competition.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving the [8-puzzle](https://8-puzzle.readthedocs.io/en/latest/) (with a slight twist)\n",
    "## Testing which heuristics perform best on for the competition\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of only being able to slide tiles vertically and horizontally (with a cost of 1), when the empty tile is at a corner, the tiles on the same row (or on the same column) can wrap around (if you have more than two rows) with a cost of 2. Similarly the diagonal tiles (both the adjacent one and the opposing corner) can slide into an empty corner with a cost of 3. We use the number 0 to represent the empty tile."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# you need to install these in your env to run this notebook\n",
    "import numpy as np\n",
    "from tqdm import tqdm\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import copy\n",
    "\n",
    "# local modules, no installs needed\n",
    "import run\n",
    "from board import Board\n",
    "from node import Node\n",
    "import search\n",
    "from heuristics import hamming_distance, manhattan_distance, row_col_out_of_place, euclidean_distance, permutation_inversion\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "These are the 25 competition puzzles:\n-\n[[7 5 1 6]\n [0 2 4 3]]\n-\n[[2 4 7 3]\n [6 5 1 0]]\n-\n[[7 2 6 0]\n [3 4 1 5]]\n-\n[[6 3 0 5]\n [4 2 1 7]]\n-\n[[7 2 6 4]\n [3 0 1 5]]\n-\n[[7 4 1 5]\n [3 2 6 0]]\n-\n[[3 0 1 4]\n [2 6 5 7]]\n-\n[[4 5 3 6]\n [2 0 7 1]]\n-\n[[3 4 0 1]\n [5 7 6 2]]\n-\n[[6 3 4 7]\n [1 2 5 0]]\n-\n[[3 5 7 2]\n [4 6 0 1]]\n-\n[[1 0 3 6]\n [5 2 7 4]]\n-\n[[2 7 3 0]\n [6 1 4 5]]\n-\n[[6 3 1 5]\n [7 4 2 0]]\n-\n[[7 1 5 4]\n [3 0 2 6]]\n-\n[[7 4 0 3]\n [5 2 6 1]]\n-\n[[2 3 7 6]\n [5 0 4 1]]\n-\n[[6 1 5 0]\n [3 2 4 7]]\n-\n[[4 3 5 0]\n [2 6 1 7]]\n-\n[[0 4 5 7]\n [2 6 1 3]]\n-\n[[2 5 6 7]\n [3 4 1 0]]\n-\n[[7 1 6 5]\n [0 2 4 3]]\n-\n[[7 6 0 3]\n [4 1 5 2]]\n-\n[[7 6 4 5]\n [3 2 1 0]]\n-\n[[7 3 6 5]\n [1 4 2 0]]\n"
     ]
    }
   ],
   "source": [
    "HEURISTICS = [hamming_distance, manhattan_distance, row_col_out_of_place, euclidean_distance, permutation_inversion]\n",
    "\n",
    "COMPETITION_PUZZLE_FILENAME = 'competitionPuzzles.txt'\n",
    "\n",
    "puzzles = run.convert_to_numpy_arrays(COMPETITION_PUZZLE_FILENAME)\n",
    "\n",
    "puzzles = [p.reshape(2,4) for p in puzzles]\n",
    "\n",
    "print(f'These are the {len(puzzles)} competition puzzles:')\n",
    "for p in puzzles:\n",
    "    print(f'-\\n{p}')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_experiment_object():\n",
    "    '''Build's the structure that will run the experiment and hold results'''\n",
    "    experiment = {}\n",
    "    for func in HEURISTICS:\n",
    "        experiment[func.__name__] = {\n",
    "            'func': func,\n",
    "            'algos': {\n",
    "                'GBF': {\n",
    "                    'func': search.greedy_best_first,\n",
    "                    'shape': {\n",
    "                        (2, 4): {'results': []},\n",
    "                        (3, 3): {'results': []}\n",
    "                    }\n",
    "                },\n",
    "                'A*': {\n",
    "                    'func': search.a_star,\n",
    "                    'shape': {\n",
    "                        (2, 4): {'results': []},\n",
    "                        (3, 3): {'results': []}\n",
    "                    }\n",
    "                }\n",
    "            },\n",
    "        }\n",
    "\n",
    "    return experiment\n",
    "\n",
    "experiment = build_experiment_object()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_experiment(experiment: dict, puzzles: list):\n",
    "    for heurist_name in tqdm(experiment):\n",
    "        heuristic_func = experiment[heurist_name]['func']\n",
    "\n",
    "        for algo_name in experiment[heurist_name]['algos']:\n",
    "            algo_func = experiment[heurist_name]['algos'][algo_name]['func']\n",
    "\n",
    "            for puzzle in puzzles:\n",
    "                b = Board(puzzle)\n",
    "                result: dict = algo_func(board=b, H=heuristic_func)\n",
    "                experiment[heurist_name]['algos'][algo_name]['shape'][puzzle.shape]['results'].append(result)\n",
    "\n",
    "    return experiment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "  0%|          | 0/5 [00:00<?, ?it/s]\n",
