{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "acaccd7b",
   "metadata": {},
   "source": [
    "<h1> TP - Arbre Binaire de recherche </h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56560ca6",
   "metadata": {},
   "source": [
    "<h2> A) Implementation </h2> \n",
    "<p> Un ABR étant un cas particulier d'un arbre binaire, on peut reprendre l'implémentation déjà existante de la classe AB en adaptant seulement le constructeur de la classe:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "df8c8aa4",
   "metadata": {},
   "outputs": [],
   "source": [
    "class ABR:\n",
    "    def __init__(self, racine=None):\n",
    "        self.racine = racine\n",
    "        if self.racine is not None:\n",
    "            self.gauche = ABR()  \n",
    "            self.droit = ABR()\n",
    "    \n",
    "    def est_vide(self):\n",
    "        return self.racine==None\n",
    "      \n",
    "    \n",
    "    def hauteur(self):\n",
    "        if self.est_vide():\n",
    "            return -1\n",
    "        else:\n",
    "            return 1+max(self.gauche.hauteur(),self.droit.hauteur())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9f1fd8f",
   "metadata": {},
   "source": [
    "<h2> B) Representation </h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5a618b0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def repr_graph(arbre, size=(8,8), null_node=False):\n",
    "    \"\"\"\n",
    "    size : tuple de 2 entiers. Si size est int -> (size, size)\n",
    "    null_node : si True, trace les liaisons vers les sous-arbres vides\n",
    "    \"\"\"\n",
    "    def parkour(arbre, noeuds, branches, labels, positions, profondeur, pos_courante, pos_parent, null_node):\n",
    "        if not arbre.est_vide():\n",
    "            noeuds[0].append(pos_courante)\n",
    "            positions[pos_courante] = (pos_courante, profondeur)\n",
    "            profondeur -= 1\n",
    "            labels[pos_courante] = str(arbre.racine)\n",
    "            branches[0].append((pos_courante, pos_parent))\n",
    "            pos_gauche = pos_courante - 2**profondeur\n",
    "            parkour(arbre.gauche, noeuds, branches, labels, positions, profondeur, pos_gauche, pos_courante, null_node)\n",
    "            pos_droit = pos_courante + 2**profondeur\n",
    "            parkour(arbre.droit, noeuds, branches, labels, positions, profondeur, pos_droit, pos_courante, null_node)\n",
    "        elif null_node:\n",
    "            noeuds[1].append(pos_courante)\n",
    "            positions[pos_courante] = (pos_courante, profondeur)\n",
    "            branches[1].append((pos_courante, pos_parent))\n",
    "    \n",
    "    \n",
    "    if arbre ==():\n",
    "        return\n",
    "    \n",
    "    branches = [[]]\n",
    "    profondeur = arbre.hauteur()\n",
    "    pos_courante = 2**profondeur\n",
    "    noeuds = [[pos_courante]]\n",
    "    positions = {pos_courante: (pos_courante, profondeur)} \n",
    "    labels = {pos_courante: str(arbre.racine)}\n",
    "    \n",
    "    if null_node:\n",
    "        branches.append([])\n",
    "        noeuds.append([])\n",
    "        \n",
    "    profondeur -= 1\n",
    "    parkour(arbre.gauche, noeuds, branches, labels, positions, profondeur, pos_courante - 2**profondeur, pos_courante, null_node)\n",
    "    parkour(arbre.droit, noeuds, branches, labels, positions, profondeur, pos_courante + 2**profondeur, pos_courante, null_node) \n",
    "\n",
    "    mon_arbre = nx.Graph()\n",
    "    \n",
    "    if type(size) == int:\n",
    "        size = (size, size)    \n",
    "    plt.figure(figsize=size)\n",
    "    \n",
    "    nx.draw_networkx_nodes(mon_arbre, positions, nodelist=noeuds[0], node_color=\"white\", node_size=550, edgecolors=\"blue\")\n",
    "    nx.draw_networkx_edges(mon_arbre, positions, edgelist=branches[0], edge_color=\"black\", width=2)\n",
    "    nx.draw_networkx_labels(mon_arbre, positions, labels)\n",
    "\n",
    "    if null_node:\n",
    "        nx.draw_networkx_nodes(mon_arbre, positions, nodelist=noeuds[1], node_color=\"white\", node_size=50, edgecolors=\"grey\")\n",
    "        nx.draw_networkx_edges(mon_arbre, positions, edgelist=branches[1], edge_color=\"grey\", width=1)\n",
    "\n",
    "    ax = plt.gca()\n",
    "    ax.margins(0.1)\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "    plt.close()       \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27ed022b",
   "metadata": {},
   "source": [
