{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cherche(tableau, elem):\n",
    "    \"\"\"Y a-t-il elem dans le tableau\"\"\"\n",
    "    for e in tableau:\n",
    "        if elem == e:\n",
    "            return 1\n",
    "    return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cherche(list(range(50)), 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "cherche(list(range(50)), 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dico_rec(tableau, elem):\n",
    "    size = len(tableau)\n",
    "    if size == 0:\n",
    "        return 0\n",
    "    \n",
    "    middle = tableau[int(size/2)]\n",
    "    \n",
    "    if elem == middle:\n",
    "        return 1\n",
    "    elif elem > middle:\n",
    "        return dico_rec(tableau[int(size/2)+1:], elem)\n",
    "    elif elem < middle:\n",
    "        return dico_rec(tableau[:int(size/2)], elem)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dico_rec(list(range(11)), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dico_rec(list(range(10)), 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dico_rec(list(range(11)), 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dico_rec(list(range(10)), 14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Triée?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_sorted(tab):\n",
    "    \"\"\" Trie croissant? \"\"\"\n",
    "    for i in range(len(tab)-1):\n",
    "        if tab[i] > tab[i+1]:\n",
    "            return 0\n",
    "    return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_sorted(list(range(10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_sorted([3, 4, 1, 2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tri insertion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def insert(tab, elem, head=[]):\n",
    "    \"\"\" Insert elem au bon endroit dans tab \n",
    "    \n",
    "    param tab: \n",
    "    param elem: élément à inserer\n",
    "    param head: élément plus petits que elem\n",
    "    \"\"\"\n",
    "    if tab == []:\n",
    "        return head+[elem]\n",
    "    first = tab[0]\n",
    "    if first >= elem:\n",
    "        return head + [elem] + tab\n",
    "    else:\n",
    "        return insert(tab[1:], elem, head+[first])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 4, 5, 6]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insert([1, 4, 5, 6], 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 4, 5, 6]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insert([1, 4, 5, 6], 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 5, 6, 10]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "insert([1, 4, 5, 6], 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tri_insertion(tab, out=[]):\n",
    "    \"\"\" Trie par insertion\n",
    "    \n",
    "    param tab\n",
    "    \"\"\"\n",
    "    if tab == []:\n",
    "        return out\n",
    "    elem = tab[0]\n",
    "    new_out = insert(out, elem)\n",
    "    return tri_insertion(tab[1:], new_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 6]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tri_insertion([3, 4, 2, 6, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tri_insertion([])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 3, 5, 6]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tri_insertion([3, 3, 5, 6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tri selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "def split_min(tab, minval=None, head = [], mid_head=[]):\n",
    "    \"\"\" coupecoupe\n",
    "    \n",
    "    return: head, min, tail\n",
    "    \"\"\"\n",
    "    if tab == []:\n",
    "        return head, minval, mid_head\n",
    "    if minval==None:\n",
    "        return split_min(tab[1:], tab[0], mid_head)\n",
    "    \n",
    "    first = tab[0]\n",
    "    if first > minval:\n",
    "        return split_min(tab[1:], minval, head, mid_head+[first])\n",
    "    \n",
    "    return split_min(tab[1:], first , head + [minval] + mid_head, [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([3, 4], 1, [6, 5])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "split_min([3, 4, 1, 6, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([6], 5, [])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "split_min([6, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([], 5, [6])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "split_min([5, 6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([], 4, [])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "split_min([4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tri_selection(tab):\n",
    "    \"\"\" Pas sur que ce soit vraiment ça qu'on demande \"\"\"\n",
    "    if len(tab)==0:\n",
    "        return []\n",
    "    if len(tab)==1:\n",
    "        return tab\n",
    "    first = tab[0]\n",
    "    head, minval, tail = split_min(tab[1:])\n",
    "    if first > minval:\n",
    "        return [minval]+ tri_selection(head + [first] + tail)\n",
    "    return [first] + tri_selection(tab[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 6]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tri_selection([3, 4, 2, 6, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tri_selection([])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 3, 5, 6]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tri_selection([3, 3, 5, 6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tri fusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fusion(head, tail):\n",
    "    \"\"\" Fusion les 2 tableaux\n",
    "    \n",
    "    param head: liste d'entiers triée\n",
    "    param tail: liste d'entiers triée\n",
    "    return: fusion des deux listes ordonnées\n",
    "    \"\"\"\n",
    "    try:\n",
    "        last_head = head[-1]\n",
    "    except IndexError:\n",
    "        return tail\n",
    "    try:\n",
    "        last_tail=  tail[-1]\n",
    "    except IndexError:\n",
    "        return head\n",
    "    \n",
    "    if last_head > last_tail:\n",
    "        return fusion(head[:-1], tail) + [last_head]\n",
    "    return fusion(head, tail[:-1]) + [last_tail]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 4]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fusion([3, 4], [2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tri_fusion(tab):\n",
    "    \"\"\"\"\"\"\n",
    "    if len(tab)<2:\n",
    "        return tab\n",
    "    middle = int(len(tab)/2)\n",
    "    head = tri_fusion(tab[middle:])\n",
    "    tail = tri_fusion(tab[:middle])\n",
    "    return fusion(head, tail)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 5, 5, 19]"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tri_fusion([3, 5, 5, 19, 1, 2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tri "
   ]
  }
 ],
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