RushHourProject.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "shitotProject.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "1LpiFXxOcBa2",
        "9GiUIQeicH5A",
        "f2XHPXGCcMOD",
        "wMNhUG4bpttB",
        "3uqtNn32pwtE",
        "OFjUJ7SIp8UY",
        "ZlzdpsZHqOYP",
        "CYz8o8HSqd0i"
      ]
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Implementation"
      ],
      "metadata": {
        "id": "1LpiFXxOcBa2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\"\"\"\n",
        "This module defines the Board and Car classes for the rush-hour game\n",
        "The Car class serve more to store car data and logic involving possible\n",
        "moves of car in the board is defined in the Board class\n",
        "\"\"\"\n",
        "from copy import deepcopy\n",
        "from collections import defaultdict\n",
        "import pdb\n",
        "\n",
        "\n",
        "class Orientation(object):\n",
        "    \"\"\" Direction of the car\"\"\"\n",
        "    HORIZONTAL = 0\n",
        "    VERTICAL = 1\n",
        "\n",
        "\n",
        "class Car(object):\n",
        "    \"\"\"Car Class for the Rushhour game\n",
        "    Attributes:\n",
        "        name: character\n",
        "        coord: Coordinate of the car in the board\n",
        "        length: length of the car (e.g space occupiying the board)\n",
        "        orientation: horizontal or vertical alighment\n",
        "        is_red_car: the car to be freed\n",
        "    \"\"\"\n",
        "\n",
        "    def __init__(self, name, coord, length, orientation, is_red_car=None):\n",
        "        self.name = name\n",
        "        self.coord = coord\n",
        "        self.length = length - 1 \n",
        "        self.orientation = orientation\n",
        "        self.is_red_car = is_red_car\n",
        "\n",
        "    def __eq__(self, other):\n",
        "        return self.__dict__ == other.__dict__\n",
        "\n",
        "    def __str__(self):\n",
        "        return str(self.__dict__)\n",
        "\n",
        "    def __ne__(self, other):\n",
        "        return not self.__eq__(other)\n",
        "\n",
        "    def __hash__(self):\n",
        "        return hash(self.__repr__())\n",
        "\n",
        "    def __repr__(self):\n",
        "        if self.orientation == Orientation.HORIZONTAL:\n",
        "            other_coord = {'x': self.coord['x'] + self.length,\n",
        "                           'y': self.coord['y']}\n",
        "            return \"{} [{},{}]\".format(self.name, self.coord, other_coord)\n",
        "        else:\n",
        "            other_coord = {'x': self.coord[\n",
        "                'x'], 'y': self.coord['y'] + self.length}\n",
        "            return \"{} [{},{}]\".format(self.name, self.coord, other_coord)\n",
        "    \n",
        "\n",
        "    def move(self, direction, distance):\n",
        "        \"\"\"Given the direction and distance, move the car according to it\n",
        "        \"\"\"\n",
        "        if direction == 'up':\n",
        "            self.coord['y'] -= distance\n",
        "\n",
        "        if direction == 'down':\n",
        "            self.coord['y'] += distance\n",
        "\n",
        "        if direction == 'left':\n",
        "            self.coord['x'] -= distance\n",
        "\n",
        "        if direction == 'right':\n",
        "            self.coord['x'] += distance\n",
        "\n",
        "    @staticmethod\n",
        "    def createFromBoardInfo(name, coords):\n",
        "        def plane(coords):\n",
        "            if coords[0]['x'] != coords[1]['x'] and coords[0]['y'] == coords[1]['y']:\n",
        "                return Orientation.HORIZONTAL\n",
        "            else:\n",
        "                return Orientation.VERTICAL\n",
        "        return Car(name, coords[0], len(coords), plane(coords), is_red_car=(name == 'r'))\n",
        "\n",
        "\n",
        "class Board(object):\n",
        "    \"\"\"Board Class for setting up the playing board\n",
        "    Attributes:\n",
        "        cars: list of cars on the play board\n",
        "        size: size of the board\n",
        "    \"\"\"\n",
        "\n",
        "    def __init__(self, cars, width=6, height=6):\n",
        "        self.size = {'x': height, 'y': width}\n",
        "        self.cars = cars\n",
        "        self.depth = 0\n",
        "        self.hval = 0\n",
        "\n",
        "    def __eq__(self, other):\n",
        "        return self.cars == other.other\n",
        "\n",
        "    def __str__(self):\n",
        "        return str(self.__dict__)\n",
        "\n",
        "    def __ne__(self, other):\n",
        "        return not self.__eq__(other)\n",
        "\n",
        "    def __hash__(self):\n",
        "        return hash(self.__repr__())\n",
        "\n",
        "    @staticmethod\n",
        "    def readFromfile(filename):\n",
        "        \"\"\"Reads a puzzle from a file and creates a new board instance, identifies the red car and board dimensions \"\"\"\n",
        "        def get_coord(row_idx):\n",
        "            def result(tup):\n",
        "                return (tup[1], {'y': row_idx, 'x': tup[0]})\n",
        "            return result\n",
        "\n",
        "        def flatten(l):\n",
        "            return [item for sublist in l for item in sublist]\n",
        "\n",
        "        puzzle_file = open(filename, 'r')\n",
        "        raw_board = [list(line.strip()) for line in puzzle_file]\n",
        "        coords_board = [map(get_coord(row_idx), enumerate(row))\n",
        "                        for row_idx, row in enumerate(raw_board)]\n",
        "        cars_board = flatten([filter(lambda t: t[0].isalpha(), list(row))\n",
        "                              for row in list(coords_board)])\n",
        "        raw_cars = defaultdict(list)\n",
        "        for (k, v) in cars_board:\n",