      "Running 2 search algorithms on 25 puzzles, 5 different times to test the 5 heuristics:\n",
      "100%|██████████| 5/5 [00:55<00:00, 11.02s/it]\n",
      "\n",
      "Total of 2x25x5 = 250 puzzles solved in 55.12 seconds\n",
      "\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(f'\\nRunning 2 search algorithms on {len(puzzles)} puzzles, 5 different times to test the 5 heuristics:')\n",
    "start = time.time()\n",
    "\n",
    "run_experiment(experiment,puzzles)\n",
    "\n",
    "elapsed = round(time.time()-start, 2)\n",
    "print(f'\\n\\nTotal of 2x{len(puzzles)}x5 = {2*len(puzzles)*5} puzzles solved in {elapsed} seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_stats(experiment):\n",
    "    prototype = {\n",
    "        'GBF': {\n",
    "            'hamming_distance': {},\n",
    "            'manhattan_distance': {},\n",
    "            'row_col_out_of_place': {},\n",
    "            'euclidean_distance': {},\n",
    "            'permutation_inversion': {}\n",
    "        },\n",
    "        'A*': {\n",
    "            'hamming_distance': {},\n",
    "            'manhattan_distance': {},\n",
    "            'row_col_out_of_place': {},\n",
    "            'euclidean_distance': {},\n",
    "            'permutation_inversion': {}\n",
    "        }\n",
    "    }\n",
    "    global_stats = {\n",
    "        (2,4): copy.deepcopy(prototype),\n",
    "        (3,3): copy.deepcopy(prototype),\n",
    "        }\n",
    "    stats = {}\n",
    "    timeouts = 0\n",
    "    result_count = 0\n",
    "\n",
    "    for heuristic in experiment:\n",
    "\n",
    "        for algo in experiment[heuristic]['algos']:\n",
    "            \n",
    "            for shape in experiment[heuristic]['algos'][algo]['shape']:\n",
    "\n",
    "                results = experiment[heuristic]['algos'][algo]['shape'][shape]['results']\n",
    "                \n",
    "                runtimes = [r['runtime'] for r in results]\n",
    "                costs = np.array([r['current_node'].total_cost for r in results])\n",
    "                num_visited_nodes = np.array([r['visited_nodes'] for r in results])\n",
    "                \n",
    "                mean_runtime = np.mean(runtimes)\n",
    "                mean_cost = np.mean(costs)\n",
    "                mean_vis_nodes = np.mean(num_visited_nodes)\n",
    "                \n",
    "                global_stats[shape][algo][heuristic]['mean_runtime'] = mean_runtime\n",
    "                global_stats[shape][algo][heuristic]['mean_cost'] = mean_cost\n",
    "                global_stats[shape][algo][heuristic]['mean_visited_nodes'] = mean_vis_nodes\n",
    "                global_stats[shape][algo][heuristic]['std_runtime'] = np.std(runtimes)\n",
    "                global_stats[shape][algo][heuristic]['std_cost'] = np.std(costs)\n",
    "                global_stats[shape][algo][heuristic]['std_visited_nodes'] = np.std(num_visited_nodes)\n",
    "                \n",
    "                timeouts += len([1 for r in results if not r['success']])\n",
    "    \n",
    "    print(f'number of timeouts = {timeouts}.')\n",
    "\n",
    "    return global_stats\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "stats = generate_stats(experiment)\n",
    "'''here is a small sample of what the stats object looks like'''\n",
    "stats[(2,4)]['GBF']['hamming_distance']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let us now compare these heuristics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''Calculating average runtime for each heuristic'''\n",
    "def plot_stats(stats, shape, algo):\n",
    "    \n",
    "    heuris_vs_runtime = {}\n",
    "    heuris_vs_cost = {}\n",
    "    heuris_vs_visited = {}\n",
    "\n",
    "    for heuristic in stats[shape][algo]:\n",
    "        alias = stats[shape][algo][heuristic]\n",
    "        heuris_vs_runtime[heuristic] = round(alias['mean_runtime'], 2)\n",
    "        heuris_vs_cost[heuristic] = round(alias['mean_cost'], 2) \n",
    "        heuris_vs_visited[heuristic] = round(alias['mean_visited_nodes'], 2)\n",
    "    \n",
    "    print(heuris_vs_runtime)\n",
    "    plt.barh(tuple(heuris_vs_runtime.keys()),heuris_vs_runtime.values())\n",
    "    plt.ylabel('Heuristics')\n",
    "    plt.xlabel('Time in Seconds')\n",
    "    plt.title(f'Mean runtime of {algo} on {shape[0]}x{shape[1]} puzzles')\n",
