analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving the [8-puzzle](https://8-puzzle.readthedocs.io/en/latest/) (with a slight twist)\n",
    "## Heuristic search vs uninformed search, admissibility, performance tests, empirical results, and some charts! Fun stuff ahead\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": 19,
   "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",
    "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": "markdown",
   "metadata": {},
   "source": [
    "We have implemented a bunch of heuristics, but we don't know which are the best for our problem. We know from theory that hamming distance and manhattan distance are both [admissible](https://en.wikipedia.org/wiki/Admissible_heuristic) and that permutation inversion is not. But we came up with two new heuristics and would like to know about their admissibility.\n",
    "\n",
    "\n",
    "1. Rows and columns out of place: \n",
    "\n",
    "    Is the sum of all tiles that are out of their goal row position and all tiles that are out of their goal column position. For example, if a tile is out of both row and column position it adds 2 to the running sum of the heuristic, if it's out of row XOR column it adds 1 to the sum and if the tile is in its goal position it add 0 to the heuristic sum. We expect it to be admissible because when conceptually compared with hamming and manhattan distance, this heuristic seems to be more optimistic than manhattan distance but slightly less optimistic than hamming distance. It s more optimistic than manhattan because it essentially three states: either in place, out of place along one axis or out of place along two axis. Manhattan will assign more add more estimated cost to tiles that are further away from their goal position, making it less optimistic than this heuristic.\n",
    "\n",
    "2. Euclidean distance:\n",
    "\n",
    "    Is the sum of the euclidean distances between each tile and it's goal position. Euclidean distance should be more optimistic than manhattan distance for the following reason: given any two coordinates on the board manhattan distance calculates the number of steps that the tile has to move but the tile is restricted to moves that are parallel to the x-axis or the y-axis. if you were to take any two tiles and draw the euclidean and manhattan distance between them, you would get a right triangle where the euclidean distance draws the hypothenuse and the manhattan distance draws the opposite and adjacent sides. The hypothenuse is always smaller than the sum of the two other sides, which is why we expect euclidean distance to be admissible.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to validate our intuition, we will generate 100 random [8-puzzles](https://8-puzzle.readthedocs.io/en/latest/) in 2x4 and 3x3 format and run algorithms A* and Greedy Best First Search using these heuristics. Of course to verify whether we get the shortest cost solution path to those puzzle we will also run Uniform Cost Search to obtain the shortest paths with certainty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "HEURISTICS = [hamming_distance, manhattan_distance, row_col_out_of_place, euclidean_distance, permutation_inversion]\n",
