Maximum_Set_Packing_Codes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "558f380f",
   "metadata": {},
   "source": [
    "# <center> CS 301 Project - Group 086 </center>\n",
    "## <center> Project Codes </center>\n",
    "### <center> Ege Demirci (28287) - Efe Tüzün (28992) </center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ca3f54c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing Necessary Packages\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm.notebook import tqdm\n",
    "from scipy.stats import t\n",
    "from scipy import stats\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import statistics\n",
    "import warnings\n",
    "import random\n",
    "import time\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bc564445",
   "metadata": {},
   "outputs": [],
   "source": [
    "pd.set_option('display.precision', 10)\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fbf90718",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generating Random Sized Set Packing of n sets, with the maximum cardinality \n",
    "# of the sets being m and the max_element being the range of the universal set\n",
    "def random_sized_set_packing_instance(n, m, max_element):\n",
    "    sets = []\n",
    "    for i in range(n):\n",
    "        set_size = random.randint(1, m)\n",
    "        s = set(random.sample(range(1, max_element+1), set_size))\n",
    "        sets.append(s)\n",
    "    return sets\n",
    "\n",
    "# Greedy Set Packing Algorithm\n",
    "def greedy_set_packing(sets):\n",
    "    start_time = time.time()\n",
    "    max_set_packing = []\n",
    "    elements = set()\n",
    "    sorted_sets = sorted(sets, key=len)\n",
    "    for s in sorted_sets:\n",
    "        if s & elements == set():\n",
    "            elements = s | elements\n",
    "            max_set_packing.append(s)\n",
    "    delta = time.time() - start_time\n",
    "    return max_set_packing, delta\n",
    "\n",
    "# Helper Function for Trials - Greedy\n",
    "def printTrial_greedy(max_pack, t):\n",
    "    print(\"Greedy Set Packing:\")\n",
    "    print(\"[\")\n",
    "    for element in max_pack:\n",
    "        print(f\"\\t{element}\")\n",
    "    print(\"]\")\n",
    "    print()\n",
    "    print(\"Cardinality:\", len(max_pack))\n",
    "    print(\"Running Time:\", format(t, \".8f\"), \"s\")\n",
    "\n",
    "# Helper Function for Trials - Greedy\n",
    "def set_packing_trial_greedy(n, m, max_th):\n",
    "    sets = random_sized_set_packing_instance(n, m, max_th)\n",
    "    print(\"Sets:\")\n",
    "    for i in range(len(sets)):\n",
    "        print(f\"\\tSet {i+1}:\\t\", sets[i])\n",
    "    print()\n",
    "    max_pack, time_spnt = greedy_set_packing(sets)\n",
    "    printTrial_greedy(max_pack, time_spnt)\n",
    "\n",
    "# Brute-Force Set Packing Algorithm\n",
    "def max_set_packing(sets):\n",
    "    start_time = time.time()\n",
    "    n = len(sets)\n",
    "    all_subsets = []\n",
    "    for i in range(2**n):\n",
    "        subset = []\n",
    "        for j in range(n):\n",
    "            if i & (1 << j):\n",
    "                subset.append(sets[j])\n",
    "        all_subsets.append(subset)\n",
    "\n",
    "    maxCard = -1\n",
    "    maxSetPacking = []\n",
    "\n",
    "    for subset in all_subsets:\n",
    "        isPairwiseDisjoint = True\n",
    "        for i in range(len(subset)-1):\n",
    "            for j in range(i+1, len(subset)):\n",
    "                if subset[i] & subset[j] != set():\n",
    "                    isPairwiseDisjoint = False\n",
    "                    break\n",
    "\n",
    "        if isPairwiseDisjoint and maxCard < len(subset):\n",
    "            maxCard = len(subset)\n",
    "            maxSetPacking = subset\n",
    "    delta = time.time() - start_time\n",
    "    return maxSetPacking, delta\n",
    "\n",
    "# Helper Function for Trials - Brute Force\n",
    "def printTrial(max_pack, t):\n",
    "    print(\"Max Set Packing:\")\n",