        "            raw_cars[k].append(v)\n",
        "        cars = []\n",
        "        for i in raw_cars:\n",
        "            cars.append(Car.createFromBoardInfo(i, raw_cars[i]))\n",
        "        return Board(cars, len(raw_board), len(raw_board[0]))\n",
        "\n",
        "    def explore_moves(self):\n",
        "        \"\"\"Explore the state space of possible moves for a single car, this also checks whether we bump into a car or a wall\"\"\"\n",
        "        board = self.game_board(self.cars)\n",
        "        for car in self.cars:\n",
        "            if car.orientation == Orientation.VERTICAL:\n",
        "                # UP\n",
        "                if car.coord['y'] - 1 >= 0 and board[car.coord['y'] - 1][car.coord['x']] == '.':\n",
        "                    new_cars = deepcopy(self.cars)\n",
        "                    new_car = [x for x in new_cars if x.name == car.name][0]\n",
        "                    new_car.coord['y'] -= 1\n",
        "                    yield [[[car.name, 'up']], Board(new_cars)]\n",
        "                # DOWN\n",
        "                if car.coord['y'] + car.length + 1 <= (self.size['x'] - 1) and board[car.coord['y'] + car.length + 1][car.coord['x']] == '.':\n",
        "                    new_cars = deepcopy(self.cars)\n",
        "                    new_car = [x for x in new_cars if x.name == car.name][0]\n",
        "                    new_car.coord['y'] += 1\n",
        "                    yield [[[car.name, 'down']], Board(new_cars)]\n",
        "            else:\n",
        "                # LEFT\n",
        "                if car.coord['x'] - 1 >= 0 and board[car.coord['y']][car.coord['x'] - 1] == '.':\n",
        "                    new_cars = deepcopy(self.cars)\n",
        "                    new_car = [x for x in new_cars if x.name == car.name][0]\n",
        "                    new_car.coord['x'] -= 1\n",
        "                    yield [[[car.name, 'left']], Board(new_cars)]\n",
        "                # RIGHT\n",
        "                if car.coord['x'] + car.length + 1 <= (self.size['y'] - 1) and board[car.coord['y']][car.coord['x'] + car.length + 1] == '.':\n",
        "                    new_cars = deepcopy(self.cars)\n",
        "                    new_car = [x for x in new_cars if x.name == car.name][0]\n",
        "                    new_car.coord['x'] += 1\n",
        "                    yield [[[car.name, 'right']], Board(new_cars)]\n",
        "\n",
        "    def game_board(self, cars):\n",
        "        \"\"\"Given a set of cars, create a 2D array of the puzzle\"\"\"\n",
        "        board = [['.' for col in range(self.size['x'])]\n",
        "                 for row in range(self.size['y'])]\n",
        "        for car in cars:\n",
        "            if car.orientation == Orientation.HORIZONTAL:\n",
        "                x_start = car.coord['x']\n",
        "                x_stop = car.coord['x'] + car.length\n",
        "                for x in range(x_start, x_stop + 1):\n",
        "                    board[car.coord['y']][x] = car.name\n",
        "            else:\n",
        "                y_start = car.coord['y']\n",
        "                y_stop = car.coord['y'] + car.length\n",
        "                for y in range(y_start, y_stop + 1):\n",
        "                    board[y][car.coord['x']] = car.name\n",
        "        return board\n",
        "\n",
        "    def prettify(self, cars):\n",
        "        \"\"\"Printable version that represents the 2D array of the puzzle\"\"\"\n",
        "        board = self.game_board(cars)\n",
        "        output = ''\n",
        "        for line in board:\n",
        "            output += \" \".join(line) + '\\n'\n",
        "        return output\n",
        "\n",
        "    def is_solved(self):\n",
        "        \"\"\"Check if the red_car is free\"\"\"\n",
        "        red_car = [car for car in self.cars if car.is_red_car][0]\n",
        "        return red_car.coord['x'] + red_car.length == self.size['x'] - 1"
      ],
      "metadata": {
        "id": "ZuE2hFXu-tDK"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import heapq\n",
        "from copy import deepcopy\n",
        "\n",
        "\n",
        "class PriorityQueue:\n",
        "    \"\"\"A simple version of a Priority Queue, that allows to give a priority value to an element\"\"\"\n",
        "\n",
        "    def __init__(self):\n",
        "        self._queue = []\n",
        "        self._dictq = {}\n",
        "        self._index = 0\n",
        "\n",
        "    def push(self, item, priority):\n",
        "        heapq.heappush(self._queue, (priority, self._index, item))\n",
        "        self._dictq[hash(str(item[1]))] = priority\n",
        "        self._index += 1\n",
        "\n",
        "    def empty(self):\n",
        "        return len(self._queue) == 0\n",
        "\n",
        "    def pop(self):\n",
        "        return heapq.heappop(self._queue)[-1]\n",
        "    \n",
        "\n",
        "class NotSolvable(Exception):\n",
        "    pass\n",
        "\n",
        "class ZeroHeuristic:\n",
        "    \"\"\"Zero Heuristcs, same as a BFS search\"\"\"\n",
        "\n",
        "    def calculate(self, board):\n",
        "        return 0\n",
        "\n",
        "    def __repr__(self):\n",
        "        return 'ZeroHeuristic'\n",
        "\n",
        "\n",
        "class BlockingCarsHeuristic:\n",
        "    \"\"\"Calculate number of cars blocking the way plus distance\"\"\"\n",
        "\n",
        "    def calculate(self, board):\n",
        "        red_car = [\n",
        "            car for car in board.cars if car.is_red_car][0]\n",
        "        if red_car.coord['x'] == 4:\n",
        "            return 0\n",
        "\n",
        "        dist = 5 - (red_car.coord['x'] + 1)\n",
        "\n",
        "        blockingcars = 0\n",
        "        for car in board.cars:\n",