    "\n",
    "NUMBER_PUZZLES = 50\n",
    "\n",
    "two_by_two = [np.random.permutation(8).reshape(2,4) for _ in range(NUMBER_PUZZLES)]\n",
    "\n",
    "three_by_three = [np.random.permutation(9).reshape(3,3) for _ in range(NUMBER_PUZZLES)]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Here are the 50 random 2x4 puzzles\n[[3 0 6 5]\n [4 2 1 7]]\n[[6 2 5 7]\n [1 4 3 0]]\n[[6 2 5 1]\n [4 7 0 3]]\n[[2 7 1 6]\n [0 5 4 3]]\n[[3 6 0 2]\n [1 5 7 4]]\n[[5 2 3 6]\n [0 4 7 1]]\n[[2 0 3 6]\n [7 4 5 1]]\n[[5 3 0 1]\n [6 2 4 7]]\n[[6 5 1 3]\n [0 7 2 4]]\n[[1 3 6 5]\n [2 4 0 7]]\n[[2 3 0 1]\n [5 6 7 4]]\n[[6 1 2 3]\n [5 0 7 4]]\n[[5 4 0 6]\n [7 1 3 2]]\n[[6 0 3 2]\n [4 7 5 1]]\n[[2 1 7 5]\n [0 3 4 6]]\n[[4 0 6 5]\n [1 3 2 7]]\n[[2 3 5 6]\n [4 0 7 1]]\n[[3 0 6 4]\n [2 1 5 7]]\n[[1 7 0 2]\n [4 5 6 3]]\n[[0 6 2 1]\n [3 4 7 5]]\n[[3 1 2 7]\n [6 5 4 0]]\n[[1 0 6 2]\n [5 4 7 3]]\n[[3 1 4 5]\n [6 0 7 2]]\n[[7 4 1 6]\n [2 3 5 0]]\n[[7 1 3 0]\n [6 4 2 5]]\n[[4 3 7 0]\n [2 5 6 1]]\n[[2 3 4 6]\n [5 0 7 1]]\n[[1 0 7 3]\n [2 6 4 5]]\n[[5 1 2 4]\n [7 0 6 3]]\n[[6 4 5 1]\n [2 7 3 0]]\n[[5 7 1 2]\n [0 3 4 6]]\n[[0 3 1 6]\n [5 2 4 7]]\n[[3 4 1 7]\n [0 2 6 5]]\n[[4 7 2 6]\n [0 5 3 1]]\n[[3 0 7 1]\n [6 5 4 2]]\n[[1 7 2 5]\n [0 6 3 4]]\n[[1 3 7 0]\n [5 2 6 4]]\n[[1 5 6 2]\n [0 3 4 7]]\n[[1 7 0 3]\n [4 6 5 2]]\n[[3 7 6 5]\n [2 1 0 4]]\n[[2 5 6 7]\n [3 0 1 4]]\n[[1 5 7 0]\n [6 3 2 4]]\n[[6 3 5 1]\n [4 0 7 2]]\n[[1 2 0 7]\n [4 6 5 3]]\n[[6 3 4 0]\n [7 1 5 2]]\n[[7 0 2 3]\n [6 1 4 5]]\n[[1 4 6 7]\n [2 0 5 3]]\n[[4 0 6 7]\n [5 2 1 3]]\n[[4 1 0 3]\n [5 6 7 2]]\n[[5 2 0 6]\n [4 3 1 7]]\n"
     ]
    }
   ],
   "source": [
    "print(f\"Here are the {NUMBER_PUZZLES} random 2x4 puzzles\")\n",
    "for puzzle in two_by_two:\n",
    "    print(puzzle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Here are the 50 random 3x3 puzzles\n[[8 1 7]\n [2 4 3]\n [0 6 5]]\n[[4 2 5]\n [6 8 0]\n [3 7 1]]\n[[0 8 2]\n [3 6 1]\n [7 5 4]]\n[[1 3 5]\n [4 6 0]\n [8 7 2]]\n[[4 6 1]\n [7 8 0]\n [5 2 3]]\n[[8 0 3]\n [5 7 1]\n [2 6 4]]\n[[4 8 6]\n [3 0 2]\n [7 1 5]]\n[[1 7 3]\n [2 5 6]\n [4 8 0]]\n[[8 5 6]\n [4 2 3]\n [1 7 0]]\n[[4 0 1]\n [3 5 2]\n [6 8 7]]\n[[4 8 5]\n [6 1 3]\n [0 2 7]]\n[[2 0 7]\n [5 1 6]\n [8 4 3]]\n[[7 6 0]\n [4 5 3]\n [2 1 8]]\n[[8 2 3]\n [4 7 5]\n [6 1 0]]\n[[4 6 7]\n [2 8 5]\n [1 0 3]]\n[[8 2 1]\n [3 5 4]\n [0 7 6]]\n[[5 3 0]\n [2 7 1]\n [4 8 6]]\n[[3 5 4]\n [0 7 8]\n [2 1 6]]\n[[3 2 6]\n [8 7 5]\n [4 0 1]]\n[[7 0 4]\n [1 2 3]\n [8 5 6]]\n[[6 4 2]\n [5 1 7]\n [0 8 3]]\n[[6 5 2]\n [1 0 3]\n [8 7 4]]\n[[5 8 6]\n [4 3 2]\n [7 1 0]]\n[[5 7 1]\n [3 2 4]\n [6 8 0]]\n[[3 7 5]\n [2 6 0]\n [1 8 4]]\n[[8 1 6]\n [0 5 3]\n [2 4 7]]\n[[0 4 5]\n [8 2 6]\n [7 3 1]]\n[[4 3 5]\n [0 1 6]\n [8 2 7]]\n[[2 4 3]\n [7 0 5]\n [8 1 6]]\n[[1 6 7]\n [4 8 5]\n [0 2 3]]\n[[6 7 4]\n [8 1 3]\n [5 2 0]]\n[[3 1 7]\n [5 6 4]\n [0 8 2]]\n[[5 4 3]\n [6 0 1]\n [2 8 7]]\n[[6 7 8]\n [4 2 1]\n [0 3 5]]\n[[5 2 1]\n [0 7 6]\n [4 3 8]]\n[[4 0 1]\n [7 8 3]\n [2 6 5]]\n[[1 5 4]\n [7 0 8]\n [3 2 6]]\n[[0 4 3]\n [1 8 2]\n [7 5 6]]\n[[5 6 4]\n [7 2 0]\n [8 1 3]]\n[[5 1 4]\n [7 6 8]\n [0 3 2]]\n[[6 4 7]\n [2 5 3]\n [8 0 1]]\n[[6 4 2]\n [5 7 3]\n [0 8 1]]\n[[0 6 5]\n [2 7 1]\n [4 8 3]]\n[[0 5 4]\n [8 2 1]\n [3 6 7]]\n[[5 8 2]\n [4 0 3]\n [6 7 1]]\n[[6 7 2]\n [0 8 3]\n [5 1 4]]\n[[1 4 3]\n [7 8 2]\n [6 5 0]]\n[[0 5 8]\n [1 4 3]\n [6 2 7]]\n[[7 1 0]\n [5 4 3]\n [2 8 6]]\n[[3 4 0]\n [5 6 7]\n [2 8 1]]\n"
     ]
    }
   ],
   "source": [
    "print(f\"Here are the {NUMBER_PUZZLES} random 3x3 puzzles\")\n",
    "for puzzle in three_by_three:\n",
    "    print(puzzle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": 7,
   "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": "markdown",
   "metadata": {},
   "source": [
    "#### Let's Run A* and Greedy Best First search on the 50 2x4 puzzles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "  0%|          | 0/5 [00:00<?, ?it/s]\n",
      "Running 2 search algorithms on 50 puzzles, 5 different times to test the 5 heuristics:\n",
      "100%|██████████| 5/5 [01:21<00:00, 16.29s/it]\n",
      "\n",
      "Total of 2x50x5 = 500 puzzles solved in 81.45 seconds\n",
      "\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print('\\nRunning 2 search algorithms on 50 puzzles, 5 different times to test the 5 heuristics:')\n",
    "start = time.time()\n",
    "\n",
    "run_experiment(experiment,two_by_two)\n",
    "\n",
    "elapsed = round(time.time()-start, 2)\n",
    "print(f'\\n\\nTotal of 2x50x5 = {2*50*5} puzzles solved in {elapsed} seconds')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Now Let's Run the same algorithms with the same heuristics on the 3x3 puzzles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "100%|██████████| 5/5 [05:12<00:00, 62.47s/it]\n",
      "\n",
      "Total of 2x50x5 = 500 puzzles solved in 312.33 seconds\n",
      "\n"
     ]
    }
   ],
   "source": [
    "start = time.time()\n",
    "\n",
    "run_experiment(experiment, three_by_three)\n",
    "\n",
    "elapsed = round(time.time()-start, 2)\n",
    "print(f'\\n\\nTotal of 2x50x5 = {2*50*5} puzzles solved in {elapsed} seconds')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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": 30,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "number of timeouts = 0.\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "{'mean_runtime': 0.0178,\n",
       " 'mean_cost': 21.66,\n",
       " 'mean_visited_nodes': 91.14,\n",
       " 'std_runtime': 0.014041367454774483,\n",
       " 'std_cost': 8.091007353846615,\n",
       " 'std_visited_nodes': 75.87200010544075}"
      ]
     },
     "metadata": {},
     "execution_count": 30
    }
   ],
   "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": [
