333+FSpUqqbf//fffwpQpU/KlzU8RFxcnPH78WIiIiBDatGkjHDlyRBCE1OFRzZo1E0JCQjI8Li+GoqUd/qbtIiIihCdPnghxcXFCyZIlhYcPHwqCIAhRUVFC/fr1Mx1+GB8fLzRs2DBHw1Fza/To0cK+ffvyvN7Crlu3bsL58+fzpC6lUinY2dkJly5dypP6PgWHohEREWWgdOnS6SaDF2Wenp4YN24czp8/r/HUeCD1V+olS5Zgw4YN+dK2o6MjgNReMm9vb/Ts2RMmJiY4d+4cHj58mC9tfgoTExP1ggIKhQLTpk3DvXv3cP78eTRv3hwlSpTIt7b79OkDmUyWb/UXJEtLS/XzrhQKBQYMGIAePXrg2LFjmDx5cobDD+Pj4zFgwAAsWLBAY+nlvLJmzRpMnjy50PVY56fQ0FA8fvwYnTt3zpP6zpw5g7p16+ZZfZ+icA5QJiIiEplUKk23zGtR9erVKyxYsACnT59GlSpV0g1nkUgkOHLkiMYqUPmhWrVq0NPTw8WLF3HixAksX748w6WPC4M6deogLCwMGzduhCAIWL9+fb62V65cOdGW0M1PderUwdu3b7Fx40ZUqlQpw6fVq5a5Xr58OXr16gWZTIZ58+blaRzm5uaYPHmyeEOoRHD06FH07ds31w+2zUhSUpL6762Y2GNDRERFTkJCApKSksQOQyt4eHigS5cu6NChAxYsWAClUolHjx5h37596jL169cvkFjs7Oxw+vRp3LhxA3369MlwGe7CYvny5bC0tETp0qUxaNCgLJ/RkpiYiISEhAKMTnvs2LEDW7ZsQZ06dTK8yY6Li0PXrl1hZWWFHTt2QBAEBAQEZPpMls/RpEkT7Nu3D8nJyTAwEH/p//x28ODBPOuVPnXqFJYvX57tctT5jYsHEBFRkfH48WP8+eefiI+PB5D6jJqmTZti7NixIkdWeC1fvjzD4V4nTpzIk19yv2S7d++Gq6srkpOTAaQOZRs3blyBJYpFwZkzZzSSbJXFixerhwXSp5k8eTI2bdokdhh5iokNERERERFpPc6xISIiIiIircfEhoiIiIiItB4TGyIiIiIi0npMbIiIiIiISOsxsSEiIiIiIq3HxIaIiIiIiLQeExsiIiIiItJ6TGyIiIiIiEjrMbEhIiIiIiKtx8SGiIiIiIi0HhMbIiIiIiLSekxsiIiIiIhI6zGxISIiIiIircfEhoiIiIiItB4TGyIiIiIi0npMbIiIiIiISOsxsSEiIiIiIq3HxIaIiIiIiLQeExsiIiIiItJ6TGyIiIiIiEjrMbEhIiIiIiKtx8SGiIiIiIi0HhMbIiIiIiLSerpiB6DNXDYvxu3NS8QOg4iKGPtGbTB4n5PYYRAREWkV9tgQEREREZHWY49NHrAp54j2o8aLGsORhbMBAO1GfQ/bchVEi+PVnVtw/+ccAGDQ0t9FiwMATv66CClJiajZtiNqte0oaiyq69O2T2/YlCklWhyvHz/F41u3AQDfTpkgWhwAcGr7bqQkJ6NG44ao2aSRqLEc+2MrAPGvz/N7bnhx/4Fo7RMREWkzJjZ5wMDEFGVr1hY7DACAbbkKosYS7OOt/rPY74lURwcAYG5jK3osKjZlSsG+oniJZ8iHAPWfxYwDAKTS1A5jcysr0WNREfv6+Ht5Z1+IiIiIMsTEhrKmZwToGea4uJl9Zdg3apP6wtgyd20lxQJKee6OocLDskyuipdp0Aqy5GSYV6idu2PlMiA2JJfBERERUVHHxIYypmcElKwJGFvl6rCqZRuj6sCZn95u2BsgjL9aaxNJ2fqQODaDJBcJMAD0a/jtJ7cpJEZD+eIyEOn/yXUQERFR0cLFAyg9qS5QtlGuk5o8YV0RsKla8O3SpylREdIqbXOd1HwuiZE5dBoOAMxsCrRdIiIiKryY2FB6Vg6pPTZitm9gJl77lGPSGp3Fbd+xmajtExERUeHBoWiUXi57akJDQ/Hy5UskJCSgVq1aKFMmd3MtMo0hOfbz66H8Y2aT656aFy9ewMfHB9bW1qhduzaMjY0/KwSJTcXPOp6IiIiKDvbY0Cd7/Pgxevfuje+//x6vXr2Cl5cXhg4divr16+PFixefV7kOc+5CT9cgR8WUSiU2bdqE5s2bY9++fYiKisLRo0dRrVo1/PDDD5DJZPkcKBEREX0JiuTd47Fjx3Dw4EG4ubmhZMmSaNasGZYtW4bixYuLHVqRoFQqMX/+fBw8eBCHDx9Gy5Yt1fumTp2K2bNno1GjRrh//z5q1qwpYqQkNk9PTwwfPhxlypTBlStXYGpqCgAYOnQo5s+fj0aNGuH58+e4dOmSyJESERGRtityPTZr167F4MGDce/ePbRp0wZGRkbYtm0bWrVqhYCAgOwroGyNHj0ae/fuxZ07dzSSGpWVK1fC1tYWEydOFCE6KizevHmDtm3bol69ejh58qQ6qVGxtrbGhg0bcPXqVRw9elSkKImIiKioKFKJTVBQEObMmYOSJUvi8ePHOHbsGFxdXbFo0SK8evUKv/zyi9ghar2FCxdi//792LVrF0qXLp1hGalUinr16sHFxQX+/lyO90sUGxuLjh07wtLSEuvXr8+0XMOGDSEIAg4fPlxwwREREVGRVKQSm/3790Mul2PChAkoVaqUevvcuXNhYmKCI0eOICkpScQItZuXlxd+//13dO/eHV27ds2ybPny5QEAL1++LIjQqJBZtmwZ3r17h9WrV8PAIPO5OKVKlYKBgQE8PDwKMDoiIiIqiopUYnP58mUAQLt27TS26+npoWXLloiKisK9e/fECK1I+PnnnyGTyTB69Ohsy4aEpD4ZPiUlJb/DokLm/fv32LhxI+zt7dG5c9bLQUdHRyM5OZkLCBAREdFnK1KJTWBgIACgbNmy6faptgUFBRVoTEVFTEwMzp8/D0tLS/To0SPb8p6engCA6tWr53doVMgcP34cMpkMgwYNgkQiybKsl5cXAH5OiIiI6PMVqcQmODgYAGBubp5un2obE5tP4+rqiuTkZDRr1gw6OjpZlg0LC8OjR49QrFgx9ZA0+nLcuHEDANC6detsy6pWQ6tTp06+xkRERERFX5FKbGJiYiCRSDJ86J9qW1RUVAFHVTSoFgGoUaNGtmXPnTsHhUKByZMnZ/uLPRU979+/B5Czz8rZs2ehr6+PCRMm5HdYREREVMQVqcTGysoKgiAgNjb9E+tV28zMzAo6rCLB2toaQMa9YWnJ5XKsWLECFhYW+OGHH9Ltf/bsGfbu3ZsfIVIhoXpelIWFRZblLly4gIcPH2LUqFFwcHBQb4+KisK6deswY8YM/Pnnn4iPj8/PcImIiKiIKFKJja2tLYDUCckfU22ztLQs0JiKijp16kAikWg8CygpKQm3b99GXFycetvWrVvx9u1bbNiwQePG9sKFCxg8eDDGjh3LZ5YUcXXr1gUAjc/Ku3fv4O7urn6tVCrx008/oWLFili6dKl6e0hICEaPHo22bdvip59+wvPnz1G7dm31MFMiIiKizBSpxKZMmTIA/puQnNabN28AcJLyp3J0dETz5s3h7OwMQRDg5+eHoUOH4sWLFxg1ahQA4OrVq5g/fz5+//13DBs2TOP47t274/DhwzlaeIC02+DBg6Gjo4N///0XALBp0yZs3rwZZ86cwc6dOyGXyzFmzBhERkbi8uXL6t5AADhy5AhiY2NRt25d2NnZ4Y8//kBkZCT+/PNPsU6HiIiItISu2AHkpT59+uDSpUu4evUq2rdvr94eFxeHu3fvwtTUFA0aNBAxQu22ZcsWtGzZEitXroRMJsOaNWvg4OCA8PBwzJw5E0ePHsXq1asxduxYsUMlEdWvXx/Tp0/Hr7/+io4dO+Lhw4fYs2cPgNQE98SJE5DJZLhx40a6xSUaNWqkXlEPACQSCaytrREWFlag50BERETap0glNgMHDsSMGTOwZcsW9O/fHw0aNIBSqcTEiRMhk8kwZcoU6OoWqVMuULVq1cLTp08xbdo03L9/HxERERAEAf/88w+qVauGFy9ewNLSEklJSXjw4AFatmwpdsgkklWrVqF+/foYOnQoIiMjsXz5cjx79gz//vsv9uzZg0GDBgFIXW2vbt266sU9mjdvjubNm6vrefLkCXx9fdXliYiIiDJTpO7yzczMcPToUXz77bdo3LgxqlatioCAAERHR6NBgwaYP3++2CFqPQcHB5w5cwYKhQKvXr2ChYUF7Ozs4OXlpZ6/tHjxYtSrV+/zGkpJzINoKV8lpp/LltagQYMwaNAgREVFwc/PDzNmzECVKlVQqVIlAKmrGE6ePBkPHjzI8PiEhASMHTsWO3bs0Eh20hJSkj/vHIiIiKjIKFKJDQD06NEDN2/exIkTJ+Dm5gZ/f3/o6Ohg+/bt2a7oRf8XGwIYW2VZREdHR72cr1KpxOHDh6GrqwtPT0/4+vpi2bJlnxdDQuTnHU/5LykGQmIMJEbFsixmYWGhXkhCqVTi22+/Rc+ePXH8+HFMmDABUmn6qX4JCQno378/fv75Z3z99deZVx7p/xknQEREREVJkVo8QKVBgwZYuXIl/v33X/zzzz8wNDRE165d8eTJE7FD0w6R74CkmBwXr1OnDuRyOXbv3o179+7h8OHD0NPT+/T2w96wx0ZLKF9cylX5OnXqwMfHBxs3boSjoyPmzJmTrkx8fDzGjBmDZcuW4euvv0ZKSgrmzp2brpyQkgzl6xufHDsREREVLUWux+ZjLVq0wNmzZzFixAj4+PjwCec55ecGWFcErByyLdqzZ09s2rQJISEhGDp0KCpUqJBp2YSEBCQmZpK0KFKAkFdAdEDG+6nwifSH4sFxSGt0ybbnBgC2bduGzZs3o06dOujbt2+6BDguLg7dunWDhYUFdu7cCUEQEBAQgE6dOmmUEyL9oXx+KVcJOBERERVtRT6xAYB27drB19c3wyEvlAmlPDXJCHkFGJgBOln3wEzo3hAA8Mr1LI4sOwcAGLT0d/X+u4+eYc+J80hITELZ4iYYM7A3vmrWAEP7dE0tkJLIXhptFekPpcsOQNcAMLPJsmhpAL/2T12Z8PS0r5GSnIwajRuiRuNGAIBrNx/ASicJiA1CgEcQAEACoIlFHBQPjqvbIyIiIvrYF5HYAGBS8zmSY3NcNNbfE373nVJfJESotzetWhpNF3yf/oA0ZUjLyZNzlXS8f3ATyYmJKGOlD1SyAwD0rGWLnrW+zfgAJjRERESUBd7tExERERGR1mNiQ0REREREWo+JDRERERERaT0mNkREREREpPWY2BARERERkdb7YlZFy08xocFwOXZQ7DAAAM+drsLvxVPR2g/0eqX+s9jviSJFBgDwf/FU9FhUnt9/AP833qK1H+Drp/6z66UrosUBAHK5HADg7+0teiwqYl8ff2/x2iYiItJ2EkEQBLGD0FYumxfj9uYlYodBREWMfaM2GLzPSewwiIiItAp7bD6DealysG/URuwwAAAhr54AACzLVoCesaloccgS4hDll/qrs03VOqLFAQBRft6QJcTBxNoOJta2osbC65Mer0/mbKvWFTsEIiIircMeGyIiIiIi0npcPICIiIiIiLQeExsiIiIiItJ6TGyIiIiIiEjrMbEhIiIiIiKtx8SGiIiIiIi0HhMbIiIiIiLSekxsiIiIiIhI6zGxISIiIiIircfEhoiIiIiItB4TGyIiIiIi0npMbIiIiIiISOsxsSEiIiIiIq3HxIaIiIiIiLQeExsiIiIiItJ6TGyIiIiIiEjrMbEhIiIiIiKtx8SGiIiIiIi0HhMbIiIiIiLSekxsiIiIiIhI6zGxISIiIiIircfEhoiIiIiItB4TGyIiIiIi0npMbIiIiIiISOsxsSEiIiIiIq3HxIaIiIiIiLQeExsiIiIiItJ6TGyIiIiIiEjrMbEhIiIiIiKtx8SGiIiIiIi0HhMbIiIiIiLSekxsiIiIiIhI6zGxISIiIiIircfEhoiIiIiItB4TGyIiIiIi0npMbIiIiIiISOsxsSEiIiIiIq3HxIaIiIiIiLQeExsiIiIiItJ6TGyIiIiIiEjrMbEhIiIiIiKtx8SGiIiIiIi0HhMbIiIiIiLSekxsiIiIiIhI6+mKHQAB7/w/QFdXF6VL2oodCgAgPiERJsZGoscQEBSMMiXtYGRkKFocSqUSXm99IZVIUKlCedHiSCs0PALGRkaiXSNvXz8AgDxFjriEBNiWKI4ypUqKEkta/h8CYV+64ONISEzEm7fvYGJirN4WExuLcvZlYGlhXuDxCIIAX7/3SEhMQsXyDjAw0C/wGNLyeP0GUqkUFR0doKOjU+DtR0RGwcrSIt32DwFBkCsUcLAvXSBxKBRKpKSkwNDQIMP98fEJGp+h/JRZW4lJSXj/IRCl7GwLLJbIqOh0f08EQYC3zzvIFQpUqegIiUSS73GkyOUQlAL09fUyjVNHRwfFzEzzPRYi+nTssRGRIAhYvWkHIqOiceOWK47+dU7UeJ6+eIX5y1fj/qPHosUgl8ux9/BJOLncRUhoGGYtWA4vbx9RYrl64xZ2HjiGpKRkHD9zATv3HxUljrRi4+KxaMVafAgIEi2GP7bvxYGjp7Bj/1GcPHsREZHRosUCAG6PnmD1ph2Ii4sXpX2/9wFYsW4L/tx9EDv3H8XO/UexfutuUWKJT0jEkt834K2vH0LDwjFv+SoEh4SJEsuHwGCs/3M3lIISbu5PsKOA//54eL7B0t834szFK+n2bdqxDx+CgvHA/Sl27DuSr3EIgoDb9x5g1vzl8HsfkG7/Ky9vLP19A67fcs3XOAAgNjYOR/76GwtXrEsX48Hjp3HNyQXhkVGYvXglnr54la+xPH3xCgt+XYMrN25pbHe5+wBbdx9EQmISLly+nu9/lxQKJW643MGMuUsRGhaeYZnkZBmW/r4Rb9765mssRPT52GMjomvOt6Gnq4u6taqjbq3qmPjDArRp0QQl7WwKPJa7D9wRHROLgKBgSCXi5bt33B7B7/0HjBjcDwDwwsMTf/19CXNmTCjQOBQKBQ4cO42ta3+BibERJBIJ1m/dhTHDBxZoHB87ceYCYmLiUAA/YGZILpfDtoQ15s6YKE4AH7l49QaePn+FH6eOE6U3AABCw8IxaugAdPyqJYDUX3b3HDohSm+N26MnMDE2Qvs2LQAAT194wP3ZC3Rp36bAY1n9x3YM6tcLNapWRrXKFTHxhwXweeeP8g72+d62l7cPAoNCkJSUBB2p5udC9V3XuH4dNK5fBz8u/BVeb31RybFcvsRy1ckFCoUCgcEh0NHR/G51f/oCwaFhCAgKQYO6tfOlfZWExERc+tcZEZFRUCgUGvseP3+JJ889sGrpzwCAt75+OH76PGrXqJovsbx45YnIqGjExydAR6r5nuw5dAIrF/+EEsWtYGZqgnnLV0Eul0NXN39uVy796wS5QoHQ8AhIdTL+t+/Y6fOIiY0rkJ4jIvo87LER0a0791GpQjn16wrlyhbIr3YZadqwHjq3aw0rS0tRv7wdHcqiR+f26