        "            if (car.orientation == Orientation.VERTICAL \n",
        "                and car.coord['x'] >= (red_car.coord['x'] + red_car.length) \n",
        "                and (car.coord['y'] <= red_car.coord['y'] and car.coord['y'] + car.length >= red_car.coord['y'])\n",
        "                ):\n",
        "                blockingcars += 1\n",
        "\n",
        "        return blockingcars + dist\n",
        "\n",
        "    def __repr__(self):\n",
        "        return 'BlockingCarsHeuristic'\n",
        "\n",
        "class BlockingBlockingCarsHeuristic:\n",
        "    \"\"\"Calculate number of cars blocking the way plus distance plus cars blocking the blocking cars\"\"\"\n",
        "\n",
        "    def calculate(self, board):\n",
        "        red_car = [\n",
        "            car for car in board.cars if car.is_red_car][0]\n",
        "        if red_car.coord['x'] == 4:\n",
        "            return 0\n",
        "\n",
        "        dist = 5 - (red_car.coord['x'] + 1)\n",
        "\n",
        "        blockingcars = 0\n",
        "        blockingBlocking = 0\n",
        "        for car in board.cars:\n",
        "            if (car.orientation == Orientation.VERTICAL \n",
        "                and car.coord['x'] >= (red_car.coord['x'] + red_car.length) \n",
        "                and (car.coord['y'] <= red_car.coord['y'] and car.coord['y'] + car.length >= red_car.coord['y'])\n",
        "                ):\n",
        "                blockingcars += 1\n",
        "                for car2 in board.cars:\n",
        "                  if (car2.orientation == Orientation.VERTICAL \n",
        "                      and car2.coord['x'] == car.coord['x'] \n",
        "                      and (car2.coord['y'] + car2.length == car.coord['y'] - 1 or car2.coord['y'] == car.coord['y'] + car.length + 1)\n",
        "                      ):\n",
        "                    blockingBlocking += 1\n",
        "                  if (car2.orientation == Orientation.HORIZONTAL \n",
        "                      and (car.coord['x'] >= car2.coord['x'] and car.coord['x'] <= car2.coord['x'] + car2.length) \n",
        "                      and (car2.coord['y'] == car.coord['y'] - 1 or car2.coord['y'] == car.coord['y'] + car.length + 1)\n",
        "                      ):\n",
        "                    blockingBlocking += 1\n",
        "\n",
        "        return blockingcars + dist + blockingBlocking\n",
        "\n",
        "    def __repr__(self):\n",
        "        return 'BlockingBlockingCarsHeuristic'\n",
        "\n",
        "\n",
        "class Solver(object):\n",
        "    \"\"\"The Solver class takes as input the board to be solved\n",
        "        Attributes:\n",
        "        board: the initial config of the puzzle\n",
        "        hfn: heuristic_function\n",
        "    \"\"\"\n",
        "\n",
        "    def __init__(self, board, hfn):\n",
        "        self.board = board\n",
        "        self.hfn = hfn\n",
        "        self.visited = 0\n",
        "        self.generated = 0\n",
        "        self.path = []\n",
        "        self.path_dict = {}\n",
        "        self.dup = {}\n",
        "\n",
        "    def solve(self):\n",
        "        frontier = PriorityQueue()\n",
        "        board = self.board\n",
        "        closed_set = set()\n",
        "        frontier.push([[], board], 0)\n",
        "        g = {}\n",
        "        g[hash(str(board))] = 0\n",
        "        while not frontier.empty():\n",
        "            moves, board = frontier.pop()\n",
        "            frontier._dictq.pop(hash(str(board)))\n",
        "\n",
        "            if board.is_solved():\n",
        "                return (moves, len(closed_set), len(frontier._queue))\n",
        "            \n",
        "            closed_set.add(hash(str(board)))\n",
        "\n",
        "            for new_moves, new_boards in board.explore_moves():\n",
        "                new_g = g[hash(str(board))] + 1\n",
        "                # f = g(u) + h(u)\n",
        "                priority = new_g + self.hfn.calculate(new_boards)\n",
        "                if hash(str(new_boards)) in frontier._dictq or new_boards in closed_set:\n",
        "                    if new_g >= g[hash(str(new_boards))]:\n",
        "                      continue\n",
        "                    else:\n",
        "                        closed_set.remove(hash(str(new_boards)))\n",
        "\n",
        "                frontier.push([moves + new_moves, new_boards], priority)\n",
        "                g[hash(str(new_boards))] = new_g\n",
        "\n",
        "        raise NotSolvable('Not able to solve!')\n",
        "\n",
        "\n",
        "    def solveIDA(self):\n",
        "      threshold = self.hfn.calculate(self.board)\n",
        "      self.path.append([[], self.board])\n",
        "      self.path_dict[hash(str(self.board))] = threshold\n",
        "      self.dup[hash(str(self.board))] = 0\n",
        "      g = {}\n",
        "      g[hash(str(self.board))] = 0\n",
        "\n",
        "      def IDArec(curThreshold):\n",
        "        moves, board = self.path[-1:][0]\n",
        "        priority = g[hash(str(board))] + self.hfn.calculate(board)\n",
        "        min = float(\"inf\")\n",
        "\n",
        "        if priority > curThreshold:\n",
        "          return priority\n",
        "\n",
        "        self.visited += 1\n",
        "        self.dup[hash(str(board))] += 1\n",
        "\n",
        "        if board.is_solved():\n",
        "          return (moves, self.visited, self.generated, self.dup)\n",
        "\n",
        "        for new_moves, new_boards in board.explore_moves():      \n",
        "          if hash(str(new_boards)) not in self.path_dict:\n",
        "            new_g = g[hash(str(board))] + 1\n",
        "            g[hash(str(new_boards))] = new_g\n",