    "We definitely did not expect any timeouts for algorithms A* and GBF as they are designed to be very fast but having the assurance is always nice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now compare these heuristics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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": 35,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "{'hamming_distance': 0.24, 'manhattan_distance': 0.1, 'row_col_out_of_place': 0.25, 'euclidean_distance': 0.25, 'permutation_inversion': 0.24}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 12.34, 'manhattan_distance': 12.36, 'row_col_out_of_place': 12.32, 'euclidean_distance': 12.28, 'permutation_inversion': 14.52}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 582.56, 'manhattan_distance': 95.4, 'row_col_out_of_place': 226.48, 'euclidean_distance': 231.52, 'permutation_inversion': 220.14}\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": 36,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 21.66, 'manhattan_distance': 21.64, 'row_col_out_of_place': 20.78, 'euclidean_distance': 25.44, 'permutation_inversion': 30.64}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 91.14, 'manhattan_distance': 82.76, 'row_col_out_of_place': 119.12, 'euclidean_distance': 116.76, 'permutation_inversion': 600.8}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plot_stats(stats,(2,4),'GBF')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "{'hamming_distance': 2.01, 'manhattan_distance': 0.26, 'row_col_out_of_place': 0.88, 'euclidean_distance': 1.29, 'permutation_inversion': 0.82}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 15.14, 'manhattan_distance': 15.02, 'row_col_out_of_place': 15.18, 'euclidean_distance': 15.02, 'permutation_inversion': 17.62}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 3734.76, 'manhattan_distance': 205.56, 'row_col_out_of_place': 782.36, 'euclidean_distance': 865.8, 'permutation_inversion': 591.46}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plot_stats(stats,(3,3),'A*')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
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Z5cqbmZlBO72z1qooJVwnXTMzaxIPTZuZmRXIidjMzKxATsRmZmYFciI2MzMrkBOxmZlZgZyIzczMCuREbGZmViB/j9iabPCAXtSv5O3ezMws4x6xmZlZgZyIzczMCuREbGZmViAnYjMzswI5EZuZmRXIidjMzKxATsRmZmYF8veIrclmz1/IwJNvX+l65vm7yGZm7hGbmZkVyYnYzMysQE7EZmZmBXIiNjMzK5ATsZmZWYGciM3MzArkRGxmZlYgJ2IzM7MCORGbmZkVyInYzMysQE7EZmZmBXIiNjMzK5ATsZmZWYGciM3MzAq02idiSYvTz/6SbqhQZoKkuraNbMV2Jd0hqXeVsidI6t5mwZmZWZtY7RNxg4h4KSJGFh1HJRGxT0S8VaXICYATsZnZaqZdJ2JJ/y1pqqQZkv4gqVNDDzetHylpXJreUNLNkmam144ldQ2UNCdNd5N0raRZkq4DuuXKfU7Sw5IekXS9pB5p+WmSpkmaI+kiSUrLJ0gam+J8StIuVfanWrvzJPWVtLak29M+zJE0StK3gf7AfZLuS+V/L6le0lxJZ5TUc0aKf7akT6blPSRdlpbNkvSVavtbJvajU3v1S99dWNPvz8zMGtduE7GkrYBRwE4RMQxYChxWZZNzgYkRMRTYDphbpeyxwLsRMQQ4Cxie2uwLnALsFRHbAfXAd9I250fEiIgYRJZA98vV1zkitifrtZ7e1HZLfB54KSKGprb+FhHnAi8Be0TEHqncjyKiDhgC7CZpSK6OBSn+3wMnpWWnAgsjYnBq/95G9ncFEXFRRNRFRF2n7r2q7KKZmTVF56IDqOIzZIlqWup8dgNeq1J+T+BrABGxFKjWbduVLHETEbMkzUrLPw1sDTyY2lwTeDit20PS98iGh/uQJfpb07qb0s/pwMBmtJs3G/ilpLHAbRFxf4W6virpaLLfYb8Ud0N9+Xi+nKb3Ag5u2Dgi3pS0X5X9NTOzNtCeE7GAyyPiBysslP4vN9t1JeqPCm3eExGHlLTZFbgAqIuIFySNKWl7Sfq5lMaPabl2l6+MeErScGAf4GeS7o6IH5fEsylZT3dESqjjaohHZdouu79mZtZ22u3QNDAeGClpAwBJfSRtArwqaStJawAHlpQ/NpXtJGmdKnVPIg1zSxpENrwLMBnYSdIn0rrukrZgeZJbkM6hNveir0rt/oek/mTD11cBvyQbZgdYBPRM0+sA7wALJW0IfKGGtu8GvplrZ10q76+ZmbWRdpuII+IxsvOXd6ch3HvIhmBPBm4D7gVezm1yPNnw8WyyIdltqlT/e6BHqvd7wNTU5uvAaOCatG4y8Ml0NfPFZMPGtwDTmrlbZdstMRiYKmkG8CPgzLT8IuBOSfdFxEzgUbLh8UuBB2to+0xg3XQB2Eyy881l97eZ+2ZmZs2giKojpWYfsVa/zaPf4eesdD3zzt535YMxM1sFSJqeLrD9iHbbIzYzM+sI2vPFWqssSXsDY0sWPxcRB5Yrb2ZmHZcTcSuIiLuAu4qOw8zM2j8PTZuZmRXIidjMzKxATsRmZmYFciI2MzMrkBOxmZlZgZyIzczMCuSvL1mTDR7Qi3rfFcvMrEW4R2xmZlYgJ2IzM7MCNTkRS1pX0kce32dmZmZNV1MiljRB0jqS+gAzgcsk/bp1QzMzM1v91doj7hURbwNfBi6LiOHAXq0XlpmZWcdQayLuLKkf8FXgtlaMx8zMrEOpNRH/mOxpQs9ExDRJHweebr2wzMzMOoaavkccEdcD1+fmnwW+0lpBmZmZdRQ1JWJJlwPHR8RbaX5d4FcR8b+tGJu1U7PnL2Tgybe3SVvzfOMQM1vN1To0PaQhCQNExJvAtq0SkZmZWQdSayJeI/WCAUhfY/LtMc3MzFZSrcn0V8BDkm5I8wcBZ7VOSGZmZh1HrRdrXSGpHtgTEPDliHisVSMzMzPrAKomYknrRMTbaSj6FeBPuXV9IuJfrR2gmZnZ6qyxHvGfgP2A6UDklivNf7yV4jIzM+sQqibiiNgv/dy0bcIxMzPrWGp96MP4WpaZmZlZ0zR2jrgr0B3om76+pLRqHaB/K8dmZma22mvsHPE3gBPIku50lifit4HftV5YZmZmHUNj54h/C/xW0rci4rw2isnMzKzDqPXOWq9I6gkg6RRJN0narhXjMjMz6xBqTcSnRsQiSTsDewOXA79vvbDMzMw6hloT8dL0c1/g9xHxF2DN1gmp7UgaI+mkFqxvmKR9mrntWpL+LmmGpFFN3LZF98PMzNpOrfeani/pD8BewFhJa1F7Eq9KkgBFxLKWqK9gw4A64I5mbLst0CUihrVkQGZm1r7Vmky/CtwFfD49DrEP8N3mNippoKTHJV0APAL8UdIcSbMbeoOSLpD0xTR9s6RL0/SRks6sUvfXJM2SNFPSlWnZJpLGp+XjJW1cY5zDJE1O293c8AQqSRMk1aXpvpLmSVoT+DEwqlqvVlIfSbekOidLGiJpA+AqYFjadrMK286TNFbS1PT6RJkyR0malvb/Rknd0/IN0z7MTK8d0/L/TnXNkPQHSZ0qtH20pHpJ9UvfXVjL4TMzsxpUTcSS1kmTXYEJwBvpvtNLgPqVbHtL4ArgTGAjYChZj/sXkvoBk4BdUtkBwNZpemfg/grxbgP8CNgzIoYCx6dV5wNXRMQQ4Grg3BpjvAL4ftpuNnB6pYIR8T5wGnBdRAyLiOsqFD0DeDTV+cMU12vA14H707b/qBLT2xGxfdqnc8qsvykiRqT9fxw4Mi0/F5iYlm8HzJW0FTAK2Cn1xJcCh1XYv4sioi4i6jp171UlPDMza4rGesQND3mYTpZ4p+deK5uIn4+IyWSJ9ZqIWBoRrwITgRFkyXYXSVsDjwGvpgS9A/BQhTr3BG6IiAUAuYdS7JDblytTm1VJ6gX0joiJadHlwK5N3Mdydk4xEBH3Auultmp1Te7nDmXWD5J0v6TZZEl1m7R8T9IFdulYLwQ+AwwHpkmakeZ9/3AzszbU6L2m0znc3SLiny3c9jvpp8qtjIj5aSj482S94z5kQ+SLI2JRhTobHkbRmFrKVPMhyz/EdG3ituX2tynxRIXpBuOAAyJipqTRwO6NxHJ5RPygCe2bmVkLavQccUQEcHMrxjCJ7LxqJ0nrk/U6p6Z1D5Pd2WsSWQ/5JCoMSyfjga9KWg+y87Fp+UPAwWn6MOCBxoJKPcY3JTUMj/8PWW8dYB5ZTxJgZG6zRUDPRqqelGJA0u7Agoh4u7F4ckblfj5cZn1P4GVJXVhxmHk8cGxqt1M67TAeGJnOUTecv96kCbGYmdlKqvVircmSRrRSDDcDs4CZwL3A9yLilbTufqBzRDxDdlFXH6ok4oiYC5wFTJQ0E/h1WvVt4AhJs8gS6vEVqih1ONk561lkV0T/OC3/JXCspIeAvrny9wFbN/IVpDFAXarz7NRGU6wlaQrZPpxYZv2pwBTgHuCJ3PLjgT3SkPV0YJuIeAw4Bbg7xXMP0K+J8ZiZ2UpQ1uFtpJD0GLAF8DzZkLLIOstDWjc8y5M0D6hrOAdelLX6bR79Dj+nTdqad/a+bdKOmVlrkjQ9IurKrav1e8RfaMF4zMzMLKk1Ea/sxU0tKp0DLvc85M9ExBvNqO93wE4li38bEZc1J75U5xF8dAj8wYg4roZtbwY2LVn8/YgY2Nx4zMysfao1Ed9OloxFdpXwpsCTLP9qTJtKyXZYC9bXaHJsRp2XAc1K5BFxYAuHY2Zm7VRNiTgiBufnlT156RutEpGZmVkH0qz7RUfEI2Q33TAzM7OVUFOPWNJ3crNrkN0i8fVWicjMzKwDqfUccf4mFR+SnTO+seXDMTMz61hqPUd8BoCktSPincbKm5mZWW1qOkcsaYd0U4/H0/zQ9AhDMzMzWwm1Xqx1DrA38AZARMykZZ5EZGZm1qHVeo6YiHghexDTfyxt+XBsVTB4QC/qfetJM7MWUWsifkHSjkBIWpPsIQqPt15YZmZmHUOtQ9PHAMcBA4AXye5q1eJ3ozIzM+toar1qegErPtvWzMzMWkDVRCzpPKo88CEivt3iEZmZmXUgjfWI63PTZwCnt2IsZmZmHU7VRBwRlzdMSzohP29mZmYrrykPfWhXzyQ2MzNbHdT8PWKzBrPnL2TgybevdD3z/F1kM7NGL9ZaxPKecHdJbzesAiIi1mnN4MzMzFZ3jZ0j7lltvZmZma2cppwjNjMzsxbmRGxmZlYgJ2IzM7MCORGbmZkVyInYzMysQE7EZmZmBXIiNjMzK5ATsZmZWYGciM3MzArkRGxmZlYgJ2IzM7MCrbaJWNLiJpbfXdKOufkDJG3d8pGt0OY4SSPT9CXV2pM0WlL/1ozHzMza3mqbiJthd2DH3PwBQKsm4ryI+HpEPFalyGjAidjMbDVTeCKWNFDSE6lHOEfS1ZL2kvSgpKclbZ9eD0l6NP3cMm07WtJNkv6Wyv68pO6zJM2UNFnShmnZ/pKmpLr+LmlDSQOBY4ATJc2QtBvwReAXaX4zSUdJmpbqu1FS91TfOEnnpriebejhVthXSTpf0mOSbgc2yK2bIKlOUqdU5xxJsyWdmOqsA65O8XSTdFqKZ46kiyQpV89YSVMlPSVpl7S8k6RfpjpnSfpWWj5c0kRJ0yXdJalfhdiPllQvqX7puwub98s2M7OPKDwRJ58AfgsMAT4JHArsDJwE/BB4Atg1IrYFTgN+mtt2GDAKGAyMkvSxtHxtYHJEDAUmAUel5Q8An051XQt8LyLmARcCv4mIYRExEfgr8N00/w/gpogYkep7HDgyF0O/FO9+wNlV9vNAYMsU61Gs2APP78+AiBgUEYOByyLiBqAeOCzF8x5wfopnENAttd2gc0RsD5wAnJ6WHQ1sCmwbEUPIknoX4DxgZEQMBy4FzioXeERcFBF1EVHXqXuvKrtoZmZNUfV5xG3ouYiYDSBpLjA+IkLSbGAg0Au4XNLmQABdctuOj4iFadvHgE2AF4D3gdtSmenAZ9P0RsB1qee3JvBcjTEOknQm0BvoAdyVW3dLRCwDHmvoeVewK3BNRCwFXpJ0b5kyzwIfl3QecDtwd4W69pD0PaA70AeYC9ya1t2Ufk4nO34AewEXRsSHABHxL0mDgEHAPalD3Ql4uUr8ZmbWwtpLj3hJbnpZbn4Z2YeFnwD3pd7f/kDXCtsuZfmHiw8iIsosP4+sNzkY+EZJXdWMA76ZtjujSgxqpJ6oujLiTWAoMAE4DriktIykrsAFZD3ZwcDFFeLJ77fKtC1gbuplD4uIwRHxuUbiNzOzFtReEnFjegHz0/ToFqzr8NzyRUDPKvM9gZfTcO5hzWx7EnBwOl/bD9ijtICkvsAaEXEjcCqwXZl4GpLuAkk9gIrnpXPuBo6R1Dm10wd4Elhf0g5pWRdJ2zRv18zMrDlWlUT8c+Bnkh4kGz5dGWOA6yXdDyzILb8VODBdDLUL2fnj76aLujYjS4pTgHvIzlk3x83A08Bs4PfAxDJlBgATJM0g64X/IC0fB1yYli8h6wXPBm4BptXQ9iXAP4FZkmYCh0bE+2RJfGxaNoPy563NzKyVaPnorVlt1uq3efQ7/JyVrmfe2fuufDBmZqsASdMjoq7culWlR2xmZrZaai9XTa9WJA0GrixZvCQiPlVEPGZm1n45EbeC9FWsYUXHYWZm7Z+Hps3MzArkRGxmZlYgJ2IzM7MCORGbmZkVyInYzMysQE7EZmZmBXIiNjMzK5C/R2xNNnhAL+p9e0ozsxbhHrGZmVmBnIjNzMwK5ERsZmZWICdiMzOzAjkRm5mZFciJ2MzMrEBOxGZmZgXy94ityWbPX8jAk29v8Xrn+bvJZtYBuUdsZmZWICdiMzOzAjkRm5mZFciJ2MzMrEBOxGZmZgVyIjYzMyuQE7GZmVmBnIjNzMwK5ERsZmZWICdiMzOzAjkRm5mZFciJ2MzMrEBOxGZmZgVq94lY0kBJcwpqu07Sua1Y/3/2rbG2UtlDWysWMzMrhh+DWEVE1AP17aStgcChwJ/aIh4zM2sb7b5HnHSSdLGkuZLultRN0lGSpkmaKelGSd0BJI2T9HtJ90l6VtJuki6V9LikcQ0VSlosaayk6ZL+Lml7SRPSNl9MZXaXdFuaHpPqaSjz7Vxdp0p6QtI9kq6RdFKlHZE0PMX8MHBcbnm+rd0kzUivRyX1BM4GdknLTkw95PslPZJeO+bqmSDphhTT1ZKU1o2Q9FBqf6qknpI6SfpFOpazJH2jQtxHS6qXVL/03YXN/T2amVmJVSURbw78LiK2Ad4CvgLcFBEjImIo8DhwZK78usCewInArcBvgG2AwZKGpTJrAxMiYjiwCDgT+CxwIPDjCnF8Etgb2B44XVIXSXUpnm2BLwN1jezLZcC3I2KHKmVOAo6LiGHALsB7wMnA/RExLCJ+A7wGfDYitgNGAflh7W2BE4CtgY8DO0laE7gOOD4ds71SvUcCCyNiBDACOErSpqUBRcRFEVEXEXWduvdqZBfNzKxWq8rQ9HMRMSNNTycbph0k6UygN9ADuCtX/taICEmzgVcjYjaApLlp2xnA+8DfUvnZwJKI+CBtM7BCHLdHxBJgiaTXgA2BnYG/RMR7qY1bK+2EpF5A74iYmBZdCXyhTNEHgV9LuprsA8eLqVOb1wU4P32wWApskVs3NSJeTG3OSPuzEHg5IqYBRMTbaf3ngCGSRqZte5F98Hmu0n6YmVnLWVUS8ZLc9FKgGzAOOCAiZkoaDexepvyykm2XsXyfP4iIKC0XEcskVToupXF0Bj6SIasQEI0VioizJd0O7ANMlrRXmWInAq8CQ8lGNv5dQ5zl2hbwrYi4q8w6MzNrZavK0HQ5PYGXJXUBDiswjgeA/SV1ldQD2LdSwYh4C1goaee0qGzckjaLiNkRMZbsAq5Pkg2f98wV60XWw10G/A/QqZE4nwD6SxqR2uiZPnDcBRybjiOStpC0diN1mZlZC1lVesTlnApMAZ4nG1ruWb1464iIaZL+CsxMsdSTDQNXcgRwqaR3WXE4Pe8ESXuQ9WYfA+4k67V/KGkm2WjABcCNkg4C7gPeaSTO9yWNAs6T1I3s/PBewCVkQ9ePpIu6XgcOaGS3zcyshWj56Kw1l6QeEbE4Xbk9CTg6Ih4pOq7Wsla/zaPf4ee0eL3zzq44mGBmtkqTND0iyl7Muyr3iNuTiyRtDXQFLl+dk7CZmbUsJ+IWEBEfueOVpN8BO5Us/m1EXNY2UZmZ2arAibiVRMRxjZcyM7OOblW+atrMzGyV50RsZmZWICdiMzOzAjkRm5mZFciJ2MzMrEBOxGZmZgVyIjYzMyuQv