    "<h3> Test  en construisant à la main un arbre binaire de recherche </h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "55988c73",
   "metadata": {},
   "outputs": [],
   "source": [
    "a=ABR(5)\n",
    "a.gauche=ABR(3)\n",
    "a.gauche.droit=ABR(4)\n",
    "a.droit=ABR(8)\n",
    "a.droit.droit=ABR(10)\n",
    "a.droit.gauche=ABR(7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "256793ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "repr_graph(a,(4,3),False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1005e80b",
   "metadata": {},
   "source": [
    "<h2> Exercice 1 : Fonction recherche dans un arbre binaire de recherche </h2>\n",
    "<p> Completer la fonction recherche qui renvoie Vraie si valeur est dans l'arbre ou Faux sinon </p> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "98353a32",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rechercher(arbre, valeur):\n",
    "    if ... :\n",
    "        return False\n",
    "    elif ... :\n",
    "        return True\n",
    "    elif valeur < self.cle:\n",
    "        return ...\n",
    "    else:\n",
    "        return ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "061f5061",
   "metadata": {},
   "outputs": [],
   "source": [
    "#tests\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "888d9b08",
   "metadata": {},
   "source": [
    "<h2> Exercice 2 : </h2> <p>  Ecrire les fonctions min_abr(arbre) et max_abr(arbre) qui renvoie respectivement le mininmum (ou le maximum) des valeurs de l'arbre </p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7249f33e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def min_abr (arbre):\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7449627a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def max_abr (arbre):\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "16c46662",
   "metadata": {},
   "outputs": [],
   "source": [
    "#tests"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca0aff60",
   "metadata": {},
   "source": [
    "<h2> Exercice 3 </h2> <p>Ecrire la fonction inserer(arbre,x) qui insere x dans l'arbre binaire de recherche arbre </p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "62171333",
   "metadata": {},
   "outputs": [],
   "source": [
    "def inserer(arbre,x):\n",
    "    if .............:\n",
    "        if ..<=..........:\n",
    "            if .................est_vide():\n",
    "                ...............=ABR(x)\n",
    "            else:\n",
    "                ................\n",
    "        else:\n",
    "            if ...............est_vide():\n",
    "                ....................\n",
    "            else:\n",
    "                ......................."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "d7b5fa4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#test de la fonction inserer qui permet de construire l'arbre binaire de rechervhe A\n",
    "A=ABR(12)\n",
    "inserer(A,15)\n",
    "inserer(A,1)\n",
    "inserer(A,3)\n",
    "inserer(A,8)\n",
    "inserer(A,5)\n",
    "inserer(A,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "35016405",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "repr_graph(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84753629",
   "metadata": {},
   "source": [
    "<h2> Exercice 4 </h2>\n",
    "<p>Ecrire la fonction list_to_ABR(liste) qui insere dans l'ordre les valeurs de liste dans un arbre binaire </p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "287cce1a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def list_to_ABR(liste):\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "4cd6ba70",
   "metadata": {},
   "outputs": [],
   "source": [
    "B=list_to_ABR([8,5,3,7,4,6,9,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "500213c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "repr_graph(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f04c0cf",
   "metadata": {},
   "source": [
    "<h3> bonus 1 : dans le cas d'une recherche d'une valeur, ecrire en cas de succès le chemin permettant d'aller de la racine à la valeur cherchée</h3> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "075c99e4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "2c0c633b",
   "metadata": {},
   "source": [
    "<h3> bonus2 : Ecriture une fonction ( ou plusieurs !!!) qui permet de verifier si un arbre binaire est un arbre binaire de recherche</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d4d867a1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}