        "            new_priority = new_g + self.hfn.calculate(new_boards)\n",
        "            if hash(str(new_boards)) not in self.dup: self.dup[hash(str(new_boards))] = 0\n",
        "            self.generated += 1\n",
        "            self.path.append([moves + new_moves, new_boards])\n",
        "            self.path_dict[hash(str(new_boards))] = new_priority\n",
        "            t = IDArec(curThreshold)\n",
        "            if isinstance(t, tuple):\n",
        "              return t\n",
        "            elif t < min:\n",
        "                min = t\n",
        "            del self.path[-1]\n",
        "            self.path_dict.pop(hash(str(new_boards)))\n",
        "\n",
        "        return min\n",
        "\n",
        "      while True:\n",
        "        t = IDArec(threshold)\n",
        "        if isinstance(t, tuple):\n",
        "          self.path = []\n",
        "          self.path_dict = {}\n",
        "          self.visited = 0\n",
        "          self.generated = 0\n",
        "          self.dup = {}\n",
        "          return (t[0], t[1], t[2], t[3])\n",
        "        if t == float(\"inf\"):\n",
        "          raise NotSolvable('Not able to solve!') \n",
        "        else:\n",
        "          threshold = t\n",
        "\n",
        "\n",
        "    def solution(self, board, moves):\n",
        "        \"\"\"Format the steps and provide a step-by-step guide to solve the puzzle\"\"\"\n",
        "        output = ''\n",
        "        output += \"; \".join([\"{} {}\".format(move[0], move[1]) for move in moves])\n",
        "        cars = deepcopy(board.cars)\n",
        "        for move in moves:\n",
        "            car = [x for x in cars if x.name == move[0]][0]\n",
        "            output += '\\nMOVE {} {}\\n'.format(move[0], move[1])\n",
        "            car.move(move[1], 1)\n",
        "            output += self.board.prettify(cars)\n",
        "        return output\n",
        "\n",
        "    def solutionMoves(self, moves):\n",
        "      output = ''\n",
        "      output += \"; \".join([\"{} {}\".format(move[0], move[1]) for move in moves])\n",
        "      return output"
      ],
      "metadata": {
        "id": "35n59Acs-r_F"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Tests"
      ],
      "metadata": {
        "id": "9GiUIQeicH5A"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import time\n",
        "\n",
        "b = Board.readFromfile('p1.txt')\n",
        "print(b.prettify(b.cars))\n",
        "astar1 = Solver(b, BlockingCarsHeuristic())\n",
        "IDAstar1 = Solver(b, BlockingCarsHeuristic())\n",
        "astar2 = Solver(b, BlockingBlockingCarsHeuristic())\n",
        "IDAstar2 = Solver(b, BlockingBlockingCarsHeuristic())\n",
        "\n",
        "start_astar1 = time.time()\n",
        "moves_astar1, closed_astar1, open_astar1 = astar1.solve()\n",
        "end_astar1 = time.time()\n",
        "\n",
        "print(f\"A* BCars - num of moves: {len(moves_astar1)}, num of nodes passes: {closed_astar1}, num of nodes gen: {open_astar1 + closed_astar1}, time: {end_astar1 - start_astar1}\")\n",
        "print(astar1.solutionMoves(moves_astar1))\n",
        "\n",
        "start_astar2 = time.time()\n",
        "moves_astar2, closed_astar2, open_astar2 = astar2.solve()\n",
        "end_astar2 = time.time()\n",
        "\n",
        "print(f\"A* BBCars - num of moves: {len(moves_astar2)}, num of nodes passes: {closed_astar2}, num of nodes gen: {open_astar2 + closed_astar2}, time: {end_astar2 - start_astar2}\")\n",
        "print(astar2.solutionMoves(moves_astar2))\n",
        "\n",
        "start_IDAstar1 = time.time()\n",
        "moves_IDAstar1, visited_IDAstar1, generated_IDAstar1, dup_IDAstar1 = IDAstar1.solveIDA()\n",
        "end_IDAstar1 = time.time()\n",
        "\n",
        "dup_IDAstar1_num = 0\n",
        "for key,val in dup_IDAstar1.items():\n",
        "  if val > 1: dup_IDAstar1_num += (val - 1)\n",
        "\n",
        "print(f\"IDA* BCars - num of moves: {len(moves_IDAstar1)}, num of nodes passes: {visited_IDAstar1}, num of nodes gen: {generated_IDAstar1}, duplicates passes: {dup_IDAstar1_num}, time: {end_IDAstar1 - start_IDAstar1}\")\n",
        "print(IDAstar1.solutionMoves(moves_IDAstar1))\n",
        "\n",
        "start_IDAstar2 = time.time()\n",
        "moves_IDAstar2, visited_IDAstar2, generated_IDAstar2, dup_IDAstar2 = IDAstar2.solveIDA()\n",
        "end_IDAstar2 = time.time()\n",
        "\n",
        "dup_IDAstar2_num = 0\n",
        "for key,val in dup_IDAstar2.items():\n",
        "  if val > 1: dup_IDAstar2_num += (val - 1)\n",
        "\n",
        "print(f\"IDA* BBCars - num of moves: {len(moves_IDAstar2)}, num of nodes passes: {visited_IDAstar2}, num of nodes gen: {generated_IDAstar2}, duplicates passes: {dup_IDAstar2_num}, time: {end_IDAstar2 - start_IDAstar2}\")\n",
        "print(IDAstar2.solutionMoves(moves_IDAstar2))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jtOwGTCp-q3H",
        "outputId": "b22f7c67-2d6e-4ed7-c25a-17dc09a08bb8"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            ". . A A . O\n",
            ". . . . . O\n",
            ". . . r r O\n",
            "B . . . . .\n",
            "B X X X . .\n",
            ". . . . . .\n",
            "\n",
            "A* BCars - num of moves: 4, num of nodes passes: 27, num of nodes gen: 102, time: 0.03453636169433594\n",
            "O down; O down; O down; r right\n",
            "A* BBCars - num of moves: 4, num of nodes passes: 27, num of nodes gen: 102, time: 0.035491943359375\n",
            "O down; O down; O down; r right\n",
            "IDA* BCars - num of moves: 4, num of nodes passes: 26, num of nodes gen: 143, duplicates passes: 7, time: 0.03542470932006836\n",
            "O down; O down; O down; r right\n",
            "IDA* BBCars - num of moves: 4, num of nodes passes: 26, num of nodes gen: 143, duplicates passes: 7, time: 0.050110578536987305\n",
