698 lines
13 KiB
Plaintext
698 lines
13 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Exercice 6"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"def cherche(tableau, elem):\n",
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" \"\"\"Y a-t-il elem dans le tableau\"\"\"\n",
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" for e in tableau:\n",
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" if elem == e:\n",
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" return 1\n",
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" return 0"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"cherche(list(range(50)), 5)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"cherche(list(range(50)), 100)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Exercice 7"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 34,
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"metadata": {},
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"outputs": [],
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"source": [
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"def dico_rec(tableau, elem):\n",
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" size = len(tableau)\n",
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" if size == 0:\n",
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" return 0\n",
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" \n",
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" middle = tableau[int(size/2)]\n",
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" \n",
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" if elem == middle:\n",
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" return 1\n",
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" elif elem > middle:\n",
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" return dico_rec(tableau[int(size/2)+1:], elem)\n",
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" elif elem < middle:\n",
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" return dico_rec(tableau[:int(size/2)], elem)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 45,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1"
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]
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},
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"execution_count": 45,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"dico_rec(list(range(11)), 1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 42,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1"
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]
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},
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"execution_count": 42,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"dico_rec(list(range(10)), 6)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 37,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0"
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]
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},
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"execution_count": 37,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"dico_rec(list(range(11)), 12)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 38,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0"
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]
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},
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"execution_count": 38,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"dico_rec(list(range(10)), 14)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Triée?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"def is_sorted(tab):\n",
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" \"\"\" Trie croissant? \"\"\"\n",
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" for i in range(len(tab)-1):\n",
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" if tab[i] > tab[i+1]:\n",
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" return 0\n",
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" return 1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"is_sorted(list(range(10)))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"is_sorted([3, 4, 1, 2])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Tri insertion"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"def insert(tab, elem, head=[]):\n",
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" \"\"\" Insert elem au bon endroit dans tab \n",
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" \n",
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" param tab: \n",
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" param elem: élément à inserer\n",
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" param head: élément plus petits que elem\n",
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" \"\"\"\n",
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" if tab == []:\n",
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" return head+[elem]\n",
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" first = tab[0]\n",
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" if first >= elem:\n",
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" return head + [elem] + tab\n",
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" else:\n",
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" return insert(tab[1:], elem, head+[first])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[1, 2, 4, 5, 6]"
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]
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},
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"execution_count": 10,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"insert([1, 4, 5, 6], 2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[0, 1, 4, 5, 6]"
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]
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},
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"insert([1, 4, 5, 6], 0)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[1, 4, 5, 6, 10]"
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]
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},
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"execution_count": 12,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"insert([1, 4, 5, 6], 10)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [],
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"source": [
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"def tri_insertion(tab, out=[]):\n",
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" \"\"\" Trie par insertion\n",
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" \n",
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" param tab\n",
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" \"\"\"\n",
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" if tab == []:\n",
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" return out\n",
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" elem = tab[0]\n",
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" new_out = insert(out, elem)\n",
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" return tri_insertion(tab[1:], new_out)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[1, 2, 3, 4, 6]"
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]
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},
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"execution_count": 14,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"tri_insertion([3, 4, 2, 6, 1])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[]"
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]
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},
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"tri_insertion([])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[3, 3, 5, 6]"
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]
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},
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"execution_count": 16,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"tri_insertion([3, 3, 5, 6])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Tri selection"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 69,
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"metadata": {},
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"outputs": [],
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"source": [
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"def split_min(tab, minval=None, head = [], mid_head=[]):\n",
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" \"\"\" coupecoupe\n",
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" \n",
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" return: head, min, tail\n",
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" \"\"\"\n",
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" if tab == []:\n",
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" return head, minval, mid_head\n",
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" if minval==None:\n",
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" return split_min(tab[1:], tab[0], mid_head)\n",
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" \n",
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" first = tab[0]\n",
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" if first > minval:\n",
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" return split_min(tab[1:], minval, head, mid_head+[first])\n",
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" \n",
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" return split_min(tab[1:], first , head + [minval] + mid_head, [])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 70,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"([3, 4], 1, [6, 5])"
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]
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},
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"execution_count": 70,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"split_min([3, 4, 1, 6, 5])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 71,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"([6], 5, [])"
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]
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},
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"execution_count": 71,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"split_min([6, 5])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 72,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"([], 5, [6])"
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]
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},
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"execution_count": 72,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"split_min([5, 6])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 73,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"([], 4, [])"
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]
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},
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"execution_count": 73,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"split_min([4])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 88,
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"metadata": {},
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"outputs": [],
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"source": [
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"def tri_selection(tab):\n",
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" \"\"\" Pas sur que ce soit vraiment ça qu'on demande \"\"\"\n",
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" if len(tab)==0:\n",
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" return []\n",
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" if len(tab)==1:\n",
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" return tab\n",
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" first = tab[0]\n",
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" head, minval, tail = split_min(tab[1:])\n",
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" if first > minval:\n",
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" return [minval]+ tri_selection(head + [first] + tail)\n",
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" return [first] + tri_selection(tab[1:])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 89,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[1, 2, 3, 4, 6]"
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]
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},
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"execution_count": 89,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"tri_selection([3, 4, 2, 6, 1])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 91,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[]"
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]
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},
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"execution_count": 91,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
|
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"tri_selection([])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 92,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[3, 3, 5, 6]"
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]
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},
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"execution_count": 92,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
|
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"tri_selection([3, 3, 5, 6])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Tri fusion"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 73,
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"metadata": {},
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"outputs": [],
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"source": [
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"def fusion(head, tail):\n",
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" \"\"\" Fusion les 2 tableaux\n",
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" \n",
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" param head: liste d'entiers triée\n",
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" param tail: liste d'entiers triée\n",
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" return: fusion des deux listes ordonnées\n",
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" \"\"\"\n",
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" try:\n",
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" last_head = head[-1]\n",
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" except IndexError:\n",
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" return tail\n",
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" try:\n",
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" last_tail= tail[-1]\n",
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" except IndexError:\n",
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" return head\n",
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" \n",
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" if last_head > last_tail:\n",
|
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" return fusion(head[:-1], tail) + [last_head]\n",
|
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" return fusion(head, tail[:-1]) + [last_tail]"
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]
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},
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{
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"cell_type": "code",
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|
"execution_count": 74,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
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"data": {
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"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 "
|
|
]
|
|
}
|
|
],
|
|
"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": "3.8.1"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|