From f6992c8cab2ff4424cf29fce8bbf342d79f5b811 Mon Sep 17 00:00:00 2001
From: thuret <thuret.come@gmail.com>
Date: Wed, 23 Oct 2024 11:58:29 +0200
Subject: [PATCH] first commit

---
 TP01/JeuNim.pdf | Bin 0 -> 50512 bytes
 TP01/Nim.ipynb  | 496 ++++++++++++++++++++++++++++++++++++++++++++++++
 TP01/code.py    | 197 +++++++++++++++++++
 3 files changed, 693 insertions(+)
 create mode 100644 TP01/JeuNim.pdf
 create mode 100644 TP01/Nim.ipynb
 create mode 100644 TP01/code.py

diff --git a/TP01/JeuNim.pdf b/TP01/JeuNim.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..b0b97f8865203652a54bc9d80e7711ab039ebadd
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diff --git a/TP01/Nim.ipynb b/TP01/Nim.ipynb
new file mode 100644
index 0000000..ca01e40
--- /dev/null
+++ b/TP01/Nim.ipynb
@@ -0,0 +1,496 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Implémentation du jeu de Nim"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "etat_jeu = [3, 4, 5] # Trois tas contenant respectivement 3, 4 et 5 objets.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercice 1 "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[3, 4, 5]\n",
+      "[0, 0, 0]\n",
+      "[1, 0, 2]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# A.\n",
+    "def afficher_etat(etat_jeu) :\n",
+    "    print(etat_jeu)\n",
+    "\n",
+    "\n",
+    "# B.\n",
+    "test1 = [3, 4, 5]\n",
+    "test2 = [0, 0, 0]\n",
+    "test3 = [1, 0, 2]\n",
+    "\n",
+    "afficher_etat(test1)\n",
+    "afficher_etat(test2)\n",
+    "afficher_etat(test3)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercice 2 : "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[(0, 1), (0, 2), (0, 3), (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5)]\n",
+      "[]\n",
+      "[(0, 1), (2, 1), (2, 2)]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# A.\n",
+    "\n",
+    "def generer_mouvement(etat_jeu) : \n",
+    "    mouvements = []\n",
+    "    for i in range(len(etat_jeu)) : # On parcourt les tas\n",
+    "        for j in range(etat_jeu[i]) : # On tire le nombre d'objets dans le tas\n",
+    "            if etat_jeu[i] > 0 :\n",
+    "                mouvements.append((i, j+1)) # On ajoute le mouvement à la liste\n",
+    "    return mouvements\n",
+    "\n",
+    "# B.\n",
+    "print(generer_mouvement(test1))\n",
+    "print(generer_mouvement(test2))\n",
+    "print(generer_mouvement(test3))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercice 3 : "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# A et B\n",
+    "def appliquer_mouvement(etat_jeu, tas_index, nombre_objets) :\n",
+    "    if nombre_objets > etat_jeu[tas_index] :\n",
+    "        print(\"Erreur : nombre d'objets à retirer supérieur au nombre d'objets dans le tas.\")\n",
+    "        return etat_jeu\n",
+    "    else : \n",
+    "        etat_jeu[tas_index] -= nombre_objets\n",
+    "        return etat_jeu\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercice 4 :"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\" étant donné que  heuristique est égale à la somme des objets dans les tas, \\nc'est donc un calcul simple qui ne dépend pas de l'ordre des tas. \""
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# A.\n",
+    "'''\n",
+    "def heuristique(etat_jeu) :\n",
+    "    return sum(etat_jeu)\n",
+    "\n",
+    "print(heuristique(test1))\n",
+    "print(heuristique(test2))\n",
+    "print(heuristique(test3))'''\n",
+    "\n",
+    "# B.\n",
+    "''' étant donné que  heuristique est égale à la somme des objets dans les tas, \n",
+    "c'est donc un calcul simple qui ne dépend pas de l'ordre des tas. '''\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercice 5 :"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1\n"
+     ]
+    }
+   ],
+   "source": [
+    "# A.\n",
+    "def est_etat_final(etat_jeu) :\n",
+    "    return sum(etat_jeu) == 0\n",
+    "\n",
+    "# B.\n",