            "O down; O down; O down; r right\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b = Board.readFromfile('p2.txt')\n",
        "print(b.prettify(b.cars))\n",
        "astar1 = Solver(b, BlockingCarsHeuristic())\n",
        "IDAstar1 = Solver(b, BlockingCarsHeuristic())\n",
        "astar2 = Solver(b, BlockingBlockingCarsHeuristic())\n",
        "IDAstar2 = Solver(b, BlockingBlockingCarsHeuristic())\n",
        "\n",
        "start_astar1 = time.time()\n",
        "moves_astar1, closed_astar1, open_astar1 = astar1.solve()\n",
        "end_astar1 = time.time()\n",
        "\n",
        "print(f\"A* BCars - num of moves: {len(moves_astar1)}, num of nodes passes: {closed_astar1}, num of nodes gen: {open_astar1 + closed_astar1}, time: {end_astar1 - start_astar1}\")\n",
        "print(astar1.solutionMoves(moves_astar1))\n",
        "\n",
        "start_astar2 = time.time()\n",
        "moves_astar2, closed_astar2, open_astar2 = astar2.solve()\n",
        "end_astar2 = time.time()\n",
        "\n",
        "print(f\"A* BBCars - num of moves: {len(moves_astar2)}, num of nodes passes: {closed_astar2}, num of nodes gen: {open_astar2 + closed_astar2}, time: {end_astar2 - start_astar2}\")\n",
        "print(astar2.solutionMoves(moves_astar2))\n",
        "\n",
        "start_IDAstar1 = time.time()\n",
        "moves_IDAstar1, visited_IDAstar1, generated_IDAstar1, dup_IDAstar1 = IDAstar1.solveIDA()\n",
        "end_IDAstar1 = time.time()\n",
        "\n",
        "dup_IDAstar1_num = 0\n",
        "for key,val in dup_IDAstar1.items():\n",
        "  if val > 1: dup_IDAstar1_num += (val - 1)\n",
        "\n",
        "print(f\"IDA* BCars - num of moves: {len(moves_IDAstar1)}, num of nodes passes: {visited_IDAstar1}, num of nodes gen: {generated_IDAstar1}, duplicates passes: {dup_IDAstar1_num}, time: {end_IDAstar1 - start_IDAstar1}\")\n",
        "print(IDAstar1.solutionMoves(moves_IDAstar1))\n",
        "\n",
        "start_IDAstar2 = time.time()\n",
        "moves_IDAstar2, visited_IDAstar2, generated_IDAstar2, dup_IDAstar2 = IDAstar2.solveIDA()\n",
        "end_IDAstar2 = time.time()\n",
        "\n",
        "dup_IDAstar2_num = 0\n",
        "for key,val in dup_IDAstar2.items():\n",
        "  if val > 1: dup_IDAstar2_num += (val - 1)\n",
        "\n",
        "print(f\"IDA* BBCars - num of moves: {len(moves_IDAstar2)}, num of nodes passes: {visited_IDAstar2}, num of nodes gen: {generated_IDAstar2}, duplicates passes: {dup_IDAstar2_num}, time: {end_IDAstar2 - start_IDAstar2}\")\n",
        "print(IDAstar2.solutionMoves(moves_IDAstar2))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FxUXlfKi4d_a",
        "outputId": "ea67ebe6-2096-4004-b2f0-1e193c87742d"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            ". . . . A A\n",
            ". . . C C O\n",
            ". r r . Q O\n",
            ". . . . Q O\n",
            ". . . . Q .\n",
            ". . X X X .\n",
            "\n",
            "A* BCars - num of moves: 7, num of nodes passes: 71, num of nodes gen: 281, time: 0.11063313484191895\n",
            "r right; X left; Q down; r right; O down; O down; r right\n",
            "A* BBCars - num of moves: 7, num of nodes passes: 18, num of nodes gen: 107, time: 0.028548479080200195\n",
            "X left; Q down; O down; O down; r right; r right; r right\n",
            "IDA* BCars - num of moves: 7, num of nodes passes: 126, num of nodes gen: 814, duplicates passes: 69, time: 0.23008060455322266\n",
            "O down; O down; r right; X left; Q down; r right; r right\n",
            "IDA* BBCars - num of moves: 8, num of nodes passes: 34, num of nodes gen: 250, duplicates passes: 14, time: 0.0709383487701416\n",
            "A left; r right; X left; Q down; O down; O down; r right; r right\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b = Board.readFromfile('p3.txt')\n",
        "print(b.prettify(b.cars))\n",
        "astar1 = Solver(b, BlockingCarsHeuristic())\n",
        "IDAstar1 = Solver(b, BlockingCarsHeuristic())\n",
        "astar2 = Solver(b, BlockingBlockingCarsHeuristic())\n",
        "IDAstar2 = Solver(b, BlockingBlockingCarsHeuristic())\n",
        "\n",
        "start_astar1 = time.time()\n",
        "moves_astar1, closed_astar1, open_astar1 = astar1.solve()\n",
        "end_astar1 = time.time()\n",
        "\n",
        "print(f\"A* BCars - num of moves: {len(moves_astar1)}, num of nodes passes: {closed_astar1}, num of nodes gen: {open_astar1 + closed_astar1}, time: {end_astar1 - start_astar1}\")\n",
        "print(astar1.solutionMoves(moves_astar1))\n",
        "\n",
        "start_astar2 = time.time()\n",
        "moves_astar2, closed_astar2, open_astar2 = astar2.solve()\n",
        "end_astar2 = time.time()\n",
        "\n",
        "print(f\"A* BBCars - num of moves: {len(moves_astar2)}, num of nodes passes: {closed_astar2}, num of nodes gen: {open_astar2 + closed_astar2}, time: {end_astar2 - start_astar2}\")\n",
        "print(astar2.solutionMoves(moves_astar2))\n",
        "\n",
        "start_IDAstar1 = time.time()\n",
        "moves_IDAstar1, visited_IDAstar1, generated_IDAstar1, dup_IDAstar1 = IDAstar1.solveIDA()\n",
        "end_IDAstar1 = time.time()\n",
        "\n",
        "dup_IDAstar1_num = 0\n",
        "for key,val in dup_IDAstar1.items():\n",
        "  if val > 1: dup_IDAstar1_num += (val - 1)\n",
        "\n",
        "print(f\"IDA* BCars - num of moves: {len(moves_IDAstar1)}, num of nodes passes: {visited_IDAstar1}, num of nodes gen: {generated_IDAstar1}, duplicates passes: {dup_IDAstar1_num}, time: {end_IDAstar1 - start_IDAstar1}\")\n",
        "print(IDAstar1.solutionMoves(moves_IDAstar1))\n",
        "\n",
        "start_IDAstar2 = time.time()\n",
        "moves_IDAstar2, visited_IDAstar2, generated_IDAstar2, dup_IDAstar2 = IDAstar2.solveIDA()\n",
        "end_IDAstar2 = time.time()\n",
        "\n",
        "dup_IDAstar2_num = 0\n",
        "for key,val in dup_IDAstar2.items():\n",
        "  if val > 1: dup_IDAstar2_num += (val - 1)\n",
        "\n",
