424 lines
71 KiB
Plaintext
424 lines
71 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "2acfa743",
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"metadata": {},
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"source": [
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"# 0. Подготовим окружение"
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]
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},
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{
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"cell_type": "code",
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"id": "4689b73e",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-09-04T06:25:55.150018Z",
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"start_time": "2026-09-04T06:25:55.134797Z"
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}
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},
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"source": [
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"import sys\n",
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"import os\n",
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"sys.path.insert(0, os.path.abspath( '../task1'))\n",
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"sys.path.insert(0, os.path.abspath( '../'))"
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],
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"outputs": [],
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"execution_count": 1
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},
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{
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"cell_type": "markdown",
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"id": "37cc11a5",
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"metadata": {},
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"source": [
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"# 1. Генерация тестовых данных\n",
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"\n",
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"Создадим список records из N=10000 элементов. Каждый элемент — кортеж (name, phone). \n",
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"Имена возъмём случайные из небольшого набора (чтобы были повторения и коллизии). \n",
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"Для проверки влияния порядка подготовим два варианта: \n",
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"\n",
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"_records_shuffled_ — случайный порядок. \n",
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"_records_sorted_ — отсортированный по имени (по алфавиту)."
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]
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},
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{
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"cell_type": "code",
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"id": "a3b5c31b",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-09-04T06:25:55.231512Z",
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"start_time": "2026-09-04T06:25:55.159161Z"
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}
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},
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"source": [
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"from util.randomNames import generate_test_data\n",
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"from util.timeTester import test\n",
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"\n",
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"records_shuffled = generate_test_data(N=10000)\n",
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"records_sorted = generate_test_data(N=10000, _sorted=True)"
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],
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"outputs": [],
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"execution_count": 2
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},
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{
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"cell_type": "markdown",
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"id": "c2f4989c",
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"metadata": {},
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"source": [
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"# 2. Проведение замеров"
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]
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},
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{
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"cell_type": "code",
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"id": "df12d41d",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-09-04T06:25:55.250684Z",
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"start_time": "2026-09-04T06:25:55.233856Z"
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}
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},
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"source": [
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"# Подготовим функции СД, которые будем тестировать\n",
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"from structures.LinkedList import *\n",
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"from structures.HashTable import *\n",
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"from structures.BinaryTree import *\n",
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"\n",
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"func_list = {\"Связанный список\" : (ll_insert, ll_find, ll_delete),\n",
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" \"Хэш-таблица\" : (ht_insert, ht_find, ht_delete),\n",
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" \"Бинарное дерево\" : (bst_insert, bst_find, bst_delete)}"
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],
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"outputs": [],
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"execution_count": 3
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},
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{
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"cell_type": "code",
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"id": "cc8d0436",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-09-04T06:25:57.233606Z",
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"start_time": "2026-09-04T06:25:55.260869Z"
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}
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},
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"source": [
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"# Проведём замеры\n",
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"report = [[\"Структура\", \"Режим\", \"Вставка\", \"Поиск\", \"Удаление\"]]\n",
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"records = {\"Cлучайный\" : records_shuffled, \"Отсортированный\" : records_sorted}\n",
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"\n",
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"TEST_ITERATIONS_NUM = 5\n",
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"\n",
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"for _ in range(TEST_ITERATIONS_NUM):\n",