0dsTTZ4QC/qfTtKM7MW4R6xmZlZgZyIzczMCuREbGZmViAnYjMzswI5EZuZmRXIidjMzKxATsRmZmYFciI2MzMrkBOxmZlZgRQRRcdgqxhJi4Ani46jCfoCC4oOookcc9twzG3DMcMmEbF+uRW+xaU1x5MRUVd0ELWSVL8qxQuOua045rbhmKvz0LSZmVmBnIjNzMwK5ERszXFR0QE00aoWLzjmtuKY24ZjrsIXa5mZmRXIPWIzM7MCORGbmZkVyInYypL0eUlPSnpG0sll1kvSuWn9LEnbFRFnSUyNxfxJSQ9LWiLppCJiLFVDzIel4ztL0kOShhYRZ0lMjcX8pRTvDEn1knYuIs6SmKrGnCs3QtJSSSPbMr4KsTR2nHeXtDAd5xmSTisizpKYGj3OKe4ZkuZKmtjWMZaJp7Hj/N3cMZ6T3h99WjSIiPDLrxVeQCfgH8DHgTWBmcDWJWX2Ae4EBHwamLIKxLwBMAI4CzhpFTnOOwLrpukvrCLHuQfLrz8ZAjzR3mPOlbsXuAMY2d5jBnYHbisyzmbE3Bt4DNg4zW/Q3mMuKb8/cG9Lx+EesZWzPfBMRDwbEe8D1wJfKinzJeCKyEwGekvq19aB5jQac0S8FhHTgA+KCLCMWmJ+KCLeTLOTgY3aOMZStcS8ONJ/LWBtoOgrQmt5PwN8C7gReK0tg6ug1pjbk1piPhS4KSL+CdnfZBvHWKqpx/kQ4JqWDsKJ2MoZALyQm38xLWtqmbbU3uKpRVNjPpJsFKJINcUs6UBJTwC3A//bRrFV0mjMkgYABwIXtmFc1dT63thB0kxJd0rapm1Cq6iWmLcA1pU0QdJ0SV9rs+jKq/lvUFJ34PNkH9ZalG9xaeWozLLSXk0tZdpSe4unFjXHLGkPskRc9PnWmmKOiJuBmyXtCvwE2Ku1A6uilpjPAb4fEUulcsXbXC0xP0J2/+LFkvYBbgE2b+3Aqqgl5s7AcOAzQDfgYUmTI+Kp1g6ugqb839gfeDAi/tXSQTgRWzkvAh/LzW8EvNSMMm2pvcVTi5piljQEuAT4QkS80UaxVdKk4xwRkyRtJqlvRBR10/9aYq4Drk1JuC+wj6QPI+KWNonwoxqNOSLezk3fIemCVeA4vwgsiIh3gHckTQKGAkUl4qa8nw+mFYalAV+s5ddHX2Qf0J4FNmX5BQzblJTZlxUv1pra3mPOlR1D+7hYq5bjvDHwDLBj0fE2IeZPsPxire2A+Q3z7TXmkvLjKP5irVqO83/ljvP2wD/b+3EGtgLGp7LdgTnAoPYccyrXC/gXsHZrxOEesX1ERHwo6ZvAXWRXFV4aEXMlHZPWX0h2Zek+ZEniXeCIouJNMTUas6T/AuqBdYBlkk4gu0Ly7Ur1Fh0zcBqwHnBB6q19GAU+xabGmL8CfE3SB8B7wKhI/83accztSo0xjwSOlfQh2XE+uL0f54h4XNLfgFnAMuCSiJjTnmNORQ8E7o6sJ9/ifItLMzOzAvmqaTMzswI5EZuZmRXIidjMzKxATsRmZmYFciI2MzMrkBOxmdVE0nq5p9C8Iml+ml4s6YJWaO+YptwCUdIa6YlgcyTNljRN0qYtHVcNcYyWdH5bt2urLn+P2MxqEtldvYYBSBoDLI6IX7Zie039fu8ooD8wJCKWSdoIaJXvfZq1JPeIzWylpOfL3pamx0i6XNLdkuZJ+rKkn6ce6t8kdUnlhkuamG78f1e5J3eluk5K0xMkjZU0VdJTknYpE0o/4OWIWAYQES9GenKVpM8pexb1I5Kul9QjLR+h7DnPM1PdPSV1lXRZivnRdJ/vhp7uTWk/npb081ysR6S4JgI75ZYflHroM9PtHM0+wonYzFraZmS3QP0ScBVwX0QMJrv7074pGZ9HdhvJ4cClZM+IbkzniNgeOAE4vcz6PwP7p+HyX0naFkBSX+AUYK+I2I7s7mrfkbQmcB1wfEQMJXswxXvAcQAp5kOAyyV1TW0MI+t5DwZGSfpY+hBxBlkC/iywdS6m04C9U/1frGEfrQPy0LSZtbQ7I+IDSbPJbhv4t7R8NjAQ2BIYBNyTbtvZCXi5hnpvSj+np3pWEBEvStoS2DO9xks6iOwpP1sDD6b21gQeTnG8HNkzqmm41amknck+KBART0h6nuzxfQDjI2JhKvcYsAnZQyImRMTrafl1ufIPAuMk/TkXv9kKnIjNrKUtAUjnaT/I3f94Gdn/HAFzI2KH5tQLLKXC/66IWEL2MJI7Jb0KHADcDdwTEYfky6anWpW7x2+15yAuyU3n4yh7r+CIOEbSp8hGCGZIGhbFP0HL2hkPTZtZW3sSWF/SDgCSuqgFHmovaTtJ/dP0GsAQ4HlgMrCTpE+kdd0lbQE8AfSXNCIt7ympMzAJOCwt24LsCVhPVml6CrB7uqq8C3BQLqbNImJKRJwGLGDFR+6ZAe4Rm1kbi4j3JY0EzpXUi+z/0DnA3JWsegPgYklrpfmpwPkR8W9Jo4FrcutOiYinJI0CzpPUjez88F7ABcCFaWj9Q2B0RCxJw9rl9ufldBX5w2RD7I+QDbcD/ELS5mS97PFkj9kzW4GfvmRmZlYgD02bmZkVyInYzMysQE7EZmZmBXIiNjMzK5ATsZmZWYGciM3MzArkRGxmZlag/w9x8q04lKyHcQAAAABJRU5ErkJggg==\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 26.9, 'manhattan_distance': 24.22, 'row_col_out_of_place': 26.24, 'euclidean_distance': 27.0, 'permutation_inversion': 32.44}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n{'hamming_distance': 179.94, 'manhattan_distance': 50.24, 'row_col_out_of_place': 92.98, 'euclidean_distance': 47.84, 'permutation_inversion': 1195.24}\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