    "    print(\"[\")\n",
    "    for element in max_pack:\n",
    "        print(f\"\\t{element}\")\n",
    "    print(\"]\")\n",
    "    print()\n",
    "    print(\"Cardinality:\", len(max_pack))\n",
    "    print(\"Running Time:\", format(t, \".4f\"), \"s\")\n",
    "\n",
    "# Helper Function for Trials - Brute Force\n",
    "def set_packing_trial(n, m, max_th):\n",
    "    sets = random_sized_set_packing_instance(n, m, max_th)\n",
    "    print(\"Sets:\")\n",
    "    for i in range(len(sets)):\n",
    "        print(f\"\\tSet {i+1}:\\t\", sets[i])\n",
    "    print()\n",
    "    max_pack, time_spnt = max_set_packing(sets)\n",
    "    printTrial(max_pack, time_spnt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46ee978b",
   "metadata": {},
   "source": [
    "### Performance Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2b4adc86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0f057a1ae03e4142b3f68a188eaa80dd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Measuring:   0%|          | 0/19 [00:00<?, ?input size/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate input sets of increasing sizes\n",
    "input_sizes = np.linspace(100, 10000, 19)\n",
    "\n",
    "# Define the number of measurements for each input size\n",
    "num_measurements = 250\n",
    "\n",
    "# Initialize lists to store mean running times and confidence intervals\n",
    "mean_running_times = []\n",
    "std_running_times = []\n",
    "confidence_intervals = []\n",
    "\n",
    "# Measure the running time and calculate statistics for each input size\n",
    "for size in tqdm(input_sizes, desc='Measuring', unit='input size'):\n",
    "    running_times = []\n",
    "    for _ in range(num_measurements):\n",
    "        # Generate random input sets\n",
    "        sets = random_sized_set_packing_instance(int(size), 50, 50000)\n",
    "\n",
    "        # Measure the running time\n",
    "        running_time = greedy_set_packing(sets)[1]\n",
    "        \n",
    "        running_times.append(running_time)\n",
    "\n",
    "    # Calculate the mean running time\n",
    "    mean_time = statistics.mean(running_times)\n",
    "    std_time = statistics.stdev(running_times)\n",
    "    \n",
    "    mean_running_times.append(mean_time)\n",
    "    std_running_times.append(std_time)\n",
    "\n",
    "    # Calculate the confidence interval\n",
    "    confidence_interval = stats.t.interval(0.9, len(running_times) - 1, loc=mean_time,\n",
    "                                           scale=stats.sem(running_times))\n",
    "    confidence_intervals.append(confidence_interval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c2b28545",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1600x900 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert lists to numpy arrays for easier manipulation\n",
    "input_sizes = np.array(input_sizes)\n",
    "mean_running_times = np.array(mean_running_times)\n",
    "std_running_times = np.array(std_running_times)\n",
    "confidence_intervals = np.array(confidence_intervals)\n",
    "\n",
    "# Fit a line to the mean running times using linear regression\n",
    "params = np.polyfit(input_sizes, mean_running_times, 1)\n",
    "line_func = np.poly1d(params)\n",
    "\n",
    "# Plot the mean running times and confidence intervals\n",
    "plt.figure(figsize = (16,9))\n",
    "plt.plot(input_sizes, mean_running_times, 'o-', markersize=10, lw = 3)\n",
    "plt.plot(input_sizes, line_func(input_sizes), \"*-\", markersize=10, lw = 3)\n",
    "plt.xlabel('Input Size')\n",
    "plt.ylabel('Running Time (s)')\n",
    "plt.legend(labels = [\"Actual Line\", \"Fitted Line\"])\n",
    "plt.title(\"Input Size vs. Mean Running Time\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "830c3fe8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running Time Expression: -0.00106538250739113141 + (0.00000817311775475218) * Input Size\n"
     ]
    }
   ],
   "source": [
    "# Derive the running time expression based on the equation of the fitted line\n",