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" for mode, data in records.items():\n",
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" for struct_name, fns in func_list.items():\n",
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" result = test(data, *fns)\n",
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" row = [struct_name, mode,\n",
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" result[\"insert_time\"],\n",
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" result[\"find_time\"],\n",
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" result[\"delete_time\"]]\n",
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" report.append(row)"
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],
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"outputs": [],
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"execution_count": 4
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},
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{
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"cell_type": "code",
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"id": "2eedf056",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-09-04T06:25:57.277790Z",
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"start_time": "2026-09-04T06:25:57.266011Z"
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}
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},
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"source": [
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"# Сохраним данные в csv\n",
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"import csv\n",
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"with open(\"data/task1/results.csv\", \"w\", newline=\"\") as f:\n",
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" writer = csv.writer(f)\n",
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" writer.writerows(report)"
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],
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"outputs": [],
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"execution_count": 5
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},
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{
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"cell_type": "markdown",
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"id": "94335af1",
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"metadata": {},
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"source": [
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"# 3. Построение графиков и их анализ"
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]
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},
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{
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"cell_type": "code",
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"id": "cad64d2f",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-09-04T06:25:58.231489Z",
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"start_time": "2026-09-04T06:25:57.280067Z"
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}
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},
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"source": [
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"import pandas as pd\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"df = pd.read_csv('data/task1/results.csv')\n",
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"mean_times = df.groupby(['Структура', 'Режим'])[['Вставка', 'Поиск', 'Удаление']].mean().reset_index()\n",
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"structures = mean_times['Структура'].unique()\n",
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"modes = mean_times['Режим'].unique()\n",
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"\n",
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"fig, axes = plt.subplots(1, 3, figsize=(15, 5))\n",
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"operations = ['Вставка', 'Поиск', 'Удаление']\n",
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"\n",
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"for ax, op in zip(axes, operations):\n",
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" # a\n",
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" x = np.arange(len(structures))\n",
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" width = 0.35\n",
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" \n",
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" random_vals = []\n",
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" sorted_vals = []\n",
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" for s in structures:\n",
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" random_row = mean_times[(mean_times['Структура']==s) & (mean_times['Режим']=='Cлучайный')]\n",
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" sorted_row = mean_times[(mean_times['Структура']==s) & (mean_times['Режим']=='Отсортированный')]\n",
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" random_vals.append(random_row[op].values[0] if not random_row.empty else 0)\n",
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" sorted_vals.append(sorted_row[op].values[0] if not sorted_row.empty else 0)\n",
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" \n",
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" ax.bar(x - width/2, random_vals, width, label='Случайный')\n",
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" ax.bar(x + width/2, sorted_vals, width, label='Отсортированный')\n",
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" ax.set_xticks(x)\n",
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" ax.set_xticklabels(structures)\n",
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" ax.set_ylabel('Время (сек)')\n",
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" ax.set_title(op)\n",
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" ax.legend()\n",
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"\n",
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"plt.tight_layout()\n",
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"plt.savefig('data/task1/performance_plot.png', dpi=150)\n",
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"plt.show()"
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],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<Figure size 1500x500 with 3 Axes>"
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],
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"
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"execution_count": 6
|
||
},
|
||
{
|
||
"metadata": {
|
||
"ExecuteTime": {
|
||
"end_time": "2026-09-04T06:25:59.106420Z",
|
||
"start_time": "2026-09-04T06:25:58.256204Z"
|
||
}
|
||
},
|
||
"cell_type": "code",
|
||
"source": [
|
||
"import sys\n",
|
||
"!{sys.executable} -m pip install pandas numpy matplotlib\n"
|
||
],
|
||
"id": "c677a727d4516f1e",
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Requirement already satisfied: pandas in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (2.3.3)\n",
|
||
"Requirement already satisfied: numpy in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (2.0.2)\n",
|
||
"Requirement already satisfied: matplotlib in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (3.9.4)\n",
|
||