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   ],
   "source": [
    "plot_stats(stats,(3,3),'GBF')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
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    "## Interpretation of performance, admissibility, and informativeness (i.e how optimal is the search path)\n",
    "\n",
    "At first look, both heuristics that we implemented are reasonably good. When looking at the charts, good means a smaller bar i.e. smaller execution time, cost, and search path. Both heuristics have a satisfactory combination of all three metrics. If you look at the bar chart for the average cost of A\\* you will find that euclidean distance clearly has an average cost <= to manhattan and hamming distances (in theory, they should be exactly equal). This reinforces our intuition that it is an admissible heurisitic. \"Row and Column\" heuristic seems to have a very slightly higher average cost but the difference is so small that we think it could be caused by slight numerical instabilities more so than anything. After all we know that hamming and manhattan are both admissible yet they don't have the exact same average cost (even though they should in theory). All in all one could safely assume that both of our heuristics are admissible (or at least very very close to being admissible).\n",
    "\n",
    "Looking at runtime alone is not sufficient for understanding a heuristic. If two heuristics have the same runtime but the first one visits many more nodes, it means that the first heuristic is probably faster to compute but less informative. If two heuristics visit the same number of nodes but one of them is way faster than you can conclude that they have the same informativeness but one is simply faster to compute.\n",
    "\n",
    "We found that heuristics can perform differently depending on the algorithm. For example, look at how permutation inversion and hamming distance perform on A\\* vs GBF. On A\\*, hamming visits an order of magnitude more nodes than permutation whereas the exact opposite happens on GBF. Remember that A\\* uses F(n) = G(n) + H(n) where G is the cost and H is the heuristic whereas GBF only looks at the value of H(n) to decide on the next state explored. The data suggests that hamming is a bad heuristic to tie break between two states that have a similar cost. On the other hand, hamming seems to be a great heuristic when used as the sole search criterion. The exact opposite happens with permutation inversion. As a stand-alone, it's a bad search criteria but when used to tie-break between nodes that have similar costs, it cuts a large amount of the search space.\n",
    "\n",
    "All in all, heuristics are a subtle science. Crafting a useful heuristic function is a little bit of science and a little bit of art because it is dependant on your domain. Remember that there does not exist a perfect heuristic. If it did we would not need state-space search to begin with!"
   ]
  }
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