    "running_time_expression = f\"{params[1]:.20f} + ({params[0]:.20f}) * Input Size\"\n",
    "print(\"Running Time Expression:\", running_time_expression)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "63a9ae2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Mean</th>\n",
       "      <th>Standard Deviation</th>\n",
       "      <th>Standard Error</th>\n",
       "      <th>90% CI Lower</th>\n",
       "      <th>90% CI Upper</th>\n",
       "      <th>95% CI Lower</th>\n",
       "      <th>95% CI Upper</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Input Size</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>100.0</th>\n",
       "      <td>0.0006329451</td>\n",
       "      <td>0.0001003543</td>\n",
       "      <td>0.0000004014</td>\n",
       "      <td>0.0006322490</td>\n",
       "      <td>0.0006336411</td>\n",
       "      <td>0.0006321017</td>\n",
       "      <td>0.0006337884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>650.0</th>\n",
       "      <td>0.0048669643</td>\n",
       "      <td>0.0003156630</td>\n",
       "      <td>0.0000012627</td>\n",
       "      <td>0.0048647748</td>\n",
       "      <td>0.0048691539</td>\n",
       "      <td>0.0048643116</td>\n",
       "      <td>0.0048696171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1200.0</th>\n",
       "      <td>0.0091817665</td>\n",
       "      <td>0.0005746240</td>\n",
       "      <td>0.0000022985</td>\n",
       "      <td>0.0091777808</td>\n",
       "      <td>0.0091857522</td>\n",
       "      <td>0.0091769375</td>\n",
       "      <td>0.0091865955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1750.0</th>\n",
       "      <td>0.0131906290</td>\n",
       "      <td>0.0006462876</td>\n",
       "      <td>0.0000025852</td>\n",
       "      <td>0.0131861462</td>\n",
       "      <td>0.0131951118</td>\n",
       "      <td>0.0131851978</td>\n",
       "      <td>0.0131960602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2300.0</th>\n",
       "      <td>0.0175009584</td>\n",
       "      <td>0.0008152447</td>\n",
       "      <td>0.0000032610</td>\n",
       "      <td>0.0174953037</td>\n",
       "      <td>0.0175066132</td>\n",
       "      <td>0.0174941074</td>\n",
       "      <td>0.0175078095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2850.0</th>\n",
       "      <td>0.0217868748</td>\n",
       "      <td>0.0009173524</td>\n",
       "      <td>0.0000036694</td>\n",
       "      <td>0.0217805118</td>\n",
       "      <td>0.0217932378</td>\n",
       "      <td>0.0217791656</td>\n",
       "      <td>0.0217945839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3400.0</th>\n",
       "      <td>0.0262993040</td>\n",
       "      <td>0.0010667967</td>\n",
       "      <td>0.0000042672</td>\n",
       "      <td>0.0262919044</td>\n",
       "      <td>0.0263067036</td>\n",
       "      <td>0.0262903390</td>\n",
       "      <td>0.0263082690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3950.0</th>\n",
       "      <td>0.0305455189</td>\n",
       "      <td>0.0010532401</td>\n",
       "      <td>0.0000042130</td>\n",
       "      <td>0.0305382133</td>\n",
       "      <td>0.0305528244</td>\n",
       "      <td>0.0305366678</td>\n",
       "      <td>0.0305543700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4500.0</th>\n",
       "      <td>0.0358999395</td>\n",
       "      <td>0.0015196376</td>\n",
       "      <td>0.0000060786</td>\n",
       "      <td>0.0358893989</td>\n",
       "      <td>0.0359104801</td>\n",
       "      <td>0.0358871690</td>\n",
       "      <td>0.0359127101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5050.0</th>\n",
       "      <td>0.0394938488</td>\n",
       "      <td>0.0014218419</td>\n",
       "      <td>0.0000056874</td>\n",
       "      <td>0.0394839865</td>\n",
       "      <td>0.0395037111</td>\n",
       "      <td>0.0394819001</td>\n",
       "      <td>0.0395057975</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5600.0</th>\n",