    "    plt.show()\n",
    "    print()\n",
    "\n",
    "    print(heuris_vs_cost)\n",
    "    plt.barh(tuple(heuris_vs_cost.keys()),heuris_vs_cost.values())\n",
    "    plt.ylabel('Heuristics')\n",
    "    plt.xlabel('Cost')\n",
    "    plt.title(f'Mean cost of {algo} on {shape[0]}x{shape[1]} puzzles')\n",
    "    plt.show()\n",
    "    print()\n",
    "    \n",
    "    print(heuris_vs_visited)\n",
    "    plt.barh(tuple(heuris_vs_visited.keys()),heuris_vs_visited.values())\n",
    "    plt.ylabel('Heuristics')\n",
    "    plt.xlabel('Number of Visited Nodes')\n",
    "    plt.title(f'Mean search path of {algo} on {shape[0]}x{shape[1]} puzzles')\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "{'hamming_distance': 0.31, 'manhattan_distance': 0.1, 'row_col_out_of_place': 0.24, 'euclidean_distance': 0.26, 'permutation_inversion': 0.33}\n"
     ]
    },
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 13.36, 'manhattan_distance': 13.4, 'row_col_out_of_place': 13.36, 'euclidean_distance': 13.32, 'permutation_inversion': 15.88}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 928.76, 'manhattan_distance': 130.84, 'row_col_out_of_place': 349.56, 'euclidean_distance': 291.0, 'permutation_inversion': 316.68}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plot_stats(stats,(2,4),'A*')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "{'hamming_distance': 0.01, 'manhattan_distance': 0.05, 'row_col_out_of_place': 0.03, 'euclidean_distance': 0.07, 'permutation_inversion': 0.34}\n"
     ]
    },
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 22.72, 'manhattan_distance': 23.92, 'row_col_out_of_place': 21.48, 'euclidean_distance': 30.04, 'permutation_inversion': 30.96}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 67.8, 'manhattan_distance': 92.32, 'row_col_out_of_place': 96.16, 'euclidean_distance': 149.12, 'permutation_inversion': 701.0}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plot_stats(stats,(2,4),'GBF')"
   ]
  },
  {
   "source": [
    "### Let's check how our heuristic cost solutions compares to the ideal cost solutions"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "puzzle 1: \tsmallest cost solution is 16 \tfound in 10.55 seconds\n",
      "puzzle 2: \tsmallest cost solution is 14 \tfound in 3.93 seconds\n",
      "puzzle 3: \tsmallest cost solution is 14 \tfound in 3.0 seconds\n",
      "puzzle 4: \tsmallest cost solution is 15 \tfound in 5.61 seconds\n",
      "puzzle 5: \tsmallest cost solution is 17 \tfound in 11.18 seconds\n",
      "puzzle 6: \tsmallest cost solution is 13 \tfound in 2.02 seconds\n",
      "puzzle 7: \tsmallest cost solution is 13 \tfound in 3.09 seconds\n",
      "puzzle 8: \tsmallest cost solution is 13 \tfound in 2.58 seconds\n",
      "puzzle 9: \tsmallest cost solution is 15 \tfound in 11.97 seconds\n",
      "puzzle 10: \tsmallest cost solution is 12 \tfound in 2.55 seconds\n",
      "puzzle 11: \tsmallest cost solution is 11 \tfound in 0.68 seconds\n",
      "puzzle 12: \tsmallest cost solution is 9 \tfound in 0.64 seconds\n",
      "puzzle 13: \tsmallest cost solution is 13 \tfound in 4.34 seconds\n",
      "puzzle 14: \tsmallest cost solution is 17 \tfound in 23.51 seconds\n",
      "puzzle 15: \tsmallest cost solution is 15 \tfound in 11.71 seconds\n",
      "puzzle 16: \tsmallest cost solution is 13 \tfound in 2.84 seconds\n",
      "puzzle 17: \tsmallest cost solution is 14 \tfound in 7.09 seconds\n",
      "puzzle 18: \tsmallest cost solution is 13 \tfound in 4.24 seconds\n",
      "puzzle 19: \tsmallest cost solution is 13 \tfound in 3.0 seconds\n",
      "puzzle 20: \tsmallest cost solution is 10 \tfound in 0.79 seconds\n",
      "puzzle 21: \tsmallest cost solution is 12 \tfound in 1.34 seconds\n",
      "puzzle 22: \tsmallest cost solution is 14 \tfound in 7.77 seconds\n",
      "puzzle 23: \tsmallest cost solution is 13 \tfound in 3.28 seconds\n",
      "puzzle 24: \tsmallest cost solution is 16 \tfound in 13.86 seconds\n",
      "puzzle 25: \tsmallest cost solution is 8 \tfound in 0.1 seconds\n"
     ]
    }
   ],
   "source": [
    "for i, p in enumerate(puzzles):\n",
    "    result = search.uniform_cost(Board(p))\n",
    "    print(f\"puzzle {i+1}: \\tcost: {result['current_node'].total_cost} \\tfound in {result['runtime']} seconds\")"
   ]
  }
 ],
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