+    "def cout_transition(etat_courant, etat_suivant):\n",
+    "    return 1\n",
+    "\n",
+    "# Exemple d'utilisation\n",
+    "etat_courant = [3, 4, 5]\n",
+    "etat_suivant = appliquer_mouvement(etat_courant, 0, 1)  # Devrait retourner [2, 4, 5]\n",
+    "print(cout_transition(etat_courant, etat_suivant))  # Devrait retourner 1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercice 6 : "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[4, 8, 5], [4, 0, 5], [0, 0, 5], [0, 0, 0]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "import heapq\n",
+    "\n",
+    "class Noeud:\n",
+    "    def __init__(self, etat, parent, cout, heuristique):\n",
+    "        self.etat = etat\n",
+    "        self.parent = parent\n",
+    "        self.cout = cout\n",
+    "        self.heuristique = heuristique\n",
+    "\n",
+    "    def __lt__(self, other):\n",
+    "        return self.cout + self.heuristique < other.cout + other.heuristique\n",
+    "\n",
+    "    def __eq__(self, other):\n",
+    "        return self.etat == other.etat\n",
+    "\n",
+    "    def __hash__(self):\n",
+    "        return hash(tuple(self.etat))\n",
+    "\n",
+    "    def __str__(self):\n",
+    "        return str(self.etat)\n",
+    "    \n",
+    "def xor_etat(etat_jeu):\n",
+    "    xor_total = 0\n",
+    "    for nb_objets in etat_jeu:\n",
+    "        xor_total ^= nb_objets\n",
+    "    return xor_total\n",
+    "\n",
+    "def heuristique(etat_jeu):\n",
+    "    xor_valeur = xor_etat(etat_jeu)\n",
+    "    if xor_valeur == 0:\n",
+    "        # Position désavantageuse (perdante)\n",
+    "        return 100 + sum(etat_jeu)  # Pénalité\n",
+    "    else:\n",
+    "        # Position avantageuse (gagnante)\n",
+    "        return sum(etat_jeu)  # Heuristique standard\n",
+    "\n",
+    "def est_etat_final(etat):\n",
+    "    return all(pile == 0 for pile in etat)\n",
+    "\n",
+    "def generer_successeurs(etat):\n",
+    "    successeurs = []\n",
+    "    for i in range(len(etat)):\n",
+    "        if etat[i] > 0:\n",
+    "            for j in range(1, etat[i] + 1):\n",
+    "                nouvel_etat = etat[:]\n",
+    "                nouvel_etat[i] -= j\n",
+    "                successeurs.append(nouvel_etat)\n",
+    "    return successeurs\n",
+    "\n",
+    "def algorithme_a_star(etat_initial):\n",
+    "    noeud_initial = Noeud(etat_initial, None, 0, heuristique(etat_initial))\n",
+    "    frontiere = []\n",
+    "    heapq.heappush(frontiere, noeud_initial)\n",
+    "    visites = set()\n",
+    "\n",
+    "    while frontiere:\n",
+    "        noeud_courant = heapq.heappop(frontiere)\n",
+    "\n",
+    "        if est_etat_final(noeud_courant.etat):\n",
+    "            chemin = []\n",
+    "            while noeud_courant:\n",
+    "                chemin.append(noeud_courant.etat)\n",
+    "                noeud_courant = noeud_courant.parent\n",
+    "            return chemin[::-1]\n",
+    "\n",
+    "        visites.add(tuple(noeud_courant.etat))\n",
+    "\n",
+    "        for successeur in generer_successeurs(noeud_courant.etat):\n",
+    "            if tuple(successeur) not in visites:\n",
+    "                cout = noeud_courant.cout + cout_transition(noeud_courant.etat, successeur)\n",
+    "                heur = heuristique(successeur)\n",
+    "                noeud_successeur = Noeud(successeur, noeud_courant, cout, heur)\n",
+    "                heapq.heappush(frontiere, noeud_successeur)\n",
+    "\n",
+    "    return None\n",
+    "\n",
+    "# Exemple d'utilisation\n",
+    "etat_initial = [4, 8, 5]\n",
+    "chemin_optimal = algorithme_a_star(etat_initial)\n",
+    "print(chemin_optimal)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercice 7 :"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "(voir cellule précédante)\n",
+    "\n",
+    "A. \n",
+    "- Initialisation:\n",
+    "    - Crée un nœud initial avec l'état initial du jeu.\n",