       "      <td>0.0440076008</td>\n",
       "      <td>0.0014709598</td>\n",
       "      <td>0.0000058838</td>\n",
       "      <td>0.0439973978</td>\n",
       "      <td>0.0440178037</td>\n",
       "      <td>0.0439952393</td>\n",
       "      <td>0.0440199623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6150.0</th>\n",
       "      <td>0.0494516821</td>\n",
       "      <td>0.0020571297</td>\n",
       "      <td>0.0000082285</td>\n",
       "      <td>0.0494374133</td>\n",
       "      <td>0.0494659509</td>\n",
       "      <td>0.0494343946</td>\n",
       "      <td>0.0494689696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6700.0</th>\n",
       "      <td>0.0533411779</td>\n",
       "      <td>0.0016494395</td>\n",
       "      <td>0.0000065978</td>\n",
       "      <td>0.0533297370</td>\n",
       "      <td>0.0533526189</td>\n",
       "      <td>0.0533273166</td>\n",
       "      <td>0.0533550393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7250.0</th>\n",
       "      <td>0.0578824940</td>\n",
       "      <td>0.0018187925</td>\n",
       "      <td>0.0000072752</td>\n",
       "      <td>0.0578698784</td>\n",
       "      <td>0.0578951096</td>\n",
       "      <td>0.0578672094</td>\n",
       "      <td>0.0578977785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7800.0</th>\n",
       "      <td>0.0626736546</td>\n",
       "      <td>0.0020334493</td>\n",
       "      <td>0.0000081338</td>\n",
       "      <td>0.0626595500</td>\n",
       "      <td>0.0626877591</td>\n",
       "      <td>0.0626565661</td>\n",
       "      <td>0.0626907430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8350.0</th>\n",
       "      <td>0.0670005455</td>\n",
       "      <td>0.0022729666</td>\n",
       "      <td>0.0000090919</td>\n",
       "      <td>0.0669847796</td>\n",
       "      <td>0.0670163114</td>\n",
       "      <td>0.0669814442</td>\n",
       "      <td>0.0670196468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8900.0</th>\n",
       "      <td>0.0722602644</td>\n",
       "      <td>0.0026159636</td>\n",
       "      <td>0.0000104639</td>\n",
       "      <td>0.0722421194</td>\n",
       "      <td>0.0722784094</td>\n",
       "      <td>0.0722382807</td>\n",
       "      <td>0.0722822481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9450.0</th>\n",
       "      <td>0.0763658257</td>\n",
       "      <td>0.0021374099</td>\n",
       "      <td>0.0000085496</td>\n",
       "      <td>0.0763510000</td>\n",
       "      <td>0.0763806513</td>\n",
       "      <td>0.0763478635</td>\n",
       "      <td>0.0763837878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10000.0</th>\n",
       "      <td>0.0815863867</td>\n",
       "      <td>0.0022649461</td>\n",
       "      <td>0.0000090598</td>\n",
       "      <td>0.0815706764</td>\n",
       "      <td>0.0816020969</td>\n",
       "      <td>0.0815673528</td>\n",
       "      <td>0.0816054206</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    Mean  Standard Deviation  Standard Error  90% CI Lower  \\\n",
       "Input Size                                                                   \n",
       "100.0       0.0006329451        0.0001003543    0.0000004014  0.0006322490   \n",
       "650.0       0.0048669643        0.0003156630    0.0000012627  0.0048647748   \n",
       "1200.0      0.0091817665        0.0005746240    0.0000022985  0.0091777808   \n",
       "1750.0      0.0131906290        0.0006462876    0.0000025852  0.0131861462   \n",
       "2300.0      0.0175009584        0.0008152447    0.0000032610  0.0174953037   \n",
       "2850.0      0.0217868748        0.0009173524    0.0000036694  0.0217805118   \n",
       "3400.0      0.0262993040        0.0010667967    0.0000042672  0.0262919044   \n",
       "3950.0      0.0305455189        0.0010532401    0.0000042130  0.0305382133   \n",
       "4500.0      0.0358999395        0.0015196376    0.0000060786  0.0358893989   \n",