tempiaIiy/4X+J1dHSwZc0y9XAv96cvUL9OzQKPI60LV66jcYO6mf7jWxDCI6JQ3MpStPbT8vV7j4tXnTBz0hjRkhoAaFivNjr8P5EAgOs3XdGmZVNRYrEwLwYvb18EhYQiKSkZnt6+aNaofoHHERsbh8DgEJS2Sx1eK5VKUbZMKTz38CyQ9itVKI92rZujdCm7dD8C3LpzXyOJqeRYDtdv5t/3bqe2rdC1w1eQSqX4OJh6tWugS/s2sLMtke8/VhgbGaH/191Rr3YN4KO2ypS0wze9uqpfm5maIDYfe0BrVK2MNi2awM7WJt17smHlQpQobgUAePTkOWpVr5pvSQ0AdO/UDp3btgaADP/tc759D5Urls90CCERFS5MbETk9z4A1v//AgcAc/NiCAwOFTEi8ZUuZaeRQLx45YUWTRuKEoupiQne+vphzaYdeO3ljeEDvxElDiB1WE9YeCRqVqssWgwAEBYRgVeeb7D4t/WYt3w1Lv97U7RYDhw7hYqODrhy4xacb99DZJQ4Q+KMDA3VN0SCIODR0xeoX7uGKLHUrVUdLZs2woJf1mDtlp2YPfV7mBczK/A4pP9PNGNi49TbLC3M8c7/Q4HGkdGN6ju/Dyie5nu3WDEzBAaFFGRY6Ug+zjQKuK0S1sXRtGE99etnL1+jZQF872aUzJmamOB9QCA27diH2/cfYtx3g/M9jsyER0ThlZe3xntDRIUbExuRREZFIzExCRbFiqm3GejrITbNjcCX7vzl6yhTyg5dO3wlWgwGBgZo16Y5bEpY4+elv+frr5iZEQQBx0+fx7d9ehR42x+rUM4Bq5bOw+KfpmPymOE4/NdZ/Ot8u8DjUCgUeOX1Fo3q1Ubblk0RFh6BWfOXw9vnXYHHktajJ89RvUpFUXs9q1ephJrVqiAgKAQn/76IFLm8wGMwMTbCVy2aYvu+I3j28jVCw8Lh/z4AJW1LFHgsaaXI5QiLiISFedrvXX3ExPF7V8X59j3o6+mhX+9uosWgp6uHlk0bobJjecxd+hvCIyJFiePQiTMY9E0vUdomok/DxEYkxczMoKOjo/GLVYpcXmhWRhPbrTv38SEwCONHDhE1jtIlbVGvVg1MGjMMMbFxuH3vQYHH8Pc/1+BYviyCQkLh6/cegiAgIChElH/sDQ0N1PMEStrZoEaVSnB79LTA4wgLj4RcLkeVio4wMTHGN726wrGcA27dcSvwWNK6cuMWWjdvIlr7d+4/wjUnF0wZ9x1WLPgRQcGh2HPohCixjB81BJPHfYeAwGB4evvA730AatesJkosKnq6ujAxNtbos5DL5eohc1+6h4+f4fGzl5gxcbSoybmtjTXq1qqO70em9tbccLlb4DH863wbNtbFEREZBV+/95DL5QgKCc10gQEiKhyY2IhER0cK2xLWiItPUG+Lio4pkIm1hd3DJ8/x4pUXvh8xGBKJBKHhEWKHBD09PVhZWkAmSynwtss72CM+PgGu9x/C9f5DKBRKPPd4Db8P6VdYKmimpiaijD23KVEcJibGCI+M+i+WAlqeNjOBwSGIjokVZclplQtXrqNHl/aQSqUwMzNF355d8KKA5rVkpEK5sujcvjUiIqPRuEGdfJugnxulS9oiPuG/793I6Bg4lisrYkSFg4fnG9y664Yp476Djo5OofjelUgksClhDVmyrMDbLlOqJJSCUv29myyT4ZWnN976+hd4LESUc0xsRNThqxbqHoAUuRy+796jqQgTfdOSpcggF2Hoikp4RCT2Hj6B0UMHAPj/MqTHTosSS9px90EhoQgODUOj+vm7clFGateoisH9eqv/09XVQae2rVCvVsHP4/D1e6+eyyIIAjy9fVC3VvUCj0MikaBGlUp4+/9n6gCpz7GpXrVSgceicvnfm2jWWNy/v8XMTBEZFaV+HR+fgNKl7MQLCKm9APceuGPk4P4F3nZSUjJSUjS/z9q3aQGXu6nfu4IgwPPNW7Rokr/zSeRyOQRByPS7NVkmg1yuyHBfXpOlpKRrKy4+Hpt37MfYYQNTFzkAcODoqXyPJSkpGfKPrk/a792Y2Di89X2Hxg3q5GscspTUH6zSXp8qlRw1vndNjI3xVcumaNKwbr7GQkSfh8s9i6hL+6+wcMVaHPnrb0RFx6B9mxYwMzURJZbomFjcdXNHaFgEXO8/hIN9aVQo71DgcfxzzQnxCYnq5yzExsahjAi/gCsUCqz/czeqVHJEvdo1cPHKDUwZ9x1K2hb8UtwqCYmJuOZ0GzJZCpxv34NNCesCnxgeEBSMX9duxsjB/fHs5SvUq1UDX4m0AtiQAV/j943bYG1liaCQMDRrXB+N6+fvDVBmkpKS4XT7Ln5fPFeU9lX69OiMHfuPQl9fH1KJBE9fvMJYkZYoT0hMxMmz/0ChUGDBj1ML9EGhycky3LxzH89evoaRkSGqV62kXh2uTYsmuHXHDXsOnYBEIkHdWjVgU6J4vsUSHBKGG7fuQBAE/Ot8G6YmJuohx/HxCbj/6An83gdAIpGgSkVHVKnkmG+xvHjlhes3XRERGYl/b7qieeP6MDI0xFUnF8TFJ2D5mk2pcSUkoJhZ/n23xCck4tad+/Dy9kV4ZBQqOpZDw3q1AADb9h2GjXVxNGtcH9ecXDBq6LeomI89fR8Cg3H1/8/SuXL9Frp3agdbG2v1fpksBTdc7iA8IhK37z1A2TKlUdzKIt/iIaLPIxEEQRA7iC+ZQqGE11sfmBgbizqEJTYuHoFBIZBKJRAAGBkaiPI0+aCQUMTHJ/y3XI4gwNTUBLYlrLM+MB8olUr4fwiEXC5HubJlRF1SGEi9efZ7HwAdHSmUSiVK2tnA1KTgE+H4+AT4vQ9AubJlYGRkWODtpxUdE4v3AUEo71AGxkZGosURGxsHH7/3+fbcj9xIlsng5/8BFhbm6mVzxRCfkAgIQoE9wT4t9XNj/v8MGwECSqWZRyMIAry8faGvr4dyZcvkayzhEZEIj4hS/701L1ZMnUglJCbi/Ycg9feuvp4eHOxL51ssPu/8IVcoIJVIoFAo4WBfGgYG+ggNC09dwS7N966xkVG+PVMtJSUFwaFh0JHqQIAAqVQKO5sS/29awIfAICQmJqGcgz308nGpZyD1OVRR0TGQSlOvj5WlhcaS9ilyOXx8/dXXT4wflIgo55jYEBERERGR1uMcGyIiIiIi0npMbIiIiIiISOsxsSEiIiIiIq3HxIaIiIiIiLQeExsiIiIiItJ6TGyIiIiIiEjrMbEhIiIiIiKtl79PviriQsLCERYeIXYYAABfv/cAADubEjA0NBAtjqSkZASFhAJAvj/4LjtBwaFISk6GuXkxWJoXEzUWXp/0eH3Si4qOQVR0DAwNDGBnW0K0OIDCeX3E/szy+qRXmL5TCtP1UXGwLw0T44J/SC3Rl4qJzWdwvn0PJ89eFDsMIiIiKoQWzp6GGlUriR0G0ReDQ9GIiIiIiEjrsccmD1SvUgmLfpomagzfjpoMABg+8Bt079RWtDguXLmB/Uf/AgAc271JtDgAYOTkH5GQkMjrkwavT8YKy/VZ8tsGvHztBWNjI+zZtEq0OIDCeX3E/szy+qRXmL5TCtP1UX1miahgsceGiIiIiIi0HhMbIiIiIiLSekxsiIiIiIhI6zGxISIiIiIircfEhoiIiIiItB4TGyIiIiIi0npMbIiIiIiISOsxsSEiIiIiIq1XpB7QuWzZMrx+/Vr92sTEBOXKlUPz5s3Rpk0bESMjIiIiIqL8VKQSm6tXr8LFxQXFihWDjo4OEhISkJycDADo2LEjzp49C0NDQ5GjJCIiIiKivFYkh6K5uroiPDwciYmJePLkCRo1aoSrV69i7ty5YodGRERERET5oEgmNmnVqlULu3btAgCcOXNG3GCIiIiIiChfFPnEBgCqVq0KiUQCf39/KBQKscMhIiIiIqI89kUkNq9fv4YgCChdujR0dHTEDoeIiIiIiPJYkU5skpKS4ObmhlGjRgEAfvzxR5EjIiIiIiKi/FCkVkVTqVmzpsbrxo0b48CBAxgyZIhIERERERERUX4qkonNoEGDYGVlhTdv3sDZ2RkhISEoVaqU2GEREREREVE+KZKJzbx581C9enUAgK+vLxo3box+/frBw8MDNjY2IkdHRERERER5rUjPsQGAcuXKYenSpYiMjMSyZcvEDoeIiIiIiPJBkU9sAGDMmDFwcHDAzp078f79e7HDISIiIiKiPPZFJDa6urqYNWsWkpOTsWLFCrHDISIiIiKiPPZFJDZAaq+NjY0Ndu/ezV4bIiIiIqIipkgtHtCjRw9UrVoVlpaW6fYZGhpi/fr1uH79Op4+fYoyZcqIECEREREREeWHIpXYzJ49O8v9AwcOxMCBAwsoGiIiIiIiKihfzFA0IiIiIiIqupjYEBERERGR1mNiQ0REREREWo+JDRERERERaT0mNkREREREpPWY2BARERERkdZjYkNERERERFqvSD3HRiyh4RE4efai2GEAAJ4890BiYqJo7Xt5+6r/LPZ7kpIiB8DrkxavT9bEvj6h4eEAUt8bsd+Twnh9xI6D1ye9wvSdUpiuDxGJQyIIgiB2ENrqxNmL/PIkIiKiDC2cPQ01qlYSOwyiLwZ7bD5D9SqV0K93N7HDAAC8fOUFAHAoWxomxsaixRGfkIh3fu8BANVF/jL39XuPhIRElLC2Qgnr4qLGwuuTHq9PeqFh4QgNi4CxsRHKlS0jWhxA4bw+Yn9meX3SK0zfKYXp+qiUsLYSOwSiLwp7bIiIiIiISOtx8QAiIiIiItJ6TGyIiIiIiEjrMbEhIiIiIiKtx8SGiIiIiIi0HhMbIiIiIiLSekxsiIiIiIhI6zGxISIiIiIircfEhoiIiIiItB4TGyIiIiIi0npMbIiIiIiISOsxsSEiIiIiIq3HxIaIiIiIiLSertgBaLO9Lmexz+Wc2GEAAB77vQYAVLS1h6mBsWhxxCUl4E2IPwCgbtkqosUBAG+C/RCXnAg78+KwM7cWNRZen/QK0/VRWTf4B9QtW1XsMIiIiOgTSARBEMQOQlstPrMVS878KXYYRJRHbszZia+qNhI7DCIiIvoE7LHJA5VKOWBG76GixjBx6y8AgOm9h6JyKQfR4rj+9D5O3r4KANgyYZ5ocQDAD7vXICE5Cd0btkb3Rq1EjYXXJ73CeH2IiIhIezGxyQNmRsaoX7G62GEAACqXchA1Fs8P79R/Fvs90ZGmTiEraWUteiwqvD7/KYzXh4iIiLQXExsqMox1DKEj0VG/blmpHhJkyahs4wAzXRMRIwPaVG0IAChlVkIjlgRFIhSCUqywiIiIiIoMJjak1XQkUpQ2skFJo/STzy/O3CJCRBlzmrMr033JChneJQQiUhZbgBERERERFS1c7pm0WrVi5TNMarSJgY4+Kps5wM6wuNihEBEREWktJjaktewMi8NE10jsMPJMaSMb6Ej4V5KIiIjoU/AuirSWpX4xsUNAeHg4AgMD86QuXakOiumJOxeIiIiISFtxjg0VWQ8ePMCCBQuQ0aOapFIpKlSogIYNG2LYsGGQSnOe4wcGBmLNmjV48OABatWqhZiYGNy5cwft27fH6tWrYWLy6cmJsY4RIsG5NkRERES5xR4bKrIaNmyIEydOwMzMDFeuXMH48eNx8uRJnDx5Etu3b0f79u2xYMECdOrUCcnJyTmqc9euXWjUqBHq1q0LJycn/PHHH9i3bx+eP38OLy8v1KtXD1FRUfl7YkRERESUDhMbKtJMTU3h6ekJMzMz9OzZE6ampjA1NUWZMmXw9ddfY+bMmbh+/TpOnz6dbV0///wzZs+ejYsXL2LoUM0Hsurr6+P48eMIDAzEzz//nF+nQ0RERESZYGJDRVpERARevHiBFi1aQEdHJ93+lJQUAICrq2uW9axbtw6//fYbtmzZgtq1a2dYxsrKCjVq1MDOnTtz3ANERERERHmDiQ0Vac7OzlAqlfjqq68y3H/nzh0AQKtWrTKt4927d5g/fz46d+6Mb7/9Nsv2qlatCrlcjtevX39yzERERESUe0xsqEhzdnYGgAwTG3d3d5w7dw5du3ZF7969M61j7ty5SExMxPfff59te6r5NREREZ8ULxERERF9GiY2VKQ5OzvDzMwMDRo0AAAIggAfHx9s3rwZ3bt3x+jRo3H69Gno6+tneHx0dDROnToFa2trdO/ePdv2fHx8AKT23BARERFRweFyz1RkRUZG4tmzZ7Czs1MPIRMEAZaWlqhatSpcXV1Rrly5LOv4999/IZPJ0KpVK+jqZv3XJTg4GC9evICVlRXs7Ozy6jSIiIiIKAeY2FCRdfPmTSiVSowYMQLLly//pDp8fX0BAHXr1s227IULF6BUKjFq1KhPaouIiIiIPh2HolGRpZpf06ZNm2zLXr58GUlJSem2GxgYAABKlCiR5fFKpRJr166FmZkZZs+enW5/aGhotiuvEREREdGnY48NFVlOTk7Q09ND8+bNM9wvk8kwceJExMbG4sSJE3j9+jUqVaqkUaZOnToAgLCwMI3tsbGxMDMzU7/etWsXXr58iXXr1sHa2lq9/ezZszhx4gQePXqEOnXqZBoLEREREX0eJjZUJEVFReHp06do1KgRTExMMiyjr6+PLVu2IDExESdOnIAgCOnKNGjQAKVKlYKbmxsAICQkBFOmTIG1tTUMDAywdu1aPHnyBPPnz8esWbMwbdo0jeNVK67NmjULAQEBeX+iRERERASAQ9GoiNq/fz+USiVatGiRZbnMVkNTMTIywtq1a3HhwgU4OTlh8+bNWLlyJTZv3oyUlBTs378f7du3x+jRo7Fq1apc109EREREeYM9NlSkHDp0CFu3bkVgYCDKlSuHs2fP4t69e9i7dy8qVKjwSXUOGDAAxsbG6kUBqlSpgsuXL+PevXt49uwZXFxc1A/m9Pf3R/ny5fPylIiIiIgoB5jYUJEyZMgQDBkyJM/r7dGjB7p37w4PDw88fvwYjo6OqFWrFkqXLq1+Zs3KlStRpUqVz0psEhSJeRUyERER0ReFiQ1prZiUeBTTy3j+TH6QSCSoXr06qlevDgC4ePEidu7ciVKlSuHRo0e4cuUKPD09P6uNBHn6ldmIiIiIKHtMbEhrBSWFoYSBBQx0xJnH4ujoiKCgIEycOBFSqRRnz579rDk17xNCkKxMycMIiYiIiL4cTGxIaykEJTxifFDJrCxMdI0+uR6lUgkAGa6KlpWxY8fC3d0dCQkJGDduHNq3b59lG1nV/z4hBB8SQ3LVPhERERH9h4kNabVkZQqeR3vDWMcQxrqGMJD+12Ny4MY5yFJSUL9CVdSrUD3D4xfPno/AD4GoVrM6pv4wHbZ2tliy+hfo6enlqP1lm39T//l9QvrExOXGLZw/dRY3b9+GUqHA14P7oXvP7ujauzuA1OF0CYpEKARlbk6biIiIiD7CxIaKhARFEhIUmvNTVpzfidjEBIzp1Bc2pawzPG7skqnptoXIIwF53sRVvmkVTGk6G4dmpS5oMG/CANSuWJ29M0RERER5jM+xISIiIiIircfEhoiIiIiItB4TGyIiIiIi0npMbIiIiIiISOsxsSEiIiIiIq3HVdHyQFxSAh55e4gdBgDAK8APkEhEa/9D+H+rfYn9nij+/3yawMgw0WNR4fX5T2G8PkRERKS9JEJun0pIaovPbMWSM3+KHQYR5ZEbc3biq6qNxA6DiIiIPgGHohERERERkdZjjw0REREREWk99tgQEREREZHWY2JDRERERERaj4kNERERERFpPSY2RERERESk9ZjYEBERERGR1mNiQ0REREREWo+JDRERERERaT0mNkREREREpPWY2BARERERkdZjYkNERERERFqPiQ0REREREWk9JjZERERERKT1dMUOgOhLcODoX2KHAACIi4+Ht887AECdmtVFjcX7rS/iEhJgW6IE7GxLiBrLk+cvAQAVyjnA1NREtDiCQkIRHBIKE2NjVHQsJ1ocQOG8PmJ/ZlVsSlijc/s2YodBREQfkQiCIIgdBFFR17H3ILFDIKI8UrtmNaz5ZaHYYRAR0UfYY0NUgMqULgVjYyPR2o+MjEZoWBgAoHKlCqLFAQBvvH2gVCpR3MoSxYtbiRqLp5c3APGvz/v3AUhITISRkRHsy5QSLQ6gcF4fsT+z4eERCI+IFDUGIiLKHBMbogI0oF8fVKlUUbT2r91wxom/zgAAZk2bLFocADDjx5+RkJiIZk0bo2e3LqLG8v3kGQDEvz5rNmyCp5c37MuU4vVJQ3V9xH5Pzl28hPMXL4saAxERZY6LBxARERERkdZjjw0RfTGKmRrDQF8Pujo6GttXL18AAChTpjSMjcQbijZtwmgkJiTCyNgIJUtoDv+SpaQgMVmGhMRkkaIjIiIq3JjYEFGRJ5VIUNLGCgb6ehnur1OrcKy2VblC+Uz3GRnqw9zMBLHxiQiNiC7AqIiIiLQDh6IRUZFXwso806RG25iZGMHc1FjsMIiIiAodJjZEVOSZGBuKHUKeMjURb7gcERFRYcWhaERUpBka6Gdbxs3NDX5+fhnuMzU1Rc2aNVG6dOlcty2Xy3H+/HlcvHgRUVFRMDIyQr169TB69GiYmZnluj6VotL7RERElJfYY0NEX7ygoCC8ePEC3377LUaNGgUvLy/4+/vD19cXly5dQqtWrdCsWTP4+/vnuM5r166hVq1aePz4MZYuXYrjx49jzpw58PDwQN26deHm5paPZ0RERPTlYY8NEX3xevbsierVq2PJkiXo0aMH5syZo7F/6dKlsLe3x4ABA3Dnzp1s65s9ezYOHTqEkydPolmzZurt1apVw7Zt29C3b1/069cPL1++hImJSZ6fDxER0ZeIPTZERACcnJwAAF999VW6fWZmZihXrhzu378PHx+fLOuZP38+1q9fj1OnTmkkNWlNmDAB79+/x/r16z8zaiIiIlJhYkNEBMDZ2RlAxolNSkoKXr16BT09PdjY2GRax5UrV7BixQr89NNPaNKkSablatWqBQC4d+/e5wVNREREakxsiIiQmtiULFkSlSpVSrfv8OHDSElJQb9+/TIdOiaXyzFjxgzo6+tjxowZWbZlaJi6StubN28+P3AiIiICwMSGiAhv376Fv79/hr01169fx5w5c9C7d2/s2bMn0zr+/vtvvHr1Cr1794aVlVWW7akWIShZsuRnxU1ERET/4eIBRPTFUw1D8/b2xsSJEwEA0dHR+PDhA3R0dLBz50507949yzr++usvAECvXr2ybU+1Ilr16tU/J2wiIiJKg4kNEX3xVAsH/Prrr6hZsyYAQFdXF5aWljmu4/nz5wCApk2bZlv2/PnzAIB27drlMlIiIiLKDBMbIvriOTs7w9zcHG3atIFU+mkjdKOiogAAZcuWzbJccHAwrly5gjp16qBPnz6f1BYRERGlxzk2RPRF8/X1hZ+fH1q0aJFpUhMWFoYrV65g4sSJ6N27d4ZlqlatColEAoVCkWV7ixYtQmJiIpYvX66xfcuWLRg+fDgGDBiAZs2a4e+///60EyIiIvpCMbEhoi+aahhamzZtMi3j6+uLoKAg6OrqIjExMcMyjRs3hiAIePv2LQAgMDAQP/zwA6ZMmYKYmBgAgLu7O3bv3o3FixejW7du6mPPnDmDkJAQ7N+/H8ePH8fixYvRr18/3L17N4/OkoiIqOhjYkNEX7SrV68CyDqxadiwIYYPH57lKmYzZsyAlZUV/vzzTwDAzJkzMWPGDEycOBG//PILnJyc0L59e0yaNAkLFizQOPb+/fs4ePCg+nXnzp1RrFgxXLx48XNOjYio0Lp58ybevXuXJ3V5eXnh2rVreVJXUeDh4YGff/4ZXbt2xcqVK8UOp0AxsSGiL9K2bdswZ84cHDt2DABw7NgxHD169JPrs7KywpEjR3D69GnMmzcPlpaWKF26NMzMzHDixAlMnToVhw4dwrp169IdO3v2bJw9e1b9OjExEXFxcShVqtQnx0NElJanpyfatWuHBw8eiB0KvLy80KVLF6xZsyZP6vvpp5/QrVs3vHr1Kk/qK0gzZszA7Nmz87TO4sWLw8zMDJcvX0ZkZGSe1l3YMbEhoi9ShQoV0KpVK/zzzz+4fPky2rVrl+3E/+x06NABT548gY2NDaKjo9G/f38sWbIEISEhuH37Nrp27QoAGD9+vMZcHAsLC9SoUUP9+vfff0f16tUxYsSIz4qHiEjF398frq6u6uGy+UUmk+HAgQPqIbgZGTduHMaMGYONGzfmSZvHjh1D79698zxByEvnz5/P8KHMTk5OcHV1zdO2bGxsMGbMGACAvr5+ntZd2HFVNCIq0pKSZRlu79ChQ760Z2lpiWnTpmls27t3L06ePImBAwdi27ZtCA4Oho6OTobHnz17FteuXcP169dhaGiYYZnEpIzPiYgoM+3bt0dUVFSm3yt5ZdGiRfjtt98QFBSEYsWKpdvv4eGBTp06Ye7cuXnWpp6eHo4dO4bp06cjNDQUJUqUyLO688L+/fsxYsQI3LhxAxUrVtTYd//+/Uz/PfgcBgYGeV6nNmBiQ0RFXnxiEkyM8vcf86xYWlpizJgxmDx5MgRBwO3btzMsd+bMGZw8eRJXr16FgYEBHj58iAYNGqQrl5CYlN8hE1ERlN9JTVqZ3VhXq1YN1apVy/P2pFJpnvUA5ZeM3hM9PT0RIim6mNgQUZEXGh4NXRsdGOiL8w/IoEGDsGnTJlhZWWH16tWoV69eujKnTp3Co0ePsGfPHgCAm5sbbt++nS6xiY1PRHRcQoHETUTaITExEfv374ebmxuUSiX69++vHvoKpA5Dc3FxgZubG1q0aIFvvvlGvU8QBBw5cgSurq6QSCTo0qULunbtql7+/v79+zh79ix0dHTQrl07fPXVVwBSH2icmJgIqVSKJUuWAABOnjyJ27dvQyKRYOXKlTAwMEDDhg3Ro0cPAIBSqcTBgwdx9+5dVKpUCT169EClSpU0zuXatWs4ffo0YmNjUapUKXTv3h2tWrXK8vwvX76Mq1evIjAwEDVq1MDcuXMhkUgyLX///n3cu3cPT58+xY4dO/DgwQMcOnQIJiYmGDx4MKpXr65RPiIiAvv27cPjx49haGiI0aNHo3Hjxur9t27dgpubG/z9/bFu3Tr1D1SzZs1CYGCgeg7lrl27cOnSJTg4OGDYsGG4du0anj17Bl9fX2zevBkA8PTpU9y5cwe3bt3C/v37cfv2bRw8eBBDhgxB69ats3wfTp06BWdnZ4SHh6NSpUqZvgdnzpzB9evXYWNjg+7du6f7N+nBgwc4cuQIgoODYWtrizZt2qBXr15Ztl1YMLEhoiJPKQj4EBwOc1Nj6OvrQfejbn/P/497ti9dGkZGRumO9/f3g6urK65d+xdv3rzBjp27UL1addTPoDclIyt/W4VJk6egdOkykEql6YaSXb16BYMGDYJcLseKFSvU20+fOasuK0tJQWKyDAmJybk6dyIq2uLi4tCwYUMsWbIE27dvx99//42+ffvCxcVF/cNIYGAgdu7ciRs3bsDR0VHj2L59+6JUqVJYvHgx/Pz8MHv2bPzyyy84duwY7O3tUbVqVZw5cwbLly+Hubm5OrHp2bMnunbtipiYGHVi4+DgAHt7ewBA06ZNYWJiok4S5HI5unbtilq1amHjxo148OAB6tevjy1btmDYsGEAgCNHjmD69Om4c+cObG1t0bZtW8TExGSZ2MycORPBwcHYsWMHkpKSUKtWLSQmJmLZsmWZHvP8+XOsWrUKAQEBqFatGvz8/NCuXTvs2bMHtWvXxvHjx9G3b18AgI+PD9q0aYOjR49ixowZWLNmDbp3744nT56oF3hxd3fHypUrIZFIYGdnBxcXF1y5cgXVqlVDp06dULlyZQBA7dq1Ua1aNTg4OEAul+PmzZvqOZUqXl5eWL9+PV6/fo02bdrgxIkTcHNzQ0pKSqaJjVKpxDfffAN9fX1s3rwZcrkc06dPz7Ds6NGjERkZiSNHjsDf3x+tWrXC+PHjsWjRIgCAq6srOnfujGvXrqFRo0b45ptv8Pz5cyY2RESFTWY9HT/MS/0HcOa0SahSqWK6/VGxiTA0KYaJU2dAKpUiJUWGBJkcgaEROW5b19AUweFRGe4zKWaJXXsP4sSpM3j/IQBlSpdC/75fw7Fy9Vy1QURfnr/++gve3t5o3749pFIpvv76a5iZmeH48ePqxKZx48ZYsmQJbty4oTGZfOXKlQgICMDFixehq6uLcuXK4cCBA6hTpw7GjBmDy5cvo1ixYhg4cCB+++03jaFstWrVQpMmTXDr1i31tkaNGqkTp7Zt22rMsdm8eTM8PDzUbTVt2hQtW7bEuHHjMHToUEgkEuzbtw+VK1dW17Fq1So8ffo003OPj4/Hpk2bsGHDBhgbG8PY2Bh9+vTBgQMHskxsRo0ahefPn2PDhg1QKBRYv349AKBbt25o2LAhhg0bhrZt28LS0hJ79uxBfHw8mjdvDiA1MZg9ezbOnz+PcePGAQCmTp2KBw8e4ODBgwgJCcG5c+fw4cMHlC5dGgBQs2ZNAECTJk00enp+/fVXnD17VuOafPPNN/Dx8cHs2bNx8uRJXL58GWFhYTA3N8/0fFavXo1Hjx7h7du36vk6GzZswPHjxzXKXbhwAUeOHIGPjw8MDAxQsWJF9OvXD0uXLsXIkSNRtmxZHD58GBYWFmjUqBGkUinWrFmjfoyBNuCqaERE2bAuUQKNmzRFvfoNUKduPTRs1AQVKlbK/sAcKu9YAc1btkIZh/KwKmGHMg7l0bxlKxgbG+dZG0RUNA0cOBBv376FtbU1ACA2NhalS5fWSDgAqG+MVUPMAGDLli1o0qQJdHX/+527UqVKaNGiBa5du4b3798DSF1ZSxAEjWNV27Ma8pXWli1bYGVlhZkzZ2LChAkYM2YMXr58CZlMhvDwcACAo6MjXF1dsXr1aiQmJqJNmzaYMmVKpnWamJjAw8MD48ePB5Dac2FhYQE/Pz/4+fllGY+FhQUAqHuLAEBXVxdDhw5FUlISXFxcAAA//vgjXr58qS4jl8thYWGh3q9ibm4OiUSijleV1GTH3Nw83fuqqmvy5MmQSCQoUaJElqubbdy4ES1atNBYhCCj0QdbtmxBiRIlsHz5ckyYMAFjx46Fk5MTBEFAYGAgAKB8+fL48OEDZs6ciYiICDg6OuL333/P0bkUBuyxISIiItJSBgYGsLCwwJYtW3DlyhXY2NggOTkZKSkpWR4XEBCA6OjoDHsCKlasiOvXr+PDhw8oU6bMZ8cYEBCAN2/eYNasWepFVJRKJebOnQtdXV11UrZ8+XK4u7tj9uzZWLVqFWbOnInZs2dnmTxVqFAB//zzDw4ePAilUonk5NThulktN53Wx5P369SpAyB19baePXvCzMwMCQkJWLlyJVxdXVGuXDno6uoiOjo6w/rKlSuXo3azIwgCypcvn2250NBQBAYGwsbGJstyCoUCLi4u6NKlC2bPng2lUqn+TxAE9WptU6dOxa1bt/DHH39g9+7dGD9+PJYuXVqgC098DiY2RERERFrK19cXnTt3Rt++fXHs2DEYGBigW7du2fZYqHoJVL/Up6W6Sc7uZjmnIiJSh9RGR0dn+bwwKysr3LlzBxcuXMDSpUsxd+5cJCYmYvHixRmWVyqVGDlyJDw9PXHs2DGULVsWe/fuxZkzZz45VlWvR5UqVQCkTqTv0aMHFi5ciDNnzkAqleLSpUufXH9eEwQBAPDu3bssy8lkMsTFxSEsLEw9Dyojenp6OHPmDO7cuYMlS5Zg9erVCAgIwMGDB/M07vzCoWhEREREWmrRokVITk7GihUrNJYTViqVWR5nZ2cHGxsbPHz4MF3vjru7O6ytrdU9BqqhaqoERSUxMVHjYcNppa2zQoUK0NfXx9mzZyGTZfwcroSEBPXiKd27d8ft27fRvHlzHDp0KNNzuHTpEg4cOIB169alS5hUN/y59ebNG+jr66NRo0YAgGnTpqFGjRqYOHGixpCxj+vPSXsZnbsgCJnWlZM6bWxsYGtrC3d3d43tiYmJAKC+PkZGRihXrhxcXFwyTGZV5s2bBwBo1qwZLl26hEGDBuHkyZOZXrfChokNERERkZb68OEDYmJi1EOwfH194e7ujsjIyAzLp527t2LFCnh7e+Onn35S30QHBQXh5s2bWLVqlbpc2bJloaOjgwsXLqi3Xb58GdeuXUN0dDROnDihvpE2MTEBkLqaWFJSEp49ewYjIyNMmDABoaGhGDx4sPpmOzk5GcuXL4dcLoe+vj6WLVumnm+jq6sLExMTtGnTJstzB4CQkBAAqcmUKkZVPdkJCgrSqG/RokVYtGiResWzDx8+IDQ0VF3mwYMH8Pf3T1e/6nVYWFi6NkxNTdXviVKpxMOHD9X7IiIi0iWM4eHhkEgkGu1mZciQIfDz81M/LiAlJQULFy4EAFy9ehUeHh4AUleQk8vl6Nu3L+Li4gCkJk+rVq1Sf14OHz6MJ0+eqOu2sLBA06ZNs5zjU5gwsSEiIiLSUtOmTUNiYiJq1aqFYcOGYc2aNejVqxeCg4NRp04d/PvvvwD+68FRTZoHgBEjRuDkyZO4cOECateujWXLlmHAgAFYtGgRhg8fri6nr6+PTZs24cmTJ2jZsiXatm2Lp0+fYuLEiTAzM8Nff/2F169fA4B6dbZOnTqhbdu26t6eFStWYNy4cTh79ixKliyJ1q1bo3PnzujTpw90dXXV5fr27YsNGzZg1KhRCA4OVi8lnZGvv/4alSpVwtChQzF06FAMGjQI7dq1g1QqxfDhw/HTTz9l+/716dMHs2fPxpgxY1C3bl1MmjQJs2fPVu//4Ycf8OLFCzRs2BCDBw/G2bNn0aFDB9y9exdNmjTBs2fPMG7cOPz1118AUnubPh621bRpUxQrVgwTJkxAnTp1EBsbCz8/P/Tr1w9eXl7w8fHBN998A19fXyxcuBCrV68GAHz//fdYuXJltuewcuVKDBw4EJMmTULLli3RpUsXDB48GLa2tkhOTsb27dsBABMnTsSSJUvg7u6O0qVLo02bNmjWrBkaNmwIS0tLAICZmRmGDRuGtWvXYvr06bhy5Uqhf/BpWhLhU/vqiCjHOvYeBACwL5Pxc1IKSlRUFEJCU39NqpzBssYFydv7LRRKJYoXt0JxKytRY/H0+v9zbES+Pu8/fEBCQiKMjYxQpkzOVtTJL4Xx+oj9mQ2PiEB4eARq16yGNb8sFDUWorSCgoLg7e0Ne3t79ZCsx48fo3Tp0ihRogQA4NGjR2jYsCFcXFzUSxen5evri5iYGFSvXl1jlbS0kpKS8Pz5c9SoUQNGRkYICAiAkZGR+qZY5c2bN1AoFOp5KmklJCTgxYsXKFu2LGxtbdPVHxoaCn9/f5iZmaFKlSrZ9hQkJibi5cuX0NHRQe3atSGVSuHv74/4+HhUrVo10+OWLl2KJUuWICAgAJGRkYiPj0e1atUyXI3y3bt3eP/+PSpVqgQbGxsoFAo8fvwYFStWhLm5OQIDA6GnpweJRAK5XK5e0CGtwMBAhISEoFatWv9/bEAKwsPDoaurC4lEgpSUFBQvXhyRkZGQSCTQ0dGBXC5Xr4qWE9HR0Xj37h1q1aoFiUSC58+fq5eaTksmk+HFixewsrKCg4NDun3h4eHw8/ODnp4eqlatqlUrdDKxISoAqsSGiLQfExvSRpcuXULPnj2zfSbKl0KV2ISEhKB48eJih0N5hKuiERWAYQO/ETsEAEBcfDy8fVJXTqlTs3o2pfOXt887xMXHw86mBGxtcvZrVH558jz1GQUVypeDqYl4v0wFh4QiKCQUpiYmqFDeIfsD8lFhvD5if2ZVxH4/iHJDqVRCKpXi3r17qFevHpOa/1MtbiCXy0WOhPISExuiAjB8UD+xQyAioi/MzZs3MXz4cIwbNw7btm3D6dOnxQ6p0FBNkHdzc0OPHj1EjobyCoeiERERERVBMpkMmzZtgoGBAQYOHMghV/83dOhQhIWFQSqVQqlUomXLlpg/f77YYVEeYGJDRERERERaj8s9ExERERGR1mNiQ0REREREWo+JDRERERERaT0mNkREREREpPWY2BARERERkdZjYkNERERERFqPiQ0RERERpePj4wOZTCZ2GEQ5xsSGiIiISIsJgoDw8PA8q+/nn3+GtbU1KlSogGfPnmnsCwkJybN28kJERASOHTuGuXPnYseOHUhISBA7pCInKioK27dvx88//4yTJ08iODhY7JAyxcSGiIiISIuNGzcO9vb2eZZ0/Prrrxg6dCgAwNDQUL3dxcUFpUqVwoYNG/Kknc/l5+eHVq1aISUlBTNmzICuri7q1q2LDx8+iB1akfH48WP0798fMpkMTZs2xf79++Ho6IgLFy6IHVqGdMUOgIiIiIg+XdeuXSGXy2FlZZVndVaoUAEAoKv7361ipUqV0LdvX7Ro0SLP2vkcgwcPRs+ePdVJ2MiRI/H27VsMGjQIN2/eFDm6wmvv3r24desWdu3alWU5hUKBiRMn4vjx4yhTpgwAoEePHmjfvj369u2LV69eoXz58gURco4xsSEqAB17DxI7BCLKI7VrVsOaXxaKHQaRWt++fdG3b988rVNHRyfdNltbWxw/fjxP2/lUb968wZ07d7Bs2TKN7Z06dcKvv/6K169fo0qVKiJFV7gtX74cpUuXzrbcixcv8ODBA6xduxZr164FAEilUgwYMAA3b97E+fPnMWXKlPwON1c4FI2IiIhIy2U0yT8lJUXjtSAI2daTkzJZLSiQk+OzolQqc1RONRTq4xt0Vc/CpwyVyui84uLi0m1TKBRITk7Odf2f0pZcLs/zBRz09PSgr6+fbTlTU1MIggB3d3eN7ba2tgCAR48eaWzPKM7Y2Nh025KSknJ8nXOLPTZEBahL546w+/8XghheerzCfbcHAIARw4eKFgcAHD56HDKZDHXr1EbdOrVFjWXv/oMAxL8+l65cRVBQMOxsbdGlc0fR4gAK5/UR+zP7+MlTPH7yVNQYiD62cOFC3Lp1C/fv38fbt29ha2uLU6dOYefOnXB1dcXdu3cRFxeHqVOn4vHjx7C0tMT+/fvRvn17jXouXryITZs2wczMDD4+PoiIiNDYf+3aNWzevBkPHz7EpEmT8NNPP6n3RUREYOHChQgLC4Ovry+USiWWL1+OTp06qctcunQJe/bsgYmJCQCgQ4cOGDx4sHr/u3fvMGnSJBgYGCAyMhLBwcHYuHFjujhVAgICAKTefKelqv/du3e5eh/37NmDO3fu4Pnz57h48SIuX76M+/fvQyqV4ty5c/jjjz/QuHFj/Prrr9DR0cHTp09hYWGBvXv3agzXy4mtW7fC3d0dL1++xKVLl3Dq1Ck8fZr63XL+/Hls374dNWrUwG+//QY9PT08fPgQpUuXxo4dOyCVZt0noVAosGTJEvj5+UFXVxc6OjqYPHkyatWqhfj4ePTq1Qt+fn4ICgpCixYtIJVKsW3bNlSvXj1dXY6OjvDx8YG1tbXG9rt37wIAatasqd42Z84cvH//HkqlEocOHcLKlSsRHR2N2NhY3Lp1C2fOnIFMJsP27dthZGSEa9euoW/fvhqfo7zAxIaoANnZ2qJcOQfR2g8K+m8lEzHjAKD+crawMBc9FhWxr4+hgUHq/w0NRH9PCuP1ETsO31zeKBEVhDFjxuDy5ctITEyEkZERAKBjx464ffs2Ll++jKVLl8LOzg779u2DIAho2bIlFixYoJEw7N27F7/88guuX78Oe3t7yOVyfP3113j79q26TPPmzXH37l38/fffGgsKJCUloVevXujZsyc2bdqkLvvtt98iODgY+vr6uHjxIoYPHw53d3fY29vj6dOnqFevHiIjIzFp0iQAqfNlGjVqhPXr10Mul6Nhw4aIiorK9LxVCyV8nFTo6ekBAMLCwnL8HsbExMDFxQW7du1C6dKl0b59e0yfPh1r1qwBACQnJ2P69Olo1aoVVq5cCQsLCwQFBaFUqVIYOXJkpslXRsLDw/H06VNs374dlpaWaNu2LX766SesXr0aQOoKZNOmTUPTpk3x+++/w8zMDG/fvkXFihUxZswYNGvWLMv6x4wZg7CwMPz999+QSCSYN28e2rVrBxcXF1SpUgX//vsvatSogVKlSuHq1avZxqvqAVORy+U4f/487OzsMHLkSACAm5sbrKysMHHiRJQvXx4BAQFYu3Yt6tevDwBo3Lgxxo8fj/r162P16tWQSqVo1KgRBgwYgAkTJqBYsWI5fv+yw8SGiL4YOjpSmBgZwdzMRGP7sIHfAABqVasECwsLESJL1bNrB0RFRcPCwhz2JW3U2+UKBeITkhATFy9abERUOJUtWxYtW7aEm5ub+qbezMwMPXv2xPr162FnZ6eeHwEAzZo1g7Ozs/p1aGgoZsyYgeXLl8Pe3h5AarLQpUsXXLx4UV3O2NgYX3/9NRYtWqRuB0jtfXj27JlGnXPmzMG///6rHu40c+ZM9cptAFC7dm1YW1vj4MGD6sTm8ePHGu1v27YNNjb/fQ9+LCYmBgAy7cGIj8/59+Xp06fRvXt3hIeHIygoCD179sSwYcPU+5OSkvDu3TtcuXJF/W+Eaphfbpc+Pn78OHr37g1/f3/ExMSgVatW6Nevn0ZbPj4+uHz5MszMzHLV1qNHj3DgwAE8ePAAEokEQGrP2MqVK/HPP//kyZyjJUuW4P3793ByclIvVrF3717MnTtX3es0YsQIdVKjOqfAwEAsX75cfb1SUlIgl8sRFhbGxIaIKLdK2hRH2ZI20NVNPyF2+KB+GRxR8MqWynr4WVKyDF6+H5jgEJEGVaKhupkF/uvJ+PgXfnt7e425HC4uLoiOjka1atU0ymWUMKjqTNvOP//8g+rVq2ssNtCrVy/06tULAPDs2TN4enri9u3b6NGjB2QyGZKTk2Fvbw9HR0f1Md26dcPJkycxcOBAzJ07F02aNMnynFVDzj6eq6Ga5/Hx8KmsdOvWDVZWVvj7778hCII62VK5d+8eOnfurDGfx8XFBQA0buBzom/fvrCxscHhw4czbOvu3bvo1auXRlLn4uICiUSSbVunT5+GgYEBFi9eDJlMBplMhsTERNStWxeWlpa5ijMjt2/fxubNm3H69GmNWObNm4dSpUrhjz/+gJmZmUZSGBsbCw8PD/z6668avWsuLi6wsrJCuXLlPjuutJjYEFGRZ1PcAo72JcUO47MZGuijVpXyePzyDeITk8QOh4i0kEQi0Zjg//LlSwCpPTK5JQgCXFxcskxCbt++DQCYP38+OnbM/Meb3bt3o2TJkti5cydOnDiBgQMHYv/+/RmuzgZA/Sv/x5P4k5JSvxuz6u35WIkSJQAATk5OsLGxQa1atdT7oqKi8OLFC4wZM0bjmHPnzqFcuXKoWrVqjtsB/pt47+TkBAcHB/Wy2gAQGBgIHx8fzJ07N11b1apVQ9myZbOs28XFBQYGBjhz5kyuYsqJN2/eYNy4cbhy5QoaNmyosa9UqVIAUs+pTZs2GtfM1dUVCoUCX331lcYx58+fR6dOnbKdM5RbXBWNiIq88mW0P6lJy75Uzv/BJiLKSsmSqd+PL168yPWxEokExYsXx+PHjzMto+pZefbsWaZlBEGAiYkJNm7cCG9vbwwZMgRHjhzBxo0bMz2mTp06AFKTgbRUw7U+ZdiV6sY8rdu3b0OpVGpsj4+Px7lz5zBw4EAA/yWHuW3r45t9VS9Q2u2RkZG4dOlSjtoyMTFBdHR0nj+gNDQ0FCNHjsRff/2lTmoSExMxZ84cdZnY2Fi4u7tneE7FihXT6OG5c+cOfH19P+v9ywwTGyIq0kyMDDMcflZQFAoF7t+/jxMnTuDWrVvqceGfw9zUJPtCRPTFUM3BSLu8s1wu1/i/ikKhAPDfEK66desCAP7991+Ncv7+/gD+6wHJrM4WLVogOjoaZ8+e1Tj+zZs3kMvlaNasGXR0dLB9+/Z0815U9fzzzz+YP38+gNREa//+/XBwcMgy2erfvz8MDAzSLUX84sULGBkZaTzXJyffu+Hh4Xjx4gVatmypsd3JyQnFixdH7dr/rQ559epVxMfHY/DgwYiNjcWKFSty1db79+/x9u1btGrVSmP7jRs3UKpUKY1enIsXLyIlJQWDBw9GeHi4ekGDjKhiTzunSuXjz0FGS0tnJCEhAePGjcPu3bs1eqfu3LkDc3Nz9etbt25BoVCke/9u3LiBFi1aaPTinDlzBhYWFujatStcXV1x/vz5HMWSE0xsiKhIy2wYQ1rz589H7dq1YWVlBSsrKzRo0AAtWrRA06ZNUa1aNXTr1i3bJzR/TCaTYenSpWjZsiWuXLkCiUSCM2fOoFatWpg7d26650vkhpiJGhEVPqpJ26r/A//1kHh4eGiUVf06ripbv359DBw4EMePH8f+/fsRGhqK9evX4/z585BIJBg3bhz++ecfAMCTJ080/g8Ay5YtQ7FixfD999/jyJEj8PPzw549e7B8+XLo6uqiYsWKmDhxIjw9PdGzZ088evQIPj4++PPPP/H7778DSF3sYOfOnepnnrx+/RoBAQEYO3ZspudsYWGBFStWYOfOneokTalUYt++ffj+++/VE+8vXLgAKysr/PLLL1m+h7du3YJSqUzX43D9+vV0vThRUVEoVaoUatasiT/++AOTJ08GAJw4cQLFixfHunXrsmxLtdDCx23duHEDbdu21dgWHR2NChUqwNHRERs2bMDUqVMzrXfKlClwdHTE+vXrsWjRIvj5+cHd3R3Tpk3D/fv31eVKliwJT09PXL9+HevWrYOPj0+G9SmVSgwYMACXLl1Co0aNYGFhAQsLC5iamqJjx44a87Ju3ryZrmcmPj4ebm5uGZ5T27Ztoaenh507d6Yb5vc5mNgQ0Rdv+fLl6t6UGjVq4OHDh7h9+zbu3r0LDw8PjBkzBt9//z1+/PHHHNX34MED1K1bFwEBAbh58ybmz5+Pfv36Yc2aNbh79y7279+v7oInIvocffv2hVKpRPv27bFkyRKcPn0aGzZswJkzZ9CuXTvcvn0be/bsAQBMnToVOjo6aNeuHWbPno07d+4AAHbt2oXFixdjw4YN6Nu3L8qXL499+/ahcePGmDhxImrUqIFt27Zhz549aNeuHXx8fDBx4kQAQKVKlfDkyRP06NEDy5cvR7t27fD69Wv8+eef6hg3bNiALVu2QCqV4ptvvsGMGTNgamqKn3/+GUDqHI2mTZuiX79+6Nu3L0aMGIGDBw9mu4DAtGnTMHHiRHz33XdYvHgxBgwYgEaNGmn0atSsWROdO3fGsWPHsqwrNjYWLVu21JhfA6T2cE2YMEFjW//+/dGmTRtMmTIFZcqUUcdZr149tG3bNtu24uPj0b59e43FE1S+//57jdeDBw9GgwYNMGXKFFSvXl09BC8jJiYmcHNzw8SJE3HhwgV07twZW7duxejRo9G8eXN1uWnTpsHS0hK//PILKleujPLly2dY39u3byGTydCqVSs0btxY/V/z5s3Rvn17dW8fkNqzM2LECI0fE0NDQ+Hg4IChQzWfQTZ9+nRIpVJMmjQJY8aMUa+ulhckwuc+IpaIstWx9yAAqQ8YFPNZHHfv3selK6nr1i9eOE+0OABg5e9rkJSUhK/atMJXbVrnWzvFTE1Qq0rGX9ppXbx4ET179sSiRYuwcOHCdPtr164NHx8fBAYGpnsgXFoPHz5Ehw4dMG3aNCxevDjDMgcOHMB3332Hc+fOoXv37jk+l7RuP3z+ScflVEFdn5xYvDT1l1axP7NOzjfh5HwLtWtWw5pf0n9GiEg8QUFBsLOzy3BfbGwsxowZk23CkRciIiIwdepUHDx4MN/bovTYY0NEhMyHBqgEBQUhISEBoaGhmdYRFBSELl26oGbNmhkmRyoNGjQAgAL5R5aI6EuQWVLz6tUrDBs2TN07lJ+ePXuGESNGYN48cX+E+ZJxuWciIqQmNoaGhmjatGm6fc+ePUNYWFiWXfZA6kPpwsPDsX79+iyXsFSt2//x2HciIsp7+/fvz9OHQGZGKpXi8OHDWfbqU/5iYkNEX7y4uDg8evQIrVq1Uj8pW0Uul2PmzJmwtrbOsofl+fPnOHjwIOrUqaPukcmMajlS1epERESUP3L7nJnPUaNGjQJrizLGxIaIvnguLi6Qy+UoX768eunQqKgoeHh4YNOmTahcuTJu3bqV5XMRDh8+DKVSiSFDhmTb3uvXrwEA1atXz5sTICIiIiY2REROTk6QSCTQ0dHBpUuXAKQuE12+fHn8/fffqFixYrZ1qObofPxcgoyo2ki7ogwRERF9HiY2RPTFc3Z2hlQqxe+//67xwLHceP/+PYDshyIIgoBz586hWLFiGDVq1Ce1RUREROlxVTQi+qLFx8fj0aNHqFOnTpZJzV9//YWpU6di7ty5uHfvXrr9JUqUgI6OTraTRvfu3QsfHx9Mnz493dr9ycnJWLVqlfqJ30RERJRzTGyI6Iumml/TunXmz2r54YcfIJPJsHLlSnTs2BE9evTA5s2bNcrUrVsXCoUCgYGB6m3Pnz/HgwcP1K8TExOxcOFCNGjQIN3DPkePHo3Jkydj3rx5ePfuXR6dHRER0ZeDiQ0RfdFUc2PatGmT4f6kpCTs378f9vb2MDY2Rrt27TBhwgQsWrRIo9x3330HiUSCq1dTH4C6ZMkSnD17FqdPn8bRo0eRkJCAb7/9FiYmJrh48SJMTEw0jt+1axd27Nih8dRmIiIiyjnOsSGiL1JSUhLev3+Pffv2QRAE2NnZQSaTpVvu2dDQEP369YOlpaV6W/HixREbGwu5XA5d3dSv0VatWuH7779X98gEBQVh69atEAQBnTt3xtq1a2Fvb4/r16+jRIkSBXquREREXwImNkT0RRo7dizi4uLQsmVLCIKAlStXokKFCli9enW6slu2bNF4ffLkSQwaNEid1KQtd+DAAYwaNQrR0dGYN28enj17BmdnZ1y8eBHt27cHAFy+fBkdOnRg7wwREVEeYmJDREVaskyW4fYDBw58Un1r166Fqakp/vzzzwz3Dxs2DMOGDUNsbCyCg4NRrlw5FCtWDGXLlgUABAQEYNGiRejcufMntQ8ASckZnxMREdGXjHNsiKhIS5al5Fki8Oeff+Lp06f4+++/YWhomGVZMzMzVKxYEbq6uhAEAV27dsXYsWNRo0YNjBgx4rPiiImL/6zjiYiIiiImNkRU5Hn5fvjsOrZu3YqIiAjs3bsXenp6+OGHHyCXy3N0bL169fD27Vvs2rULbdq0wfjx4z85DrlCgbf+gdkXJCIi+sJwKBoRFXkxcfF4/PINytuXhLmZSfYHfGTTpk1Yu3Yt2rRpg5EjR0Iul8PHxyfdHJvMHDx4EHv37kWTJk3QpUuXTMslJiZCoVAgNjY2w/0h4ZF46x8IhUKZ63MgIiIq6pjYENEXIT4xCc89fQAAxUw1k5t9+w8CALp07ghbW1uNfSkpKbh46SqqVq+J4NBw9fbGzVri2WufHLYuQf8hIwEAL9/4ZVhi88Z1cHd/hKo1amPR0uXYu/8QJk+bCQtLSygUCsQnJuWwLSIioi8TExsi+uJ8PEflyfOXAIB69evDyMQ0Xfl5S37JUT2fY9iocVDsOwDfd34o51AWI74bludtEBERFWWcY0NERERERFqPiQ0REREREWk9JjZERERERKT1mNgQEREREZHWY2JDRERERERaj6uiERWgx0+ewvddxsv9FoT379+r/+zkfEu0OACoH27p+85P9FhUxL4+UdEx6v+L/Z4UxusjdhxifjaIiCh7EkEQBLGDICrqOvYeJHYIRJRHateshjW/LBQ7DCIi+gh7bIgKQO2a1cQOAQCQmJSEwMBgAIBjeQdRYwkIDEZSUhIsLSxgaWkuaixvfd4BAEra2cLIyFC0OCKjohEZGQVDQ0OUKmmb/QH5qDBeH7E/syoVypcTOwQiIsoAe2yIiIiIiEjrcfEAIiIiIiLSekxsiIiIiIhI6zGxISIiIiIircfEhoiIiIiItB4TGyIiIiIi0npMbIiIiIiISOsxsSEiIiIiIq3HxIaIiIiIiLQeExsiIiIiItJ6TGyIiIiIiEjrMbEhIiIiIiKtx8SGiIiIiIi0nq7YARARUaq9Lmexz+Wc2GEAAN4E+yEuORF25sVhZ24taiyP/V4DAOqWrSJqHEHRYQiKDoepoREq2pQVNZbCcn3ikhLwJsQfAK9PRtYN/gF1y1YVOwyiL4ZEEARB7CCIiAhYfGYrlpz5U+wwiCiP3JizE19VbSR2GERfDPbYEBEVMtbmlmhdu4GoMZy744wUeQqqlXVENQdHUWM5desaAKBvqw6ixnHr6UOERkfy+qTh/cEPT956AuD1SUv1mSWigsXEhoiokClhbolvRL5JvOx2O/XG2cFR9FhUN4lix+Hx7i1CoyN5fdK4dN9FndiI/Z4UpuvDxIZIHFw8gIiIiIiItB57bIiIiNIoY2qLKhYOsDQoBn0dPfX2wUu7ihiVpsF/ZhyLTJGCyOQYPAt/g5DEiAKOiohIXExsiIiI/q9W8YqoVbyS2GF8Mn0dPdgaF4etcXHcDXqKtzEfxA6JiKjAcCgaERERAEsDM61Oaj5Wv0Q1mOgaiR0GEVGBYWJDRESE1CFoRYm+jl6ROycioqxwKBoREREAG6PiWe6PiIjA6tWrIZfL0+2TSCSwt7dH7dq10bp161y3fe7cORw8eBAAEBcXh7i4OLRr1w5z586Fvr5+rutT0dfhP/NE9OVgjw0REVEOmJubo3fv3oiKisLq1asRExODXr164euvv0aHDh2gUCgwYMAA9O7dG3FxcTmq09vbG+3bt8ehQ4ewevVqHDt2DBcuXMCxY8fg6uqKxo0bIzg4OJ/PjIioaGBiQ0RElAM6Ojpo0qQJBEEAAEyePBktW7ZE8+bN0bFjR0ybNg1btmzBuXPnsGPHjmzrc3V1Rb169dCpUyccPXoU9vb26n12dnY4duwYwsLCMGvWrHw7JyKiooSJDRERUS44OTnB2toaNWvWTLfPwsICEokEFy5cyLKOJ0+eoHv37vj666/x008/ZVjGwsICrVu3xpEjR+Dt7Z0nsRMRFWVMbIiIiHLow4cPePv2babzaB48eABBEFC3bt1M6xAEAaNGjYK+vj42bdqUZXuq5OnZs2efHDMR0ZeCiQ0REVEOOTs7QxAEfPXVV+n2JSUlYevWrbCxscG4ceMyrWPXrl14/Pgxhg8fjmLFimXZnkwmAwC8f//+s+ImIvoSMLEhIiLKIScnJ0gkknSJjYeHB3r16gVdXV1cv34dlStXzrSOzZs3AwBGjhyZbXvv3r0DADg6On560EREXwiuA0lERJRDzs7O0NXVxaJFiyCRSKBUKhEVFYUSJUpg6NChGDJkCHR0dDI93s/PD0+fPkXp0qVRvXr1bNu7efMmAOSoLBHRl46JDRERUQ4EBATgzZs36NChA/76669PqsPLywsA0KhRo2zLvnz5Er6+vqhfvz7KlSv3Se0REX1JOBSNiIgoB1Tza7J7AGdISAgePXqEyMjIdPtSUlIAACVLlsy2vS1btgAAli5dqrFdLpfj+fPn8PT0hFKpzGn4RERFHntsiIiIcsDZ2RkA0KZNm0zLzJ49G4IgwNbWFvv27UOHDh2wbt069f7atWsDAGJjY7Nsy9PTEzt27EC7du3QtWtX9fZHjx5hzZo1aNy4MZ4/f45bt27h0KFDaNCgweecGhFRkcDEhoiIKAecnJxgZGSExo0bZ7j/5MmT+F97dx5XY/r/D/x1n06bkmQLyT52ZWtElC2VlLGTdTJMEyLLZDC2wTBmsw6DoRljGQyTJcSUikLWKcpW0YrSXqrz/v3R99w/xzmdk5Sm+byfj4fHzLnu67ru6z7n7j73+z7XkpWVhW3btgEAJkyYgKZNm6Jjx45wd3cHADRq1AitWrVCZGSkWG7lypV48OAB6tWrh2+//Rb5+fnw9PRE+/btcfjwYYV9eHp64tdff0WrVq0AAF5eXhg2bBiePHlSGYfMGGPVCndFY4wxxjSIiorC/fv38eGHH0JHR0dlnhcvXuDYsWPia1NTU7Ru3RpXrlxRyPfDDz/gxo0bOHPmDE6ePIkmTZrA19cXDRo0wLlz5zBgwAA8f/4c/v7+qFWrlkLZ+Ph4nD17Vnzdt29fJCYmIiEhoeIOljHGqikObBhjjLFShIeHY8yYMRgyZAiICHfu3MHw4cMREhKilHfGjBmIjY0VX2dnZyMuLg5du3ZVyOfo6IhffvkF06ZNw9q1a1GvXj3cuHEDsbGxmDRpEiZMmICIiAg0aNAAOTk5CmUfPXqEzz77THx9584dNGzYEKamphV74IwxVg1xVzTGGGMMQE5hLgAThbTu3bvjxx9/hI6ODqRSKYqLi1FQUIB69eqprENXV1f8/yVLlqBv375iN7TXTZo0Cc7OzggODkZYWBj09fUhk8lgb28PDw8PACVB1ZEjR7B+/XqV9cfHx2PHjh3Ys2eP2immGWPsfwUHNowxxhiA9ALlAf1aWlrl+jVk06ZNSEpKwrFjxyCVqv6qNTExgaurK1xdXQEA27dvx9KlS3HmzBm8ePECy5Ytw9GjR1WWTU1Nxfjx47Fv3z7069fvrY6JMcb+q7grGmOMMQbgUeZT5BTmvXM9GzduRHJyMg4ePAhtbW388ccfZSrXqFEjvHjxAk5OTpg4cSIGDBiATp06KeVLTU2Fu7s7fv75Z/Tr1w/nz59XObV0ekEmnmanvPPxMMZYdcGBDWOMMQagUFaEi4kRSC/ILHcd33//PSIjIzFkyBCEhoZi//79iI6OLlNZe3t72Nvbw8zMDJ9//jk2bdqklCclJQVjxoyBu7s70tPTERwcjI0bN6JmzZoK+dILMhGWfLvcx8EYY9URd0VjjDHG/k96QRZOx4XCzLABausqBgsXb1/H84x01K1VG307d1UqG3DiLObPnw8A2Llzp5i+YfdG3Hlxv0z7X//bRvH/72XGKm0fNdAF96NiEHQx6P9SBLRs0wp3Mx6LeVJy05Cal1am/THG2H8JBzaMMcbYG55mpyh149ry9wHcjX+EduYtULuxkVKZOt2a4Odryt3OdPR1cefFgwpp10Lf1QCAWZvXIjc/Dy69+uGjPgMqrH7GGKvOOLBhjDHGKoBURxtSHe1K3YeegT4AQNDWAoq1INXTgY6eroZSjDH2v4HH2DDGGGOMMcaqPQ5sGGOMMcYYY9UeBzaMMcYYY4yxao8DG8YYY4wxxli1x4ENY4wxxhhjrNoTiIiquhGMMcaA5ce2YcWxn6q6GYyxCvK3z07Yte1R1c1g7H8G/2LDGGOMMcYYq/b4FxvGGPuXiH2egNjniVXdDADAg5R4ZBfkwbRWHZjWqlulbbkZHw0AsDRvU6XtSM54juSMFzDU1UerBuZV2pZ/y+eTnZ+LB6lPAPDno4qleRsY11BezJUxVjk4sGGMMcYYY4xVe9wVjTHGGGOMMVbtcWDDGGOMMcYYq/Y4sGGMMcYYY4xVexzYMMYYY4wxxqo9DmwYY4wxxhhj1R4HNowxxhhjjLFqjwMbxhhjjDHGWLXHgQ1jjDHGGGOs2uPAhjHGGGOMMVbtcWDDGGOMMcYYq/Y4sGGMMcYYY4xVexzYMMYYY4wxxqo9DmwYY4wxxhhj1Z60qhvAGGP/a27evImtW7ciKysLBgYGmDt3Ljp06FDVzWKMMcaqNf7Fhv1nFRYW4tWrV1XdDFaBsrKyqroJ7ywmJgYbN27Epk2bsH//fvTu3RvW1ta4fft2VTeNMcZUSkhIqOomMFYm1SKwefLkCQICAnD+/Hk8f/68qpvz3uTl5SE8PBx+fn64d+8eZDJZVTep2igqKsLMmTPx7Nmz977v+Ph4nDt3DhcuXMCLFy/e+/7/je7fvw9/f38EBwcjMzOzXHUQEby8vJCUlFTBrXu//Pz8EBQUBF1dXQDA1KlTYWxsjL1791Zxy95OTk4OwsLC4Ofnh5iYGBBRVTeJVaLCwsJqeXMbFxdX1U0oFRGpbF9ycjLy8vKqoEWq3bp1CyNGjKjqZjBWJpXSFS0tLQ0jR45EfHw8cnNzoaurC1NTU0gkEuTm5kJHRwedOnWCj48PWrVqVWo9586dw7p169C4cWPY2dkhKSkJ8+bNg6mpKX755Rc0bNiwMppfZkQEZ2dnPHz4EJmZmZBKpWjYsCGkUikKCgogk8nQsWNHzJo1Cz169Chzvc+fP8eXX36JqKgoODs7o06dOvD19UV4eDh+/PFHfPTRR5V4VO8mIyMDLi4uSE1NBRGhsLAQUqkUx44dQ7t27QAANjY2SExMhI6ODoqLizFy5EisXbsWz58/x3fffYeOHTtizJgx2LFjB5KSktC0aVO4u7vD398f4eHhKCgowOeff45atWqV2o6ZM2dixowZaNy4sdK206dPY+XKlYiPjwcRoVatWjAxMRHb37BhQ1hbW+OLL76Anp5emY/99OnT2LBhA5o2bYo+ffogISEBc+bMgbm5OXbt2oUGDRq85bv5/uzZswdbt27F06dPAQB16tSBkZERiAgZGRlo2rQp+vfvD29vb0gkZX8esm/fPvz000+wsLDAhx9+iIsXL+Ljjz9G7969sWnTJtSsWbPMdQmCgG+//RbTpk2Dr68vDAwM3vo4K5Kbmxtu3bqFoqIiFBcXo6ioCN988w1GjhwJAJg1axb8/Pygq6uL4uJitGnTBidPnsTw4cOVzl2JRAJBEACU3ECuW7cO+vr6mDdvHg4dOoSoqCjo6+vD29sbt2/fhr+/P9LS0uDp6YkWLVqobF9RURGGDBmC2NhYZGVlQVtbGw0bNoSWlhby8/MhCAI6duyIOXPmwNLSsszHnZycjKVLl+Lhw4dwdnaGsbExfvnlF1y/fh1btmzBkCFDyveGsn+lhIQEjBkzBteuXYOlpSXCwsLKVU9GRgaMjIzE87yyTZo0CX5+fsjIyEBaWhqMjY3fy35Lk5WVhRo1akBLSwsAMHToUFy8eBHZ2dkoLCyERCLB119/jU2bNiEpKQmnTp2Cg4NDlbZZ7rffflMZ2Pz111+4fv06mjVrBhsbG7X3c4y9N1SJvv/+exIEgXbu3KmQnpaWRsOHDydjY2O6ceOGUrmsrCyaPHkytW/fnqKjo5W2u7q6kqmpKb148aKymv5Wjh07RoIg0BdffKGQnpubS56enqSnp0enTp0qU10HDx6kRo0a0aZNm5S2nTx5kqRSKW3fvr1C2l2ZgoODSSKRUN26dSkzM1NhW0xMDNWsWZO+++47ys7OFtPnzp1LGRkZpKOjQ25ubvTw4UMiImrdujVNnDiRTpw4QUREn3zyCS1atKjUfZ85c0btdjlbW1uSSqWUkpKikH7z5k1q3rw5devWjYqKijTWk5GRQW5ubtS5c2d68OCBwjaZTEaOjo5kZmZGL1++1FhXVWvevDmZmJhQQUGBQnpgYCDVqVOHnJ2dy1RPYmIiOTg4kK2trdL7m5ubS127diULCwsqLCx86zaePn1a6W+tqqSkpFCdOnVIEASKiIhQ2FZUVESmpqY0a9YsSk5OLrUOf39/qlmzJt2/f5+ISq6bkZGRZGlpSQ4ODnTx4kUiIhoxYgQNGzaMtmzZQsXFxbR582ZycnLS2Mbff/+dJBIJffXVVwrp2dnZ5O7uTjVq1KALFy6U6Xh9fX3J1NSUfv75Z6Vthw8fJi0tLfL19S1TXaz6yM7OJmNjY7K1tS1X+bS0NDIyMqLJkydXaLs0cXJyIolEQnl5ee91v2/Kzc2levXq0bBhwxTSbWxsSFdXVyFt5cqVJJFI6O+//36PLSydTCajJk2a0NOnT8W03NxcGjZsGC1YsIBOnDhBs2fPJqlUSosXL67CljJWolIDm1GjRpFEIqH4+HilbeHh4SQIAk2bNk0hPS8vj+zs7Khr166UlZWlst6XL1+SVCqlTz75pFLa/bYWLlxIgiBQYGCg0rbU1FQSBIH69++vsZ49e/aQtrY2nT59utQ8kyZNotq1ayvdLFYUe3v7ct1sqtKnTx8SBIHOnj0rpuXn59PQoUMpLCxMKf/hw4cpKiqKJBIJXb9+XUw3NTWlNWvWiK9Hjx5NPj4+KvdZVFRE3bp1U3sjSUT06tUrMjQ0pK5du6rcvmjRIhIEgfz8/NTWk5OTQzY2NvThhx8qBGmve/bsGUkkEvL09FRbV3kFBATQ6tWr37mexMREkkgk9NFHH6nc7ubmRhKJhG7fvq22ntTUVGrbti25uLiUei5dv36dBEGg9evXl6utPXv2pNjY2HKVJSKaM2cO3bx5s9zlX7dgwQISBIFWrVqlkD537lylhzpvio+Ppw4dOtClS5fEtMOHD1NhYSEZGBjQnj17xPTBgwfTmDFjxNerV68mR0dHje2bOXMmSSQSunLlitK22NhYkkgkNHToUI31bNu2jXR0dNTecI0cOZLq169P6enpGuurzuLi4mjy5Mkq39P/qrZt29KAAQPKVba4uJjc3Nzo999/V0g/dOhQpQY7Xl5eJJFIKuQ7LSQkhBwdHam4uLhc5adNm6b0QGDq1KlkYGCgkHbw4EGSSCQUHBxc7rZWpICAAKX7l9mzZ9PBgwcV0lauXEmCINCuXbveZ/MYU1KpgU2DBg2oRYsWKrf5+fmRIAhkZ2enkD5q1CiqUaMGRUVFqa27bdu2ZGhoWGFtfRcffvgh6evrU35+vtK2f/75hwRBoKZNm6qtIyAggLS1tWn+/Plq823atIkkEgn98ssv79Di0jVo0IBycnIqpK5Dhw6RIAjk4uJCRCVBx+jRo+n8+fOlltm6dSv17NlTfP3gwQOSSCTiTWxhYSHVrVtXIVh6nZ+fH40dO1Zj20JDQ0kQBPL29la53d3dnQRBoB9++EFtPS4uLmRoaCg+bS9NixYtyMTERGO7ymPfvn00Y8aMd65n//79JJFISj3mQYMGkUQioaNHj5ZaR1FREXXv3p0aNmxIz58/V5tPT0+PLC0ty9XWrVu30oIFC8pVlqjkV1915+HbePz4MUmlUjIzMxN/4Vu5ciV9++23asvFxcVR//796Z9//iEiUni/QkNDycjISLwhKy4uplq1atFff/0l5unTpw998803GtvXqVMnqlWrlsobsitXrpBEIqF27dqprcPPz4+0tLToyy+/VJtv3bp1JAiC0k3Pf8327dtJEAS6fPlyVTflvenQoUO5A5vSdO7cmbp161ahdb7O29u7wgKbCRMmkLa2dgW06v9zd3dXCmwOHTr0rwpspkyZQrt371ZIMzMzo549e9KrV6/EtIcPH5IgCDRkyJD33UTGFFTa5AFRUVFITU2FnZ2dyu2BgYEAAHt7ezHtzJkzOHLkCDw9PcXxGKVp0aIFcnNzER8fX1FNLpfs7Gxcv34dPXv2FAcDv07Vcb6pqKgIs2bNgpGREb766iu1+2vevDmICHfv3n2ndr8Pw4cPR+PGjXHq1Ck8evQI06dPx9ixY9G/f/9SywQGBipsDwwMhIWFBZo2bQoACAgIgJaWFvr374+dO3cqld+/fz8GDBigsW1BQUEAoPL8lMlkCA4OhiAIGDRoUKl1/PXXX/Dz84OXl5fGvsXNmzdHeno6kpOTNbatqsjPVVXvSU5ODq5duwapVKr289u2bRsiIiKwYsUK1KlTp9R8WlpaaNKkSbkHnQ8cOBAHDx5863KVoVmzZhgyZAgSEhJw9OhRbNmyBfn5+fD29i61TFxcHHx8fLB//3506NABOTk5WLt2rbg9MDAQffr0gVRaMgzy+vXrKCwsxODBgwGUjHu4fPkyxowZg927d5f6Hr548QJRUVGwsbFROTaqLNengoICeHl5oUGDBli6dKna96J58+YQBKFaXJ/ehba2NgBAR0dH5fbi4uIK32dZJ4+pjH1XlKKiIoXX2trapb6H/zZSqfSd2/rm8b8Pqs6HgoKCMpXNz8/H6dOnlcbXGBgY4NatWwqzVJqamkIQBERERLxbgxl7R5UW2Ki7cbx//z62bdsGe3t7zJ07V0xfsGABAMDd3V1j/SkpKQBQ5dP5hoSEoKioCLa2tkrb0tLSsHr1alhaWirctLxp586duHfvHtzc3FQGR69LTU0FUDLA+N9OS0sLM2bMQHFxMQYMGABbW1uNEx8EBQUpnDNBQUHo16+f+Pru3bsYMGAAQkJCkJubq1BWJpPBz89P5WfxpsDAQGhpaaFPnz5K27Zu3YoHDx5gw4YNaN++fal1LFy4EBKJBB9//LHG/VWHzy0oKAi1a9dG586dlbYtX74c2dnZ8PX1LXXShtzcXCxbtgwGBgYYO3asxv2lpqaiuLi4XDdirVu3RlFREa5evfrWZSvDzJkzAQDz5s1DdHQ0Vq9eXWre+Ph42NnZITIyEkOHDoWVlRUsLS3Rpk0bMU9gYKDS34G1tbV4YxUdHY02bdqAiHD79u1SB2QHBQWBiFT+TaSkpGDdunXo0aMHVqxYUWp7t2zZgtjYWEyaNEkMtEpTkef5kSNH8OjRI435Hjx4gLFjx8LZ2Rl9+/bFwIEDsXDhQnzzzTcASiah6datGzp16oQdO3aI5caNG4eOHTvCwsJCob6UlBR4enpixowZsLe3h42NDV6+fClu37hxI9asWQOgZEa73r17Y8mSJXj+/DmmTp2Kjh07Yvbs2bh9+zb69u2L5s2bIzY2FkDJNeqrr77ClClTMG3aNHh6eiIqKqrUY7tz5w7GjRuHZs2aYfv27bh+/TocHR1Rp04djBs3Djdu3BDzHj9+HK6urqhfvz5u3bqFH374AY0bN1b4Pk1ISMC4cePg5OSErl27YurUqYiMjFTab35+Pnx8fDBixAg4OTnB2toajx8/FrdnZGSgb9++6NixI8aNGyemb926FZ07d0bHjh0RGhoKoOT7fvLkybCwsMD48eMBlHxv29vbIyYmBpGRkejduzdsbGzE40lMTMTw4cMxbNgwDBw4EBYWFjh37lyp75Pcb7/9hqFDh2L48OGwsrLC4cOHVeY7cOAA3NzcMHXqVEyfPh1nz55VW6+7uztOnz6NgoIC9O7dG7179xbrLigowJIlS+Dh4YHRo0fjgw8+wJ07d8SyT58+xdSpU9GtW7d3mlgjLi4Obm5u+OSTT+Du7o5169ZpDJT27dsHDw8P9OnTB8+ePYOfnx+8vb2xaNEidOnSBRcvXlRb/vjx47C1tYWRkZFCenh4OO7fvy9OuiNPA6D2O5Ox96KyfgoaPXo0CYJA/v7+FBUVRf/88w/5+/vT0qVLqWHDhuTj46PQdevmzZskkUioR48eGusuLi6m2rVrk76+vtr+rkVFReTt7U2enp5l/uft7V3q2B5VfHx8xAkSoqKiKCoqis6fP0/r168nMzMzmjFjBqWlpamto3fv3iQIQpn6a8v3p2rwbkWoyK5oRCWDq3V1dcnY2Jhyc3PV5i0qKqIvv/xSYeD6tm3bFAbkp6en06pVq1ROoBAfH08SiURll8DXFRYWkqGhIX3wwQfiZ3bjxg06fPgwjRkzhlq3bk0HDhxQW4d8jJiNjY3afPL91axZk4yMjDTmLY+K6IqWlJREEomEbG1txffk2rVrtH//frK3t6cuXbqU2v1P7o8//iCJRELjx4/XuL/k5GSSSCTUoUOHcre5Z8+e9Ouvv5arbEV2RZNr27atykkE3hQaGkqrVq1S+iefLIOI6JtvvlEYJ3bs2DGFrikymYw2bNhA69evV3u+z549myQSCf32228UFRVFkZGRdO7cOVqzZg01btyYZs6cSRkZGWrb26VLF5JIJGKXOXXk+9u3b5/GvOrcvHmzTN1arl+/TjVr1qRjx46JaUuWLCGJREJLliwR0+QTvHz33XcK5bt160a1atUSX8tkMmrfvj19//33RFTyXdO+fXulcSB79uxR+qxlMhmFhISQVCqlHj16kIuLC23dupWsrKwoKSmJiEomPnl9nIaPjw/Vq1ePYmJiVB5fQUEB7d69mwRBoB49etDcuXMpPT2dHj16RFZWVlS3bl2xbHp6Onl5eZEgCPTRRx/R4sWLacqUKeTl5UVEJV0m69evL07uIJPJ6PPPPyd9fX06cuSIuM/i4mKysbGhWbNmkUwmIyKiGzdukJ6enkJXtIyMDDI0NFQaf/Hll1+SRCKhoKAgIiq5/smvDRMmTFDI26NHD7K2tlY67v79+9Onn34qlu/atavS+Jw3LV++nKysrMRJhV6+fEmdO3cmQRAUuqLt2rWLmjVrJn4vHzt2jLS1tRW6eaqiqtsYEdHkyZMVxr5NnjyZ2rRpI74uKioif39/lWPZytoVLTU1lerVq0eHDx8mopKxnU2aNKFRo0aV2t6cnBwaPXo0EZVMwNO9e3eF701vb2+Fbt+qODs7a3xf5GbPnk1aWlrk7+9fpvyMVZZKme4ZAC5evAgTExNcunQJly5dAgAYGhqie/fumDNnjkKkDwB///03AKBv374a6w4LC0NGRga6deumdupZLS0t2NnZlflnV3kZeTeDsggKCoKWlhZiY2PFbnF6enpo3bo1wsPD0ahRI7XlCwoKEBYWBkNDQ3Tt2lXj/vz9/QFA5VP1f6MDBw7AxMQEycnJ2LdvH6ZNm1ZqXi0tLaUnx59++qnCa2NjYyxZskRl+bi4OBgZGWn81evatWvIyclB3bp1ceDAATG9QYMG+PTTT9G3b1+NUxrLz1dVv/i8KTg4GNnZ2ejVq5fGvFVF/mS/Ro0aCu+JmZkZli9fDmtra411vM3fsPw8fvNp+duoX7/+v2aNiqCgIPE6s3XrVpXdJOV69eql8VyYP3++wmtXV1eF14IgYN68eRrbFRgYCB0dHcTExCAmJgYAoK+vjzZt2iAiIkLjFOQvX77ErVu3YGJigg4dOmjcX0Vdnzp06IDFixdj4MCBavPNmTMHvXr1Unh/vLy8xF9U5D744AMAULo2tGrVSqE78/PnzyGVStG9e3cAJdNwDxgwAEeOHNHYZkEQ0Lt3b7Ro0QLXr1/Hw4cP0bRpU3h4eAAAbt68id27dyM8PFy8vgwePBjr16/HyZMnMWfOHKU6dXR0MG7cOEybNg0GBgb47rvvAJRcB3fs2IGuXbti7dq12L17N4yNjTFs2DBs3LgReXl5St2aFy9ejA8++AATJ04U27ty5UocOnQIM2fOhKOjI/T19bF582Zcv34d/v7+4i+BlpaWaNasmUJ9RkZGMDU1Veqe1bp1a4X3WiqVYuTIkdDV1S1zV65r166J9whSqRRbt25Vumd4XWRkJNasWYNjx46J+WrVqoV+/fop/HqSk5ODRYsWYdmyZahduzYAYNCgQSAi7Nu3D0OHDi1T+1739OlTcYp3oKRbp6+vL+Li4tC0aVNoaWlh8ODBqFev3lvdW7xuxYoVaNq0qdglrEaNGrCxscHBgweRm5uLGjVqKJU5e/YsnJyckJubi7i4OIwcORLTp08XtxcWFqpdE+z58+eIiIiAo6OjxvZdunQJW7duxbp168TusoxVlUoJbO7du4eUlBSMGDFCbReH1z158gQAyvTlefz4cQDA7NmzNeYtz4WqrHJychAREQELCwusWrWqXHU8ffoUMpkMbdq0Eee3L01cXBxu376Nnj17wsrKqlz7A0ouaCNHjlQZ8L18+RKurq5KbdHT08Mvv/wifhmUha+vLx4+fIgDBw7Azs4OW7ZsURvYvKvMzEyVF/g3yccVfPbZZ3BzcyvXvuTna8eOHTXmfZvzVZ0///wT27dvV0pPSkpCenq6yjUPHB0d4eXlpbFuedfRRYsWlSlYU6Wy/oZLU6NGDYU+3qrMmTMH9+7dU0q/efMmEhMTVd4srV27Fl26dClzOyIiIrBhwwaEhoaidevWOHDgAL755pu3+lupDGlpaYiMjESvXr3KfB1+k/wzLUv3krt37+LBgwfo169fmf4u1JFKpRqvqRkZGQgJCVEK8FQ92CjtQcXr6wcBQL169XDr1i0AJeMnL168iOjoaCQnJyMpKalMa6dpa2ujW7du4rhAuT///BO6urpYtWoVXr16hVevXiEnJwcdOnRQ6urzZn0AlM5JCwsL1K1bV6E7kTzv6zfacn5+fkpdgXV0dGBtbY0DBw4gOjoalpaW8PPzg7m5udI6Uaq+n958/+Rpqmj6fnudo6MjDh8+jPHjx2PRokX48MMP1eb39/dHYWGh0nn65j4vXryI58+f46+//sKpU6dQUFCA/Px8tG/fHqampmVu3+sCAgIAlIyfCQsLE8dnRkREKJwDUqm03Gv4HDlyBCYmJnBxcRHPnZcvX8LS0hL5+fkqv/f69OkDAwMDBAcHo7CwEJ6engrbQ0JC1D5MPXjwID766CON3U8zMzMxefJkfP7552V62MJYZauUwEZ+41iWsQ5ydevWBQCNi2g9e/YM27dvR9u2bcX+ulUlNDQUhYWFZTrO48ePw9jYWClvnTp1IAiC2sUm5VauXAkiwsqVK5W2vXjxAtu3b8cXX3yhsR5tbW0sXbpU5fikq1evwsfHB/r6+grpWlpaar9833T8+HEEBgZi9+7dAIBOnTrh1q1bCA0NRe/evctcz9vQ0tIq0wDboKAgCIKg8XN7+fIltmzZgi+++ELpC0l+vmr63JKSkrBr1y507twZo0ePFtOLi4uxb98+3Lx5E6amphg/fjzMzMzU1mVra6vyCfvZs2dx8+ZNLFy4UGlbWRexDQwMhL6+vtobiKtXr+LYsWMAgH79+ik9TS/r3/CtW7fw119/wcnJSeX+Dh48iObNm2sM3mUymcabJQ8PD7x48UIp3cfHB6NGjUK3bt2Utr3NInP37t3D4sWL8ccff6BmzZoYP348du7cid27d1f5l/zFixdLHV8jl5+fj7179+LevXswNzfHxIkTxc8RKPt5DkC8Lr15fbp+/TqOHj0KmUwGW1vbCnuiK5+goKIHnz99+hRLlizBs2fPMGbMGHTr1g0BAQFvNfBb1cKzISEh0NXVFf+GKkK7du1UTtTw5v5TUlKQnZ2t8ia1devWICKkpaUBKJn4p6oXv/75559Rt25d7Nq1C4cOHcLYsWOxZ8+eUm+y5eOEVN3gv37tDgkJARHhxx9/VBjT9i7y8/OxfPlyXL58GSNGjIC1tTW2b99eYRMFPHjwACkpKZg8eTK+/vrrMpeTT94SGBiImjVrKlxrExIScOvWLaUeEa/bt28fvv32W7X7KCwsxIgRIzBz5swyPUBj7H2olMBG/vT3bQIbeZeUhIQEMS0jIwORkZHo0aOH+CRq+fLlKCwsxPbt2zV2FyoqKkKvXr3eqiuarq4uTp48iXr16mnMKw/g1HW92bBhA27duoWLFy/i008/VXpPjI2NYW5ujsTERDGNiBAREYFGjRqJXdnu3LkDX19fTJkyReGG8vHjx1iyZAlycnJw6tSpMgU2AMSuFm/S1taGtbV1mX75KM2FCxewf/9+7Nu3T0zz9PTEp59+ii1btlRaYNOoUSPxy7k0xcXFCA0NRbNmzUoNJJKSkjB//nwUFBTg6NGjmDdvHvT09BTyyM/X1z+3ly9f4u7du+jevbt4vspnkXr9lxaZTIaJEydiypQpWLp0KQ4ePIj27dvj9OnTat8bExMTlV2YYmNjkZycXO6ubikpKYiOjoatrW2pN4m//vor7t+/j9mzZyM+Ph4TJkyAg4MDfvzxRzGPhYUFiAgJCQniE/uUlBTExcWhR48e4g3GggULUKdOHXz//fcK+1i5ciUePHiAgIAALF68WGNg8+LFC43d3kq7eZF3rXqX7oFxcXGYPXs2fv/9d/FG0tPTE7t27cJPP/0Eb2/v97bKuiqark/5+flwc3ODt7c3RowYgR07dqBt27YIDg4WZ6Vs2LAh6tatq3R9unr1Kpo2bSoG2leuXMGhQ4fg4eGh8J4eOnQIN27cgJeXFxITEzFx4kTY2Nio/OXxbcm7RmkaAP02kpOTYW1tjWnTpmHPnj0ASiYLqAj6+vrIyMhAYmKixi7KZZWRkVGmbn8mJiaQSqVqZxGVB/Smpqa4d+8eiKhM5y+VY1ZDTWrWrInNmzdj0aJF8PHxwb59+2BpaanURVNOPiNXVFSU2vsO+fdaZGRkhQU2gwYNgrGxMf7++29IJBJcuXKlQuqVkz9kVDXJQ1kEBgbCxsZG4SHQgQMHoKWlheHDhyMvLw9paWlo3LixuP3Bgwd49uyZxi7I7u7umDBhAiZPniymzZ07V+nazth7VRkDdxo2bEh16tR5qzI5OTlkbm4uLg4YFhZGY8eOpc2bN4sLG+7cuZP09fXp+PHjZa43PT2dUlJSyvzv2bNnZa67V69epKWlJQ5WVGfQoEEKi0y+bunSpaSjo0NxcXFUXFxMEydOpI0bN9KoUaMoNjaW4uLiqH379uTi4iKuk/GmS5cuVcgc++86ecCZM2fI0dFRaUBzTk4O1a5dm3R1dTUunlleGRkZJJFI1H4eYWFhJAgCTZ06VWN9d+7cIUEQVK5anZmZSY0aNRLXzAkODqbx48fTpk2bxMG6W7duJX19fTp16pRC2atXr1LLli3FAcVEJStkDxw4sCyHqeRdJw+Qrze0bNmyUvNYWlrSb7/9Jr4+ePAgCYJAT548EdPi4+PJ0NCQFi5cSEQlC01Onz6dNmzYIC5euXjxYqpVq5baAfZWVla0efNmje3u2LGjxgVUS/OukwdER0dT3759FVbjlrOxsSFBEJQ+9/fN0tKSdHR0Sl049vjx49S5c2eFST0sLCxo0qRJCvnmzZtHNWrUoOTkZHr16hWNHz+eNm/eTCNGjKDExER68OABtW7dmsaMGSMONpezsrJSWHNLPoj/9QlBSrN37166e/eu2jwffPAB6erqUmJiopiWmZmpNHnAkydPSBAEmjt3rkL5Pn36KEzqsWHDBpJIJPTo0SOltNcnd5BPHnDx4kWVbbK1tVVKX716NQmCoHL9JU2T4EgkEvG6IpeYmEg1a9ZUGBD+999/kyAIKidvGDBgABkYGCituTVo0CDq3Lmz+Hrq1KkkCILCorGFhYVUr149pclSunTpQq1atVJIW7duHUkkEqUFq/X09JTOrR49eijsm4jo3Llz4jVErnXr1jRx4kSlY5KTX4/eXGdJPomRfEKg8+fPi+vnvfmea1p4093dnaRSqUK+kJAQEgRBYWIDedqbn0GDBg3I1dVVIW3y5Mmkq6urkPb777+TRCJRWAi3efPmpK2trfT3oKnN2dnZpKOjo3TvYW1tTYMHDyYioq+//lppwezly5drXLNq0aJFSscoX4CbsapUoYFNQUEB7d27V5wtqrQv1NIcP36cdHV16ciRI+Th4SHeUH788cc0d+5catGiBZ08ebIim1wur169ogsXLpC2tjaZm5vTy5cvNZZRF9jk5eVRhw4dyMXFhfz9/cXFsMLCwmjSpElkbm5OXl5eKm+w5aoysJHJZHTjxg2aP38+SaVSOnTokFKelJQU6tOnDwmCQJ999pnGGdLKq1OnTqXesMpniREEgdasWaOwuJgq6gIbopIbd11dXfLz86Pp06eL9U2aNIm8vLyoVatWdObMGaVyycnJNH78eIUAbMqUKdSlS5eyHqaC8gY2MpmMMjMzxRtxX1/fUheyW7p0qcIDhcDAQBIEgW7evKmQ74cffiBDQ0MKDw+nKVOmiOnDhw+nCRMmUJcuXTTO/leWwCYnJ4cMDAwoNTVV02GqVN7A5uHDh/Tjjz+SkZGRysV0c3JyyMPDgwRBIGtra40zjlWGV69e0alTp0hLS4vatGlDmZmZKvNFR0fThAkTFGYhtLe3V5qJLCsri1q1akWjRo2i48ePizMGXrhwgaZOnUqNGzemBQsWqPx7WrlypTiTExHR5cuXSRAECg8PV3sMN27cIIlEQk5OTmrz3bt3jxo0aEB2dnaUlJREMpmMzp49S4IgKAQ2RESNGzcmMzMzSkpKoidPntCsWbPIzMyMBEGgcePG0d27d8nX15ckEgl9/fXXJJPJKDg4mNq3b08SiYQOHDggBjf+/v4kCAItXLiQzp8/Tzt37iQiomfPnpGRkRGZmZkpffZZWVnUvHlzkkgktHLlSkpMTKR//vmH5s6dq3YxRnlgY21tLV6bY2JiqHfv3uLNqdyPP/5IgiDQvHnzlOq5e/cuNWrUiLp27Sr+3V6+fJkMDAwUbmxjYmLI2NiYunfvTtHR0XT//n1yc3Oj2rVrk1QqpTlz5oiLyX7yySckkUjo5MmTlJWVRdu2baPOnTuTRCKhrl27iteMmJgYcdbT14PfoUOHkpGREQUGBtK2bdvo7t27FBYWRnXq1BHP28ePH5Oenp5SoPS6goIC6tmzJxkaGlJAQAA9f/6cli1bRi1atCCJREJDhgyhq1evElHJTF/yzzwmJoYePXpEGzZsoB07dpRaP1HJQxn5eXDw4EE6d+4cxcTEkCAINHbsWMrNzaVHjx6Rg4MDCYJA8+fPp+joaCIiSkhIIB0dHWrXrp14jZXJZGRlZUUSiUQh2JTv5/Vr4KFDh0gqlVKTJk0oICCAnj17RmfOnKGpU6eq/R47d+4cCYJAoaGhCunt2rWj77//ntLS0sjNzU2p3AcffCC2XZXNmzeTtrY21a1bV/xnYmJCurq6FbJYNGPvosICmytXrtDAgQPJycmJXFxcaMiQITRw4MC3nvovIiKC+vbtS6amprRs2TKaNm0amZqa0syZM8VfAZKSkujOnTsV1fS3Eh8fTwMHDiRHR0dycXEhZ2dnsre3V3gqqYq6wIaIKDc3l+bOnUstW7YkJycnWrx4MfXq1YtatWpFkZGRYr7SptytysDm559/psGDB5OLiws5OjqSvb09paeni9tlMhmNGTOGHBwcFM6NGzduvHN737RmzRpavHixUvr3339P9vb25OzsTC4uLuTk5EQODg4K7XyTpsCGqOS8t7GxoYYNG9Ly5cvJ3d2d6tevT3PnzhVvGJ8+fUpRUVGl1pGTk0ONGzcu0yryqpQ3sPHx8VF4TxwdHcnV1VXpqbsqs2fPJgsLC5VPDP39/cnKyorMzc1p1apVNGHCBDIyMqJvvvlGrPuff/5ReMr+urIENmfOnCEHB4cyHKVq5QlsQkNDadCgQTR06FDxF7Y3g7SlS5fS4MGDaejQoeTs7EyDBg1656mP38b9+/eVrk+DBg2i/fv3ayybnJxMNWvWVNnerKws8vT0pObNm5OrqystWrSIrKysqF27dgpTFWuaEnzhwoXUrl27Un95lisuLqY1a9bQ5cuXNbY7ISGBvv76a7KwsCArKyvxF4c3A5t//vmHhg8fTubm5jRixAiKjIykjRs3kqurKx08eJDS0tKooKCA3N3dyczMjLp06UJr166lu3fvUteuXalTp07ie5OXl0cDBw6kli1b0meffUaZmZl05coVsre3p759+1Lfvn3J3t5e4ak7EdGLFy9oxowZ1LlzZ2rZsiVNnjxZ4/Tg8sCmffv25ODgQA4ODmRlZUXr1q1TeBCxatUqsrW1JVtbW+rTpw+NGDFCqa60tDRasmQJWVlZ0bBhw2jSpEkqv0vDwsLIzc2NmjVrRuPHj6enT5/Sp59+StOnTyc/Pz/xmpibm0uzZs2ili1bko2NDf3xxx90//596tSpE23bto2io6MpICCABgwYILbL2dlZfLDl7+9PTZs2pd69e4sB8+PHj8nBwYEGDBhAw4cPpx49etDevXs1nAUl9wXe3t7UunVr6tevHwUFBdGhQ4dowIAB9Ouvv4q/kBcVFdGKFSuoZ8+eZGZmRsOHD6c///xTY/3R0dHUtm1bsrS0VLhWr1u3jlq1akVt27YlDw8PSkpKIgcHB2rRogUtXryYLl26RAMHDhTPCycnJ3r69CkNHTqU+vTpQ7a2tjRo0CAKCAggHx8f6tu3L9na2pKdnR2tX79e3E9AQAANGTKEmjRpQr169aKlS5eq/W4iKgmIunTpovTA6ujRozRq1CiaMWOGQs8BopLP3srKSm29H330EdnZ2an8p2mpBMYqW6WtY/Ou8vPz6datW5SamkoTJ06kr7/+Wtzm6uqq9KT4305TYPO6R48eUUxMDAUHB5O5ubmYfubMGZo+fbrKMv+WrmhVLTY2liwtLSukrrIENnJ5eXl069YtevbsGY0ZM0ZcB4OIyNHRUW1g4+7uTh4eHuVuZ0WsY/M2Lly4QO3bt6f4+Hi1+bKysujmzZuUnp5O1tbW4loZhYWFZGVlVer6TmUJbDw8PDSua6GOq6srXbhwodzl/2uKi4vJ2dmZVqxYoTHvgwcP6P79+3T27Flq27atmP7nn3/SnDlzSi0XEhJCbdu2VejmVRkyMzNVBjbVVVFRkcpudIxVhlmzZtHGjRuruhmMlVulrWPzrnR1dcVBkTKZDGvWrEFiYiKCgoJgbGz8Tutf/Ns1b94cQMkMcE+ePIGjoyNMTExw7NgxXL58uVL3vXfv3neaOKCqNW3aFLa2tjh16hScnJze23719PTE87W4uBjLly/H48ePceHCBTRq1EgcjP0mb29vNG7cuNzT8QLAwIEDyzTFckUICQnB6tWrceHCBY1roBgaGop/p8XFxfD09ERISAiOHz+O/v37l3s65GfPnuHOnTvYsmVLucoDJdNal/aZ/K+RyWSYMmUKHBwclKaEVaVly5YASiatiImJgaurK/T09HDy5Elx5fg3hYeHY+nSpTh//nyFDZxnjFWsoqIiHDlypNS/Y8aqA/XTiv1LWFhYIDs7G5s3b0ZCQoI4W81/XZs2baCnp4czZ85g//79WLp0aaUvzPlfWFxr2bJl+Omnn8o09XNlsLCwQGZmJjZt2oRnz55h165dKvN9/vnn6N69uxjUlHd64Pr167+XQD84OBi7d+/GiRMn0KBBA+zdu1dh8Tt1LCwskJKSgh9++AHa2toapxFVZ8OGDVizZs07zTj24YcfvtX05f9VxcXF8PDwgJubmxjUlPU8bN++PbS1tXHixAkcPnwYa9asERdnfF1YWBi2bt2KEydOoFGjRjhw4ACuXbtWocfxury8PIX/Vnf/teNh/15nzpyBpaUl6tevX9VNYazc/rW/2LzOy8sLr169gp6eHiZMmKDxSfG/UW5u7lt/MdWpUwfHjx/H2bNnMWzYMLVTAefk5EAmk+HVq1cVvq5DdVO7dm0sWLAACxcuxIYNG8pdT05ODgRBQF5entJ0z+osWLAARARDQ0NMmDBB5dThs2fPRlhYGLKyshASEoKCggIUFhaWu62VLSgoCG5ubnB2doa3tzeKi4sREhJS5hvUtWvXon79+jA3N8fYsWPVBhV5eXml/q3s378fpqam5V5ElP1/xcXFGD9+PFJTU3H8+HEcO3YM2dnZZb6+NmrUCEePHkVgYCCGDx+Onj17KuW5dOkSRo8eDWdnZ8yfPx8ymQwhISEIDQ2t6MMBAMTHx2PHjh0AgBMnTsDZ2Rl2dnaVsq/3ISEhQXwwcvLkSZw8eRJ2dnZKi2cyVhH27dtX7kWrGfu3EIgqYRJ6JvL19cXFixdRUFAAIoKBgQE+/vhjjSspl1V6ejq++OIL5OTkgIigpaUFMzMzfPXVVxVSf3V2/vx5NG/eHC1atHircnl5efD29lZ4T+vWrftOQdLr7t+/r3IxzVGjRlX5orOlmTlzpsIaU0DJ2hil/RpVHjt27EB4eLi4cKyBgQE8PDzEX6OICLt27cK0adMqbJ//y8LDw1Uu+Ddjxgw4ODhUyD7mzp2L2NhYhbSaNWvC19e3Qup/09WrVxEREQGpVAqZTAYiwowZMyplX+/DjRs3EBYWBm1tbchkMhQVFWHUqFFlWmeNsbe1YMECrFixolp3R2eMAxvGGGOMMcZYtVctxtgwxhhjjDHGmDoc2DDGGGOMMcaqPQ5sGGOMMcYYY9UeBzaMMcYYY4yxao8DG8YYY4wxxli1x4ENY4wxxhhjrNrjwIYxxhhjjDFW7XFgwxhjjDHGGKv2OLBhjDHGGGOMVXsc2DDGGGOMMcaqPQ5sGGOMMcYYY9UeBzaMMcYYY4yxao8DG8YYY4wxxli1x4ENY4wxxhhjrNrjwIYxxhhjjDFW7XFgwxhjjDHGGKv2OLBhjDHGGGOMVXv/D04devhrANSNAAAAAElFTkSuQmCC"
    }
   },
   "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": null,
   "id": "reponse-code-28e72621",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-28e72621",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-03d5dc76",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-03d5dc76",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "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": [],
   "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": "reponse-texte-a5f73052",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "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": null,
   "id": "reponse-code-bc53983b",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-bc53983b",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-59716255",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-59716255",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "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": "reponse-texte-627062da",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "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": null,