        "print(f\"IDA* BBCars - num of moves: {len(moves_IDAstar2)}, num of nodes passes: {visited_IDAstar2}, num of nodes gen: {generated_IDAstar2}, duplicates passes: {dup_IDAstar2_num}, time: {end_IDAstar2 - start_IDAstar2}\")\n",
        "print(IDAstar2.solutionMoves(moves_IDAstar2))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y5hvOkei4c6S",
        "outputId": "b512dafc-4862-4684-c29d-08a691213e6e"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            ". . . . . O\n",
            ". . . Q . O\n",
            ". r r Q . O\n",
            ". . . Q . .\n",
            "B X X X . .\n",
            "B . . . . .\n",
            "\n",
            "A* BCars - num of moves: 11, num of nodes passes: 170, num of nodes gen: 334, time: 0.25678372383117676\n",
            "B up; B up; X left; Q down; Q down; r right; r right; O down; O down; O down; r right\n",
            "A* BBCars - num of moves: 11, num of nodes passes: 155, num of nodes gen: 334, time: 0.2231903076171875\n",
            "B up; B up; X left; Q down; Q down; r right; r right; O down; O down; O down; r right\n",
            "IDA* BCars - num of moves: 11, num of nodes passes: 3987, num of nodes gen: 19336, duplicates passes: 3853, time: 4.8596673011779785\n",
            "O down; O down; O down; B up; B up; X left; Q down; Q down; r right; r right; r right\n",
            "IDA* BBCars - num of moves: 11, num of nodes passes: 2338, num of nodes gen: 11463, duplicates passes: 2222, time: 2.9450652599334717\n",
            "O down; O down; O down; B up; B up; X left; Q down; Q down; r right; r right; r right\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b = Board.readFromfile('p4.txt')\n",
        "print(b.prettify(b.cars))\n",
        "astar1 = Solver(b, BlockingCarsHeuristic())\n",
        "IDAstar1 = Solver(b, BlockingCarsHeuristic())\n",
        "astar2 = Solver(b, BlockingBlockingCarsHeuristic())\n",
        "IDAstar2 = Solver(b, BlockingBlockingCarsHeuristic())\n",
        "\n",
        "start_astar1 = time.time()\n",
        "moves_astar1, closed_astar1, open_astar1 = astar1.solve()\n",
        "end_astar1 = time.time()\n",
        "\n",
        "print(f\"A* BCars - num of moves: {len(moves_astar1)}, num of nodes passes: {closed_astar1}, num of nodes gen: {open_astar1 + closed_astar1}, time: {end_astar1 - start_astar1}\")\n",
        "print(astar1.solutionMoves(moves_astar1))\n",
        "\n",
        "start_astar2 = time.time()\n",
        "moves_astar2, closed_astar2, open_astar2 = astar2.solve()\n",
        "end_astar2 = time.time()\n",
        "\n",
        "print(f\"A* BBCars - num of moves: {len(moves_astar2)}, num of nodes passes: {closed_astar2}, num of nodes gen: {open_astar2 + closed_astar2}, time: {end_astar2 - start_astar2}\")\n",
        "print(astar2.solutionMoves(moves_astar2))\n",
        "\n",
        "start_IDAstar1 = time.time()\n",
        "moves_IDAstar1, visited_IDAstar1, generated_IDAstar1, dup_IDAstar1 = IDAstar1.solveIDA()\n",
        "end_IDAstar1 = time.time()\n",
        "\n",
        "dup_IDAstar1_num = 0\n",
        "for key,val in dup_IDAstar1.items():\n",
        "  if val > 1: dup_IDAstar1_num += (val - 1)\n",
        "\n",
        "print(f\"IDA* BCars - num of moves: {len(moves_IDAstar1)}, num of nodes passes: {visited_IDAstar1}, num of nodes gen: {generated_IDAstar1}, duplicates passes: {dup_IDAstar1_num}, time: {end_IDAstar1 - start_IDAstar1}\")\n",
        "print(IDAstar1.solutionMoves(moves_IDAstar1))\n",
        "\n",
        "start_IDAstar2 = time.time()\n",
        "moves_IDAstar2, visited_IDAstar2, generated_IDAstar2, dup_IDAstar2 = IDAstar2.solveIDA()\n",
        "end_IDAstar2 = time.time()\n",
        "\n",
        "dup_IDAstar2_num = 0\n",
        "for key,val in dup_IDAstar2.items():\n",
        "  if val > 1: dup_IDAstar2_num += (val - 1)\n",
        "\n",
        "print(f\"IDA* BBCars - num of moves: {len(moves_IDAstar2)}, num of nodes passes: {visited_IDAstar2}, num of nodes gen: {generated_IDAstar2}, duplicates passes: {dup_IDAstar2_num}, time: {end_IDAstar2 - start_IDAstar2}\")\n",
        "print(IDAstar2.solutionMoves(moves_IDAstar2))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NIFcX4KZjMcu",
        "outputId": "fa238090-9b58-47c5-fcad-1d43e90e830c"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            ". . A A P .\n",
            ". . . Q P .\n",
            ". r r Q P .\n",
            ". . . Q C C\n",
            ". X X X . .\n",
            ". . . . . .\n",
            "\n",
            "A* BCars - num of moves: 15, num of nodes passes: 336, num of nodes gen: 719, time: 0.8422539234161377\n",
            "A left; Q up; C left; C left; C left; Q down; X left; Q down; Q down; r right; P down; P down; P down; r right; r right\n",
            "A* BBCars - num of moves: 15, num of nodes passes: 283, num of nodes gen: 666, time: 0.6268978118896484\n",
            "A left; Q up; C left; C left; C left; X left; Q down; Q down; Q down; r right; P down; P down; P down; r right; r right\n",
            "IDA* BCars - num of moves: 15, num of nodes passes: 472301, num of nodes gen: 2034804, duplicates passes: 471989, time: 608.4634916782379\n",
            "A left; Q up; C left; C left; P down; P down; P down; C left; Q down; X left; Q down; Q down; r right; r right; r right\n",
            "IDA* BBCars - num of moves: 15, num of nodes passes: 131870, num of nodes gen: 651617, duplicates passes: 131608, time: 195.66246104240417\n",
            "A left; Q up; C left; C left; P down; P down; P down; C left; Q down; X left; Q down; Q down; r right; r right; r right\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b = Board.readFromfile('p5.txt')\n",
        "print(b.prettify(b.cars))\n",
        "astar1 = Solver(b, BlockingCarsHeuristic())\n",
        "IDAstar1 = Solver(b, BlockingCarsHeuristic())\n",
        "astar2 = Solver(b, BlockingBlockingCarsHeuristic())\n",
        "IDAstar2 = Solver(b, BlockingBlockingCarsHeuristic())\n",
        "\n",
        "start_astar1 = time.time()\n",