       "5050.0      0.0394938488        0.0014218419    0.0000056874  0.0394839865   \n",
       "5600.0      0.0440076008        0.0014709598    0.0000058838  0.0439973978   \n",
       "6150.0      0.0494516821        0.0020571297    0.0000082285  0.0494374133   \n",
       "6700.0      0.0533411779        0.0016494395    0.0000065978  0.0533297370   \n",
       "7250.0      0.0578824940        0.0018187925    0.0000072752  0.0578698784   \n",
       "7800.0      0.0626736546        0.0020334493    0.0000081338  0.0626595500   \n",
       "8350.0      0.0670005455        0.0022729666    0.0000090919  0.0669847796   \n",
       "8900.0      0.0722602644        0.0026159636    0.0000104639  0.0722421194   \n",
       "9450.0      0.0763658257        0.0021374099    0.0000085496  0.0763510000   \n",
       "10000.0     0.0815863867        0.0022649461    0.0000090598  0.0815706764   \n",
       "\n",
       "            90% CI Upper  95% CI Lower  95% CI Upper  \n",
       "Input Size                                            \n",
       "100.0       0.0006336411  0.0006321017  0.0006337884  \n",
       "650.0       0.0048691539  0.0048643116  0.0048696171  \n",
       "1200.0      0.0091857522  0.0091769375  0.0091865955  \n",
       "1750.0      0.0131951118  0.0131851978  0.0131960602  \n",
       "2300.0      0.0175066132  0.0174941074  0.0175078095  \n",
       "2850.0      0.0217932378  0.0217791656  0.0217945839  \n",
       "3400.0      0.0263067036  0.0262903390  0.0263082690  \n",
       "3950.0      0.0305528244  0.0305366678  0.0305543700  \n",
       "4500.0      0.0359104801  0.0358871690  0.0359127101  \n",
       "5050.0      0.0395037111  0.0394819001  0.0395057975  \n",
       "5600.0      0.0440178037  0.0439952393  0.0440199623  \n",
       "6150.0      0.0494659509  0.0494343946  0.0494689696  \n",
       "6700.0      0.0533526189  0.0533273166  0.0533550393  \n",
       "7250.0      0.0578951096  0.0578672094  0.0578977785  \n",
       "7800.0      0.0626877591  0.0626565661  0.0626907430  \n",
       "8350.0      0.0670163114  0.0669814442  0.0670196468  \n",
       "8900.0      0.0722784094  0.0722382807  0.0722822481  \n",
       "9450.0      0.0763806513  0.0763478635  0.0763837878  \n",
       "10000.0     0.0816020969  0.0815673528  0.0816054206  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calulate standard Error\n",
    "standard_errors = std_running_times / num_measurements\n",
    "\n",
    "# Calculate the degrees of freedom\n",
    "df = len(mean_running_times) - 1\n",
    "\n",
    "# Calculate the critical values for the t-distribution\n",
    "t_critical_90 = t.ppf(1 - (1 - 0.90) / 2, df)\n",
    "t_critical_95 = t.ppf(1 - (1 - 0.95) / 2, df)\n",
    "\n",
    "# Calculate the margin of error\n",
    "margin_of_errors_90 = t_critical_90 * standard_errors\n",
    "margin_of_errors_95 = t_critical_95 * standard_errors\n",
    "\n",
    "# Calculate the confidence intervals\n",
    "confidence_intervals_90 = np.column_stack((mean_running_times - margin_of_errors_90, mean_running_times + margin_of_errors_90))\n",
    "confidence_intervals_95 = np.column_stack((mean_running_times - margin_of_errors_95, mean_running_times + margin_of_errors_95))\n",
    "\n",
    "# Create a DataFrame for the table\n",
    "table_data = {'Input Size': input_sizes,\n",
    "              'Mean': mean_running_times,\n",
    "              'Standard Deviation' : std_running_times,\n",
    "              'Standard Error': standard_errors,\n",
    "              '90% CI Lower': confidence_intervals_90[:, 0],\n",
    "              '90% CI Upper': confidence_intervals_90[:, 1],\n",
    "              '95% CI Lower': confidence_intervals_95[:, 0],\n",
    "              '95% CI Upper': confidence_intervals_95[:, 1]\n",
    "             }\n",
    "\n",
    "# Create the DataFrame\n",
    "df = pd.DataFrame(table_data)\n",
    "\n",
    "# Set the Sample column as the index\n",
    "df.set_index('Input Size', inplace=True)\n",
    "\n",