+    "    - Utilise une file de priorité (heap) pour gérer les nœuds à explorer.\n",
+    "    - Utilise un ensemble (set) pour stocker les états déjà visités.\n",
+    "- Boucle principale:\n",
+    "    - Tant que la file de priorité n'est pas vide, extraire le nœud avec le coût total (coût + heuristique) le plus bas.\n",
+    "    - Si l'état du nœud courant est un état final, reconstruire et retourner le chemin depuis l'état initial jusqu'à l'état final.\n",
+    "    - Ajouter l'état courant à l'ensemble des états visités.\n",
+    "    - Générer les états successeurs et les ajouter à la file de priorité s'ils n'ont pas été visités.\n",
+    "- Retour: Si aucun chemin n'est trouvé, retourner None.\n",
+    "\n",
+    "B.\n",
+    "- Vérification des états visités, avant d'ajouter un successeur à la file de priorité, on vérifie si ils ont été visité.\n",
+    "- Une fois qu'un successeur est ajouté, il est ajouté à la file de priorité et marqué comme visité.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercice 8 : "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "A. \n",
+    "Une représentation de son parent est crée dans la classe noeud. Lorsque qu'un successeur est crée, le noeud courant est défini comme parent\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[3, 4, 5], [3, 4, 4], [3, 4, 0]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# B.\n",
+    "\n",
+    "def reconstruire_chemin(noeud_final):\n",
+    "    \"\"\"\n",
+    "    Reconstruit la séquence de mouvements depuis l’état initial jusqu’à l’état final.\n",
+    "    \n",
+    "    :param noeud_final: Le nœud final de l'algorithme A*.\n",
+    "    :return: Une liste des états représentant le chemin de l'état initial à l'état final.\n",
+    "    \"\"\"\n",
+    "    chemin = []\n",
+    "    noeud_courant = noeud_final\n",
+    "    while noeud_courant:\n",
+    "        chemin.append(noeud_courant.etat)\n",
+    "        noeud_courant = noeud_courant.parent\n",
+    "    return chemin[::-1]\n",
+    "\n",
+    "# Création d'un chemin d'exemple pour tester la fonction\n",
+    "etat_initial = [3, 4, 5]\n",
+    "etat_intermediaire = [3, 4, 4]\n",
+    "etat_final = [3, 4, 0]\n",
+    "\n",
+    "noeud_final = Noeud(etat_final, Noeud(etat_intermediaire, Noeud(etat_initial, None, 0, 0), 1, 0), 2, 0)\n",
+    "chemin = reconstruire_chemin(noeud_final)\n",
+    "print(chemin)  # Devrait retourner [[3, 4, 5], [3, 4, 4], [3, 4, 0]]\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercice 9 : "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[3, 4, 5]\n",
+      "[3, 4, 5]\n",
+      "\n",
+      "L'IA joue...\n",
+      "[3, 4, 0]\n",
+      "[0, 4, 0]\n",
+      "\n",
+      "L'IA joue...\n",
+      "\n",
+      " L'IA a gagné !\n"
+     ]
+    }
+   ],
+   "source": [
+    "def jeu_nim(etat_initial):\n",
+    "    etat = etat_initial[:]\n",
+    "    while not est_etat_final(etat):\n",
+    "        afficher_etat(etat)\n",
+    "        try:\n",
+    "            pile = int(input(\"Entrez le numéro de la pile (1, 2, 3, ...): \")) - 1\n",
+    "            nb_objets = int(input(\"Entrez le nombre d'objets à retirer: \"))\n",
+    "            appliquer_mouvement(etat, pile, nb_objets)\n",
+    "            afficher_etat(etat)\n",
+    "        except ValueError:\n",
+    "            print(\"Entrée invalide. Veuillez entrer des nombres entiers.\")\n",
+    "            continue\n",
+    "\n",
+    "        if est_etat_final(etat):\n",
+    "            print(\"\\nFélicitations ! Vous avez gagné !\")\n",
+    "            break\n",
+    "\n",
+    "        # Tour de l'IA\n",
+    "        chemin_optimal = algorithme_a_star(etat)\n",
+    "        if chemin_optimal and len(chemin_optimal) > 1:\n",
+    "            etat_ia = chemin_optimal[1]\n",
+    "            print(\"\\nL'IA joue...\")\n",
+    "            etat = etat_ia\n",
+    "\n",
+    "        if est_etat_final(etat):\n",