   "id": "reponse-code-7f572962",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-7f572962",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "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": [],
   "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": null,
   "id": "reponse-code-0f39b4ea",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-0f39b4ea",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-aad54456",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-aad54456",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": "reponse-texte-b159886b",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "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": null,
   "id": "reponse-code-2266da39",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-2266da39",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": {
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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": null,
   "id": "reponse-code-e2765334",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-e2765334",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "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": [],
   "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": "code",
   "execution_count": null,
   "id": "reponse-code-dced3bc8",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-242cd7ab",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "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": null,
   "id": "reponse-code-65ae195d",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-65ae195d",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "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": [],
   "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": null,
   "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": [],
   "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": "reponse-texte-9c449ad2",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "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": null,
   "id": "reponse-code-91995a4e",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-91995a4e",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "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": [],
   "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": null,
   "id": "reponse-code-120b80d7",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-120b80d7",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-b7ce82db",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-b7ce82db",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "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": [],
   "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": null,
   "id": "reponse-code-342832ff",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-342832ff",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-950793a2",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-950793a2",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": "code",
   "execution_count": null,
   "id": "reponse-code-c201bdff",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-f188ab69",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-9b54bfb2",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-9b54bfb2",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": "code",
   "execution_count": null,
   "id": "reponse-code-cc5e9072",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-074eced3",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": {
     "image/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": "code",
   "execution_count": null,
   "id": "reponse-code-83e2e144",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-a3164af9",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-aaabbf21",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-aaabbf21",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": "reponse-texte-269710b8",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "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": null,
   "id": "reponse-code-2c798842",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-2c798842",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-f4f99b3c",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-f4f99b3c",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-4de04f3b",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-4de04f3b",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": "reponse-texte-bead3755",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "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": null,
   "id": "reponse-code-9b6d214d",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-9b6d214d",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "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": [],
   "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": null,
   "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": [],
   "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": null,
   "id": "reponse-code-f2d57e44",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-f2d57e44",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-d9d17d68",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-d9d17d68",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "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": [],
   "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": null,
   "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": null,
   "id": "reponse-code-9a85df0b",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-9a85df0b",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": "reponse-texte-d586c952",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "attachments": {
    "fig_logimage.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": null,
   "id": "reponse-code-30a70c50",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-30a70c50",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-0c3be223",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-0c3be223",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-bd75bb7e",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-bd75bb7e",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "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": [],
   "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": null,
   "id": "reponse-code-9b858b8d",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-9b858b8d",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-0c12468b",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-0c12468b",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "id": "reponse-code-14281d26",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-14281d26",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": [],
   "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": null,
   "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": [],
   "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": null,
   "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": null,
   "id": "reponse-code-0b9c3f28",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "outputs": [],
   "source": [
    "# Votre réponse"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reponse-texte-0b9c3f28",
   "metadata": {
    "tags": [
     "reponse"
    ]
   },
   "source": [
    "*Votre réponse :*"
   ]
  }
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