    "# Display the table\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2c5dc731",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00109975, 0.00044987, 0.00043409, 0.00033985, 0.00032311,\n",
       "       0.00029206, 0.00028136, 0.00023917, 0.00029361, 0.00024972,\n",
       "       0.00023185, 0.00028854, 0.00021449, 0.00021795, 0.00022505,\n",
       "       0.00023531, 0.00025111, 0.00019414, 0.00019256])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# b/a\n",
    "margin_of_errors_90 / mean_running_times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4346b7d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00133242, 0.00054505, 0.00052593, 0.00041175, 0.00039147,\n",
       "       0.00035384, 0.00034088, 0.00028977, 0.00035573, 0.00030255,\n",
       "       0.00028089, 0.00034958, 0.00025986, 0.00026406, 0.00027266,\n",
       "       0.00028509, 0.00030423, 0.00023521, 0.0002333 ])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# b/a\n",
    "margin_of_errors_95 / mean_running_times"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a57e156",
   "metadata": {},
   "source": [
    "### Quality Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "11eab958",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "10fd0eda55de46379d2290d92fece88a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/16 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "input_sizes = np.linspace(5, 20, 16)\n",
    "\n",
    "quality = {}\n",
    "\n",
    "for s in tqdm(input_sizes):\n",
    "    for _ in range(100):\n",
    "        sets = random_sized_set_packing_instance(int(s), 30, 10000)\n",
    "        sets_bf = len(max_set_packing(sets)[0])\n",
    "        sets_gd = len(greedy_set_packing(sets)[0])\n",
    "        if str(s) not in quality:\n",
    "            quality[str(s)] = [float(sets_gd)/sets_bf]\n",
    "        else:\n",
    "            quality[str(s)].append(float(sets_gd)/sets_bf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "23a07061",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Mean Quality</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Input Size</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.9980000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.9980000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.0000000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.9985714286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.9905555556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.9930555556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.9980909091</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.9974242424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.9859599845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.9962545788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.9963290043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.9928603480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.9910753609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.9920171569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.9914694272</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Mean Quality\n",
       "Input Size              \n",
       "5           1.0000000000\n",
       "6           0.9980000000\n",
       "7           0.9980000000\n",
       "8           1.0000000000\n",
       "9           0.9985714286\n",
       "10          0.9905555556\n",
       "11          0.9930555556\n",
       "12          0.9980909091\n",
       "13          0.9974242424\n",
       "14          0.9859599845\n",
       "15          0.9962545788\n",
       "16          0.9963290043\n",
       "17          0.9928603480\n",
       "18          0.9910753609\n",
       "19          0.9920171569\n",
       "20          0.9914694272"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "means = [np.mean(q) for q in list(quality.values())]\n",
    "\n",
    "df = pd.DataFrame({\"Input Size\": input_sizes, \"Mean Quality\": means})\n",
    "df[\"Input Size\"] = df[\"Input Size\"].astype(\"int64\")\n",