+    "            print(\"\\n L'IA a gagné !\")\n",
+    "            break\n",
+    "\n",
+    "# Exemple d'utilisation\n",
+    "etat_initial = [3, 4, 5]\n",
+    "jeu_nim(etat_initial)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Exercice 10 :"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def xor_etat(etat_jeu):\n",
+    "    xor_total = 0\n",
+    "    for nb_objets in etat_jeu:\n",
+    "        xor_total ^= nb_objets\n",
+    "    return xor_total\n",
+    "\n",
+    "def heuristique_amelioree(etat_jeu):\n",
+    "    xor_valeur = xor_etat(etat_jeu)\n",
+    "    if xor_valeur == 0:\n",
+    "        # Position désavantageuse (perdante)\n",
+    "        return 100 + sum(etat_jeu)  # Pénalité\n",
+    "    else:\n",
+    "        # Position avantageuse (gagnante)\n",
+    "        return sum(etat_jeu)  # Heuristique standard"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/TP01/code.py b/TP01/code.py
new file mode 100644
index 0000000..556bc06
--- /dev/null
+++ b/TP01/code.py
@@ -0,0 +1,197 @@
+import heapq
+import random
+
+class Noeud:
+    def __init__(self, etat, parent, cout, heuristique):
+        self.etat = etat
+        self.parent = parent
+        self.cout = cout
+        self.heuristique = heuristique
+
+    def __lt__(self, other):
+        return self.cout + self.heuristique < other.cout + other.heuristique
+
+    def __eq__(self, other):
+        return self.etat == other.etat
+
+    def __hash__(self):
+        return hash(tuple(self.etat))
+
+    def __str__(self):
+        return str(self.etat)
+    
+def afficher_etat(etat_jeu) :
+    print(etat_jeu)
+    
+def xor_etat(etat_jeu):
+    xor_total = 0
+    for nb_objets in etat_jeu:
+        xor_total ^= nb_objets
+    return xor_total
+
+def heuristique(etat_jeu):
+    xor_valeur = xor_etat(etat_jeu)
+    if xor_valeur == 0:
+        # Position désavantageuse (perdante)
+        return 100 + sum(etat_jeu)  # Pénalité
+    else:
+        # Position avantageuse (gagnante)
+        return sum(etat_jeu)  # Heuristique standard
+    
+def appliquer_mouvement(etat_jeu, tas_index, nombre_objets) :
+    if nombre_objets > etat_jeu[tas_index] :
+        print("Erreur : nombre d'objets à retirer supérieur au nombre d'objets dans le tas.")
+        return etat_jeu
+    else : 
+        etat_jeu[tas_index] -= nombre_objets
+        return etat_jeu
+    
+def cout_transition(etat_courant, etat_suivant):
+    return 1
+
+
+def est_etat_final(etat):
+    return all(pile == 0 for pile in etat)
+
+def generer_successeurs(etat):
+    successeurs = []
+    for i in range(len(etat)):
+        if etat[i] > 0:
+            for j in range(1, etat[i] + 1):
+                nouvel_etat = etat[:]
+                nouvel_etat[i] -= j
+                successeurs.append(nouvel_etat)
+    return successeurs
+
+def algorithme_a_star(etat_initial):
+    noeud_initial = Noeud(etat_initial, None, 0, heuristique(etat_initial))
+    frontiere = []
+    heapq.heappush(frontiere, noeud_initial)
+    visites = set()
+
+    while frontiere:
+        noeud_courant = heapq.heappop(frontiere)
+
+        if est_etat_final(noeud_courant.etat):
+            chemin = []
+            while noeud_courant:
+                chemin.append(noeud_courant.etat)
+                noeud_courant = noeud_courant.parent
+            return chemin[::-1]
+
+        visites.add(tuple(noeud_courant.etat))
+
+        for successeur in generer_successeurs(noeud_courant.etat):
+            if tuple(successeur) not in visites:
+                cout = noeud_courant.cout + cout_transition(noeud_courant.etat, successeur)
+                heur = heuristique(successeur)
+                noeud_successeur = Noeud(successeur, noeud_courant, cout, heur)
+                heapq.heappush(frontiere, noeud_successeur)
+
+    return None
+
+
+def reconstruire_chemin(noeud_final):
+    """
+    Reconstruit la séquence de mouvements depuis l’état initial jusqu’à l’état final.