        "moves_astar1, closed_astar1, open_astar1 = astar1.solve()\n",
        "end_astar1 = time.time()\n",
        "\n",
        "print(f\"A* BCars - num of moves: {len(moves_astar1)}, num of nodes passes: {closed_astar1}, num of nodes gen: {open_astar1 + closed_astar1}, time: {end_astar1 - start_astar1}\")\n",
        "print(astar1.solutionMoves(moves_astar1))\n",
        "\n",
        "start_astar2 = time.time()\n",
        "moves_astar2, closed_astar2, open_astar2 = astar2.solve()\n",
        "end_astar2 = time.time()\n",
        "\n",
        "print(f\"A* BBCars - num of moves: {len(moves_astar2)}, num of nodes passes: {closed_astar2}, num of nodes gen: {open_astar2 + closed_astar2}, time: {end_astar2 - start_astar2}\")\n",
        "print(astar2.solutionMoves(moves_astar2))\n",
        "\n",
        "start_IDAstar1 = time.time()\n",
        "moves_IDAstar1, visited_IDAstar1, generated_IDAstar1, dup_IDAstar1 = IDAstar1.solveIDA()\n",
        "end_IDAstar1 = time.time()\n",
        "\n",
        "dup_IDAstar1_num = 0\n",
        "for key,val in dup_IDAstar1.items():\n",
        "  if val > 1: dup_IDAstar1_num += (val - 1)\n",
        "\n",
        "print(f\"IDA* BCars - num of moves: {len(moves_IDAstar1)}, num of nodes passes: {visited_IDAstar1}, num of nodes gen: {generated_IDAstar1}, duplicates passes: {dup_IDAstar1_num}, time: {end_IDAstar1 - start_IDAstar1}\")\n",
        "print(IDAstar1.solutionMoves(moves_IDAstar1))\n",
        "\n",
        "start_IDAstar2 = time.time()\n",
        "moves_IDAstar2, visited_IDAstar2, generated_IDAstar2, dup_IDAstar2 = IDAstar2.solveIDA()\n",
        "end_IDAstar2 = time.time()\n",
        "\n",
        "dup_IDAstar2_num = 0\n",
        "for key,val in dup_IDAstar2.items():\n",
        "  if val > 1: dup_IDAstar2_num += (val - 1)\n",
        "\n",
        "print(f\"IDA* BBCars - num of moves: {len(moves_IDAstar2)}, num of nodes passes: {visited_IDAstar2}, num of nodes gen: {generated_IDAstar2}, duplicates passes: {dup_IDAstar2_num}, time: {end_IDAstar2 - start_IDAstar2}\")\n",
        "print(IDAstar2.solutionMoves(moves_IDAstar2))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sxUGfpm_4Zkp",
        "outputId": "b7851c05-1f9b-4dc2-8359-53c7ea8d2b1b"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            ". . . . . O\n",
            "P . . Q . O\n",
            "P r r Q . O\n",
            "P . . Q . .\n",
            "B . C C . .\n",
            "B . X X X .\n",
            "\n",
            "A* BCars - num of moves: 13, num of nodes passes: 337, num of nodes gen: 539, time: 1.1522634029388428\n",
            "P up; B up; C left; Q down; X left; X left; Q down; r right; r right; O down; O down; O down; r right\n",
            "A* BBCars - num of moves: 13, num of nodes passes: 329, num of nodes gen: 599, time: 1.1312661170959473\n",
            "C left; P up; B up; X left; X left; Q down; Q down; r right; r right; O down; O down; O down; r right\n",
            "IDA* BCars - num of moves: 13, num of nodes passes: 547301, num of nodes gen: 2975775, duplicates passes: 546974, time: 965.9517261981964\n",
            "O down; O down; O down; P up; B up; C left; Q down; X left; X left; Q down; r right; r right; r right\n",
            "IDA* BBCars - num of moves: 13, num of nodes passes: 349274, num of nodes gen: 1946577, duplicates passes: 348963, time: 657.1327524185181\n",
            "O down; O down; O down; P up; B up; C left; Q down; X left; X left; Q down; r right; r right; r right\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Graphs"
      ],
      "metadata": {
        "id": "f2XHPXGCcMOD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Setup"
      ],
      "metadata": {
        "id": "wMNhUG4bpttB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "import seaborn as sns\n",
        "import pandas as pd\n",
        "\n",
        "sns.set(rc={'figure.figsize':(5,3)})\n",
        "sns.set_theme(style=\"whitegrid\")"
      ],
      "metadata": {
        "id": "412eC9N9Elyw"
      },
      "execution_count": 72,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "d1 = {\n",
        "      'algorithm': [\"A* B\", \"A* BB\", \"IDA* B\", \"IDA* BB\"],\n",
        "      'problem': [1, 1, 1, 1],\n",
        "      'time': [0.0345, 0.0355, 0.0354, 0.0501],\n",
        "      'nodes passed': [27, 27, 26, 26],\n",
        "      'nodes generated': [102, 102, 143, 143],\n",
        "      'duplicates': [0, 0, 7, 7]\n",
        "\n",
        "     }\n",
        "df1 = pd.DataFrame(data=d1)\n",
        "\n",
        "d2 = {\n",
        "      'algorithm': [\"A* B\", \"A* BB\", \"IDA* B\", \"IDA* BB\"],\n",
        "      'problem': [2, 2, 2, 2],\n",
        "      'time': [0.1106, 0.0285, 0.2301, 0.0709],\n",
        "      'nodes passed': [71, 18, 126, 34],\n",
        "      'nodes generated': [281, 107, 814, 250],\n",
        "      'duplicates': [0, 0, 69, 14]\n",
        "\n",
        "     }\n",
        "df2 = pd.DataFrame(data=d2)\n",
        "\n",
        "d3 = {\n",
        "      'algorithm': [\"A* B\", \"A* BB\", \"IDA* B\", \"IDA* BB\"],\n",
        "      'problem': [3, 3, 3, 3],\n",
        "      'time': [0.2568, 0.2232, 4.8597, 2.9451],\n",
        "      'nodes passed': [170, 155, 3987, 2338],\n",
        "      'nodes generated': [334, 334, 19336, 11463],\n",
        "      'duplicates': [0, 0, 3853, 2222]\n",
        "\n",
        "     }\n",
        "df3 = pd.DataFrame(data=d3)\n",
        "\n",
        "d4 = {\n",
        "      'algorithm': [\"A* B\", \"A* BB\", \"IDA* B\", \"IDA* BB\"],\n",
        "      'problem': [4, 4, 4, 4],\n",
        "      'time': [0.8423, 0.6269, 608.4635, 195.6625],\n",
        "      'nodes passed': [336, 283, 472301, 131870],\n",
        "      'nodes generated': [719, 666, 2034804, 651617],\n",
        "      'duplicates': [0, 0, 471989, 131608]\n",
        "\n",
        "     }\n",
        "df4 = pd.DataFrame(data=d4)\n",
        "\n",
        "d5 = {\n",
        "      'algorithm': [\"A* B\", \"A* BB\", \"IDA* B\", \"IDA* BB\"],\n",