    "df = df.set_index(\"Input Size\")\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d61c3fd",
   "metadata": {},
   "source": [
    "### Black-Box Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "503384aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test case 1 passed successfully!\n",
      "Set Packing: []\n"
     ]
    }
   ],
   "source": [
    "sets = [] \n",
    "result = greedy_set_packing(sets) \n",
    "assert len(result[0]) == 0, \"Test case 1 failed\"\n",
    "print(\"Test case 1 passed successfully!\")\n",
    "print(\"Set Packing:\", result[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a6dd2c94",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test case 2 passed successfully!\n",
      "Set Packing: [{1, 2, 3}, {4, 5, 6}, {8, 9, 7}]\n"
     ]
    }
   ],
   "source": [
    "sets = [\n",
    "    {1, 2, 3},\n",
    "    {4, 5, 6},\n",
    "    {7, 8, 9}\n",
    "]\n",
    "result = greedy_set_packing(sets)\n",
    "assert len(result[0]) == 3, \"Test case 2 failed\"\n",
    "print(\"Test case 2 passed successfully!\")\n",
    "print(\"Set Packing:\", result[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "de1f6729",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test case 3 passed successfully!\n",
      "Set Packing: [{1, 2, 3}, {4, 5, 6}]\n"
     ]
    }
   ],
   "source": [
    "sets = [\n",
    "    {1, 2, 3},\n",
    "    {2, 3, 4},\n",
    "    {3, 4, 5},\n",
    "    {4, 5, 6}\n",
    "]\n",
    "result = greedy_set_packing(sets)\n",
    "assert len(result[0]) == 2, \"Test case 3 failed\"\n",
    "print(\"Test case 3 passed successfully!\")\n",
    "print(\"Set Packing:\", result[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cc9b0d1f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test case 4 passed successfully!\n",
      "Set Packing: [{2, 3}, {4, 5, 6}]\n"
     ]
    }
   ],
   "source": [
    "sets = [\n",
    "    {1, 2, 3},\n",
    "    {2, 3},\n",
    "    {3, 4},\n",
    "    {4, 5, 6}\n",
    "]\n",
    "result = greedy_set_packing(sets)\n",
    "assert len(result[0]) == 2, \"Test case 4 failed\"\n",
    "print(\"Test case 4 passed successfully!\")\n",
    "print(\"Set Packing:\", result[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "759bbd63",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test case 5 passed successfully!\n",
      "Set Packing: [{1, 2, 3}]\n"
     ]
    }
   ],
   "source": [
    "sets = [\n",
    "    {1, 2, 3},\n",
    "    {2, 3, 4},\n",
    "    {2, 3, 4},\n",
    "    {3, 4, 5}\n",
    "]\n",
    "result = greedy_set_packing(sets)\n",
    "assert len(result[0]) == 1, \"Test case 5 failed\"\n",
    "print(\"Test case 5 passed successfully!\")\n",
    "print(\"Set Packing:\", result[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "380c97ab",
   "metadata": {},
   "source": [
    "### White-Box Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "057c6360",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Excepted Result: []\n",
      "Actual Result:   []\n",
      "Excepted Result: [{1, 2}, {3, 4}, {5, 6}]\n",
      "Actual Result:   [{1, 2}, {3, 4}, {5, 6}]\n",
      "Excepted Result: [{1, 2}, {3, 4}]\n",
      "Actual Result:   [{1, 2}, {3, 4}]\n",
      "Excepted Result: [{1, 2}, {3, 4}, {5, 6}]\n",
      "Actual Result:   [{1, 2}, {3, 4}, {5, 6}]\n"
     ]
    }
   ],
   "source": [
    "test_set_1 = []\n",
    "oracle_1 = []\n",
    "test_set_2 = [{1, 2}, {3, 4}, {5, 6}]\n",
    "oracle_2 = [{1, 2}, {3, 4}, {5, 6}]\n",
    "test_set_3 = [{1, 2}, {2, 3}, {3, 4}]\n",
    "oracle_3 = [{1, 2}, {3, 4}]\n",
    "test_set_4 = [{1, 2}, {3, 4}, {4, 5}, {5, 6}]\n",
    "oracle_4 = [{1, 2}, {3, 4}, {5, 6}]\n",
    "\n",
    "tests = [[test_set_1, oracle_1], [test_set_2, oracle_2], [test_set_3, oracle_3], [test_set_4, oracle_4]]\n",
    "\n",
    "for t in tests:\n",
    "    max_pack = greedy_set_packing(t[0])\n",
    "    print(\"Excepted Result:\", t[1])\n",
    "    print(\"Actual Result:  \", max_pack[0])"
   ]
  }
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