+    
+    :param noeud_final: Le nœud final de l'algorithme A*.
+    :return: Une liste des états représentant le chemin de l'état initial à l'état final.
+    """
+    chemin = []
+    noeud_courant = noeud_final
+    while noeud_courant:
+        chemin.append(noeud_courant.etat)
+        noeud_courant = noeud_courant.parent
+    return chemin[::-1]
+
+def sauvegarder_partie(historique, fichier="historique_parties.txt"):
+    """
+    Sauvegarde l'historique de la partie dans un fichier.
+    
+    :param historique: Liste des coups effectués pendant la partie.
+    :param fichier: Nom du fichier où sauvegarder l'historique.
+    """
+    with open(fichier, "a") as f:
+        f.write("Nouvelle partie\n")
+        for coup in historique:
+            f.write(f"{coup}\n")
+        f.write("\n")
+
+
+def jeu_nim(etat_initial):
+    etat = etat_initial[:]
+    historique = []
+    while not est_etat_final(etat):
+        afficher_etat(etat)
+        try:
+            pile = int(input("Entrez le numéro de la pile (1, 2, 3, ...): ")) - 1
+            nb_objets = int(input("Entrez le nombre d'objets à retirer: "))
+            historique.append(f"Joueur: Pile {pile + 1}, Objets retirés: {nb_objets}")
+            appliquer_mouvement(etat, pile, nb_objets)
+            afficher_etat(etat)
+        except ValueError:
+            print("Entrée invalide. Veuillez entrer des nombres entiers.")
+            continue
+
+        if est_etat_final(etat):
+            print("\nFélicitations ! Vous avez gagné !")
+            break
+
+        # Tour de l'IA
+        chemin_optimal = algorithme_a_star(etat)
+        if chemin_optimal and len(chemin_optimal) > 1:
+            etat_ia = chemin_optimal[1]
+            historique.append(f"IA: Pile {pile + 1}, Objets retirés: {nb_objets}")
+            print("\nL'IA joue...")
+            etat = etat_ia
+
+        if est_etat_final(etat):
+            print("\n L'IA a gagné !")
+            break
+    sauvegarder_partie(historique)
+
+def pile_random(etat) :
+    piles_non_vides = [i for i, pile in enumerate(etat) if pile > 0]
+    return random.choice(piles_non_vides)
+
+
+def nb_objets_random(etat, pile):
+    return random.randint(1, etat[pile])
+
+
+def jeu_nim_random(etat_initial):
+    etat = etat_initial[:]
+    historique = []
+    while not est_etat_final(etat):
+        afficher_etat(etat)
+        try:
+            pile = pile_random(etat)
+            nb_objets = nb_objets_random(etat, pile)
+            historique.append(f"Joueur: Pile {pile + 1}, Objets retirés: {nb_objets}")
+            appliquer_mouvement(etat, pile, nb_objets)
+            afficher_etat(etat)
+        except ValueError:
+            print("Entrée invalide. Veuillez entrer des nombres entiers.")
+            continue
+
+        if est_etat_final(etat):
+            print("\nFélicitations ! Vous avez gagné !")
+            break
+
+        # Tour de l'IA
+        chemin_optimal = algorithme_a_star(etat)
+        if chemin_optimal and len(chemin_optimal) > 1:
+            etat_ia = chemin_optimal[1]
+            historique.append(f"IA: Pile {pile + 1}, Objets retirés: {nb_objets}")
+            print("\nL'IA joue...")
+            etat = etat_ia
+
+        if est_etat_final(etat):
+            print("\n L'IA a gagné !")
+            break
+    sauvegarder_partie(historique)
+
+
+etat_initial = [3, 4, 5]
+jeu_nim_random(etat_initial)
\ No newline at end of file