{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partiel 2027"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def addwithsize(B, x):\n",
    "    if B == None:\n",
    "        return (BinTreeSize(x, None, None, 1), True)\n",
    "    else:\n",
    "        if x == B.key:\n",
    "            return (B, False)\n",
    "        elif x > B.key:\n",
    "            (B.left, res) = addwithsize(B.left, x)\n",
    "            if res == True:\n",
    "                B.size = B.size + 1\n",
    "                return (B, True)\n",
    "        else:\n",
    "            (B.right, res) = addwithsize(B.right, x)\n",
    "            if res == True:\n",
    "                B.size = B.size + 1\n",
    "        return (B, res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lca(B, x, y):\n",
    "    if x <= B.key:\n",
    "        if y >= B.key:\n",
    "            return B.key\n",
    "        else:\n",
    "            return __lca(B.left, x, y)\n",
    "    else:\n",
    "        if y >= B.key:\n",
    "            return __lca(B.right, x, y)\n",
    "        else:\n",
    "            return B.key"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mystery(B, x, y):\n",
    "    if (B == None):\n",
    "        return None\n",
    "    else:\n",
    "        if B.key < x:\n",
    "            return mystery(B.right, x, y)\n",
    "        elif y < B.key:\n",
    "            return mystery(B.left, x, y)\n",
    "        else:\n",
    "            B.left = mystery(B.left, x, y)\n",
    "            B.right = mystery(B.right, x, y)\n",
    "            return B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partiel 2025"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1\n",
    "1. 14 / 4 / 2\n",
    "2. 1 / 2\n",
    "\n",
    "### Exercise 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def __testBST(B, inf, sup):\n",
    "    if B == None:\n",
    "        return None\n",
    "    else:\n",
    "        if B.key > inf and B.key <= sup:\n",
    "            return __testBST(B.left, inf, B.key) and __testBST(B.right, B.key, sup)\n",
    "        else:\n",
    "            return False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def __searchlevel(B, x):\n",
    "    if B == None:\n",
    "        return -1\n",
    "    else:\n",
    "        if x == B.key:\n",
    "            return 0\n",
    "        else:\n",
    "            if x < B.key:\n",
    "                res = __searchlevel(B.left, x)\n",
    "            else:\n",
    "                res = __searchlevel(B.right, x)\n",
    "            if res == -1:\n",
    "                return -1\n",
    "            else:\n",
    "                return 1 + res\n",
    "\n",
    "def generation(B, x, y):\n",
    "    res_x = __searchlevel(B, x)\n",
    "    if res_x == -1:\n",
    "        return False\n",
    "    else:\n",
    "        return res_x == __searchlevel(B, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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