        "      'problem': [5, 5, 5, 5],\n",
        "      'time': [1.1523, 1.1313, 965.9517, 657.1328],\n",
        "      'nodes passed': [337, 329, 547301, 349274],\n",
        "      'nodes generated': [599, 539, 2975775, 1946577],\n",
        "      'duplicates': [0, 0, 546974, 348963]\n",
        "\n",
        "     }\n",
        "df5 = pd.DataFrame(data=d5)"
      ],
      "metadata": {
        "id": "79TUmE5wfiow"
      },
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "frames = [df1, df2, df3, df4, df5]\n",
        "  \n",
        "df = pd.concat(frames)"
      ],
      "metadata": {
        "id": "GtUyb0c2mJ29"
      },
      "execution_count": 57,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def graph(problem, y):\n",
        "  ax = sns.barplot(x=\"algorithm\", y=y, data=df[df['problem'] == problem])"
      ],
      "metadata": {
        "id": "VQUlZB9NfBbL"
      },
      "execution_count": 68,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Time"
      ],
      "metadata": {
        "id": "3uqtNn32pwtE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "graph(1, \"time\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "-v2NDwA3hJtG",
        "outputId": "d2aedf9b-bc31-4319-d5e7-761f709b3820"
      },
      "execution_count": 91,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(2, \"time\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "SBtnrAA4p0do",
        "outputId": "87ec1371-70d5-44af-b283-1cc3714033df"
      },
      "execution_count": 92,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(3, \"time\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 231
        },
        "id": "rJkPTHV8p2cL",
        "outputId": "43a648a2-207d-4600-ad73-fce098acd336"
      },
      "execution_count": 93,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(4, \"time\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "pWtxAJPrp3Zo",
        "outputId": "9dfd3473-b83b-4d69-bb3f-b32f922ca75b"
      },
      "execution_count": 94,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(5, \"time\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 232
        },
        "id": "QtnLDNnDp4gG",
        "outputId": "627bf205-af57-449d-e292-9bf5370caaeb"
      },
      "execution_count": 95,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Nodes Passed"
      ],
      "metadata": {
        "id": "OFjUJ7SIp8UY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "graph(1, \"nodes passed\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "J_VPUZxPp7lt",
        "outputId": "1c4572c4-06e0-4644-949b-76b2a2b33469"
      },
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(2, \"nodes passed\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "lEr4tksNqIxi",
        "outputId": "121f1198-b17c-4586-c43e-681b94bd2c86"
      },
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(3, \"nodes passed\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "DFzVDdM3qKs1",
        "outputId": "4328854f-aae8-46e1-a0f0-7814de96ef1a"
      },
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(4, \"nodes passed\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "ilXCTgylqLxk",
        "outputId": "828f6551-be20-48ea-cbe2-bc88975d7b76"
      },
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(5, \"nodes passed\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "L-zAVmiBqMzs",
        "outputId": "13e2fdba-aa20-460c-826f-94de01a56440"
      },
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Nodes Generated"
      ],
      "metadata": {
        "id": "ZlzdpsZHqOYP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "graph(1, \"nodes generated\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 234
        },
        "id": "IfQEGKQ3qVja",
        "outputId": "4177a937-f3af-4767-e3ea-f1a0be5a6c94"
      },
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(2, \"nodes generated\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "AGFlQxnyqY-U",
        "outputId": "4d754a3a-ff77-4dbc-ebe6-93c8f2be6055"
      },
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(3, \"nodes generated\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 232
        },
        "id": "Ub3eAOvxqaL5",
        "outputId": "fc0de972-5e2a-4518-c397-ced6ffc198b9"
      },
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(4, \"nodes generated\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 241
        },
        "id": "8oQgdHSxqbUM",
        "outputId": "b8010ac2-58ed-4098-d56d-6602a48bb55e"
      },
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(5, \"nodes generated\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 241
        },
        "id": "ywWEsK1_qcaE",
        "outputId": "0bc0995e-19a6-405a-f700-021ab961c1b1"
      },
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Duplicates"
      ],
      "metadata": {
        "id": "CYz8o8HSqd0i"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "graph(1, \"duplicates\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "UB2RZIXsqgyS",
        "outputId": "387a364d-8f43-43c4-9df5-6f6532e3fdf7"
      },
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(2, \"duplicates\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "BZctheGwqs-O",
        "outputId": "ea6f6459-1794-4992-f50e-5f7d06b3478e"
      },
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(3, \"duplicates\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 233
        },
        "id": "eVNEAwtHqug3",
        "outputId": "90879388-9496-4b78-8472-33b8f400e791"
      },
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(4, \"duplicates\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "fGCukFIKqvbX",
        "outputId": "9c7dc7fa-7d7b-4d37-950a-5cb749074ef1"
      },
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "graph(5, \"duplicates\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "id": "saR1kKiKqw0V",
        "outputId": "7cbbf00e-c01b-4ac1-b18a-a047d1902427"
      },
      "execution_count": 99,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    }
  ]
}