"Requirement already satisfied: python-dateutil>=2.8.2 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from pandas) (2.9.0.post0)\n",
|
||
"Requirement already satisfied: pytz>=2020.1 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from pandas) (2026.3.post1)\n",
|
||
"Requirement already satisfied: tzdata>=2022.7 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from pandas) (2026.3)\n",
|
||
"Requirement already satisfied: contourpy>=1.0.1 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from matplotlib) (1.3.0)\n",
|
||
"Requirement already satisfied: cycler>=0.10 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from matplotlib) (0.12.1)\n",
|
||
"Requirement already satisfied: fonttools>=4.22.0 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from matplotlib) (4.60.2)\n",
|
||
"Requirement already satisfied: kiwisolver>=1.3.1 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from matplotlib) (1.4.7)\n",
|
||
"Requirement already satisfied: packaging>=20.0 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from matplotlib) (26.3)\n",
|
||
"Requirement already satisfied: pillow>=8 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from matplotlib) (11.3.0)\n",
|
||
"Requirement already satisfied: pyparsing>=2.3.1 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from matplotlib) (3.3.2)\n",
|
||
"Requirement already satisfied: importlib-resources>=3.2.0 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from matplotlib) (6.5.2)\n",
|
||
"Requirement already satisfied: zipp>=3.1.0 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from importlib-resources>=3.2.0->matplotlib) (3.23.1)\n",
|
||
"Requirement already satisfied: six>=1.5 in /Users/cvrse/Desktop/пересдача/.venv/lib/python3.9/site-packages (from python-dateutil>=2.8.2->pandas) (1.17.0)\n"
|
||
]
|
||
}
|
||
],
|
||
"execution_count": 7
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"id": "1d86131d",
|
||
"metadata": {
|
||
"ExecuteTime": {
|
||
"end_time": "2026-09-04T06:25:59.170550Z",
|
||
"start_time": "2026-09-04T06:25:59.127903Z"
|
||
}
|
||
},
|
||
"source": [
|
||
"df = pd.read_csv('data/task1/results.csv')\n",
|
||
"df.groupby(['Структура', 'Режим'])[['Вставка', 'Поиск', 'Удаление']].mean().reset_index()"
|
||
],
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
" Структура Режим Вставка Поиск Удаление\n",
|
||
"0 Бинарное дерево Cлучайный 0.008477 0.000095 0.000073\n",
|
||
"1 Бинарное дерево Отсортированный 0.089950 0.000914 0.000636\n",
|
||
"2 Связанный список Cлучайный 0.067483 0.000662 0.000383\n",
|
||
"3 Связанный список Отсортированный 0.133676 0.001328 0.000733\n",
|
||
"4 Хэш-таблица Cлучайный 0.042672 0.000473 0.000228\n",
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"5 Хэш-таблица Отсортированный 0.044273 0.000492 0.000236"
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
|
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" <th>Структура</th>\n",
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" <th>Режим</th>\n",
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" <th>Вставка</th>\n",
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" <th>Поиск</th>\n",
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" <th>Удаление</th>\n",
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" <td>Cлучайный</td>\n",
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" <td>0.008477</td>\n",
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" <td>0.000073</td>\n",
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" <td>0.089950</td>\n",
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" <td>0.000636</td>\n",
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|
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|
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" <td>0.067483</td>\n",
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" <td>0.000662</td>\n",
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"source": [
|
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"# 4. Анализ результатов\n",
|
||
"---\n",
|
||
"### 4.1 Влияние порядка данных на вставку в BST\n",
|
||
"При вставке элементов в отсортированном порядке в бинарное дерево оно превращается в связный список - это связанно с тем, что все элементы вставляются в одну ветвь дерева. Сложность всех операций приблтижается к **O(n)**. Вставка в BST на отсортированных данных заняла 0.122171c вместо 0.011921с, разница более чем в 10 раз. Причём, время вставки даже хуже, чем у чистого связнного списка - это связанно с дополнительными расходами бинарного дерева. Поиск так же ухудшился, примерно в 10 раз, а с ним ухудшилось и удаление.\n",
|
||
"\n",
|
||
"### 4.2 Почему хэш-таблица почти не чувствительна к порядку\n",
|
||
"По графикам видно, что для хэш-таблицы время операций почти не изменяется. Исключение составляет лишь поиск, его время больше на отсортированных данных. Это связано с особенностями теста - поиск 10 несуществующих записей ухудшают результат для отсортированных данных. Все эти наблюдения связаны с механизмом работы хэш-таблицы - она распределяет данные по корзинам независимо от порядка поступления. Получается, что сложность всех операций **O(1)**\n",
|
||
"\n",
|
||
"### 4.3 Почему связный список всегда медленен при поиске\n",
|
||
"Для поиска в связном списке нужно просматривать все элементы по порядку, так что сложность всех операций **O(n)**\n",
|
||
"\n",
|
||
"### 4.4 Сравнение удаления\n",
|
||
"\n",
|
||
"- **Связаный список** удаление требует сначала найти элемент за O(n), затем переставить ссылки за O(1). Время удаления (0.000605 с) близко ко времени поиска, что логично.\n",
|
||
"- **Хеш-таблица:** при удалении, поиск корзины за O(1) и поиск в коротком связаном списке за O(n) удаляется элемент. Время удаления (0.000324) меньше, чем в списке.\n",
|
||
"- **BST:** на случайных данных удаление очень быстрое (0.000137 с) благодаря логарифмической высоте. На отсортированных данных время возрастает до 0.000873, что отражает деградацию до O(n)."
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"source": [
|
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"# 5. Вывод\n",
|
||
"На основе полученных результатов можно сформулировать следующие рекомендации:\n",
|
||
"\n",
|
||
"- Хеш-таблица – хороший выбор, если приоритетом является максимальная скорость вставки, поиска и удаления по ключу, а порядок элементов не имеет значения. Время операций близко к **O(1)** и практически не зависит от упорядоченности входных данных. Идеальна для кэшей, словарей и частых запросов по идентификатору.\n",
|
||
"\n",
|
||
"- Двоичное дерево поиска – следует применять, когда необходимо получать данные в отсортированном порядке. На случайных данных демонстрирует хорошую производительность **O(log n)**, однако при поступлении заранее отсортированных элементов вырождается в связный список с падением скорости до **O(n)**.\n",
|
||
"\n",
|
||
"- Связный список – демонстрирует линейную сложность поиска и удаления **O(n)** что делает его непригодным для задач с частым доступом к произвольным элементам. Может быть оправдан только в узких случаях, где вставки и удаления происходят исключительно в начале или конце коллекции (очереди, стеки) и не требуется поиск.\n",
|
||
"\n",
|
||
"Таким образом, для реальных задач чаще всего выбирают хеш-таблицы или сбалансированные деревья в зависимости от требований к упорядоченности данных.\n"
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