Search/05-Search_Strategies_OOP.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "<div class='alert alert-success'>\n",
    "    <h1 align=\"center\">Search Algorithms: Uninformed Search Strategies</h1> \n",
    "    <h3 align=\"center\">Artificial Intelligece Course (Fall 2021)</h3>\n",
    "    <h5 align=\"center\">Seyed Naser RAZAVI <a href='http://www.snrazavi.ir/ai-slides/'>(website)</a></h5>\n",
    "</div>"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "%matplotlib inline\n",
    "%reload_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import namedtuple\n",
    "\n",
    "from utils import *\n",
    "from npuzzle import NPuzzleState"
   ],
   "outputs": [],
   "metadata": {
    "scrolled": true
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Uninformed Search Strategies: OOP implementation\n",
    "\n",
    "In uniformed (blind) search strategies, we don't have any additional information other than the information provided in the problem formulation (states, actions, initial state and goal state(s)). \n",
    "\n",
    "Later you will see informed search strategis in which you have other information (heuristics) that during the search process guide you towards the goal state.\n",
    "\n",
    "- BFS (Breadth First Search)\n",
    "- UCS (Uniform Cost Search)\n",
    "- DFS (Depth First Search)\n",
    "- DLS (Depth Limitted Search)\n",
    "- IDS (Iterative Deepening Search)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "start_state_tiles = [\n",
    "    2, 8, 3, \n",
    "    1, 6, 4, \n",
    "    7, 0, 5]\n",
    "\n",
    "goal_state_tiles = [\n",
    "    1, 2, 3, \n",
    "    8, 0, 4,\n",
    "    7, 6, 5]\n",
    "\n",
    "# define start state and goal state\n",
    "start_state = NPuzzleState(tiles=start_state_tiles)\n",
    "goal_state = NPuzzleState(tiles=goal_state_tiles)\n",
    "\n",
    "# plot the start state and the goal state\n",
    "fig, axes = plt.subplots(1, 2, figsize=(6, 3))\n",
    "start_state.plot(axes[0], 'Start')\n",
    "goal_state.plot(axes[1], 'Goal')\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### BFS\n",
    "- Frontier is a FIFO list (or queue) and is implemented in the `utils.py`."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "Node = namedtuple('Node', 'state parent action cost')\n",
    "\n",
    "\n",
    "class BFS:\n",
    "    ''' Breadth-First Search strategy'''\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.frontier = Queue()\n",
    "        self.reached = set()\n",
    "        self.num_generated = 0\n",
    "\n",
    "        \n",
    "    def search(self, start_state, goal_state):\n",
    "\n",
    "        node = Node(start_state, None, None, 0)\n",
    "\n",
    "        if start_state == goal_state:\n",
    "            return solution(node)\n",
    "\n",
    "        self.frontier.push(node)\n",
    "        self.reached.add(start_state)\n",
    "\n",
    "\n",
    "        while not self.frontier.is_empty():        \n",
    "            # select a candidate node\n",
    "            node = self.frontier.pop()\n",
    "\n",
    "            # expand\n",
    "            for successor, action, step_cost in node.state.successors():\n",
    "                self.num_generated += 1\n",
    "\n",
    "                if successor == goal_state:\n",
    "                    return self._solution(Node(successor, node, action, node.cost + step_cost))\n",
    "\n",
    "                if successor not in self.reached:\n",
    "                    self.reached.add(successor)\n",
    "                    self.frontier.push(Node(successor, node, action, node.cost + step_cost))\n",
    "\n",
    "        return None  # if no solution found\n",
    "    \n",
    "    @staticmethod\n",
    "    def _solution(node):\n",
    "        path = []\n",
    "        while node.parent is not None:\n",
    "            path = [(node.state, node.action)] + path\n",
    "            node = node.parent\n",
    "        return path"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "bfs = BFS()\n",
    "solution_path = bfs.search(start_state, goal_state)\n",
    "\n",
    "print(f\"Number of generated nodes: {bfs.num_generated}\")\n",
    "show_solution(start_state, solution_path, ncols=6)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of generated nodes: 70\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x216 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {
    "scrolled": true
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Using `__call__()`"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "class BFS:\n",
    "    ''' Breadth-First Search strategy'''\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.frontier = Queue()\n",
    "        self.reached = set()\n",
    "        self.num_generated = 0\n",
    "\n",
    "        \n",
    "    def search(self, start_state, goal_state):\n",
    "\n",
    "        node = Node(start_state, None, None, 0)\n",
    "\n",
    "        if start_state == goal_state:\n",
    "            return solution(node)\n",
    "\n",
    "        self.frontier.push(node)\n",
    "        self.reached.add(start_state)\n",
    "\n",
    "\n",
    "        while not self.frontier.is_empty():        \n",
    "            # select a candidate node\n",
    "            node = self.frontier.pop()\n",
    "\n",
    "            # expand\n",
    "            for successor, action, step_cost in node.state.successors():\n",
    "                self.num_generated += 1\n",
    "\n",
    "                if successor == goal_state:\n",
    "                    return self._solution(Node(successor, node, action, node.cost + step_cost))\n",
    "\n",
    "                if successor not in self.reached:\n",
    "                    self.reached.add(successor)\n",
    "                    self.frontier.push(Node(successor, node, action, node.cost + step_cost))\n",
    "\n",
    "        return None  # if no solution found\n",
    "    \n",
    "    def __call__(self, start_state, goal_state):\n",
    "        return self.search(start_state, goal_state)\n",
    "    \n",
    "    @staticmethod\n",
    "    def _solution(node):\n",
    "        path = []\n",
    "        while node.parent is not None:\n",
    "            path = [(node.state, node.action)] + path\n",
    "            node = node.parent\n",
    "        return path"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "bfs = BFS()\n",
    "solution_path = bfs(start_state, goal_state)\n",
    "\n",
    "print(f\"Number of generated nodes: {bfs.num_generated}\")\n",
    "show_solution(start_state, solution_path, ncols=6)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of generated nodes: 70\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x216 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## UCS\n",
    "- Frontier is a priority queue, in which nodes are sorted according to their path costs. \n",
    "- Again, the implementation of priority queue is given in the `utils.py`.\n",
    "\n",
    "<img src='imgs/Best_First.png' width='80%'>"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "class UCS:\n",
    "    '''Uniform Cost Search'''\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.frontier = PriorityQueue()\n",
    "        self.reached = dict()  # a dictionary of (state, node)\n",
    "        self.num_generated = 0\n",
    "        \n",
    "    def search(self, start_state, goal_state):\n",
    "\n",
    "        node = Node(start_state, None, None, 0)\n",
    "        self.frontier.push(node, 0)  # push node and its priority\n",
    "        self.reached[start_state] = node\n",
    "\n",
    "        while not self.frontier.is_empty():\n",
    "            # select a candidate node\n",
    "            node = self.frontier.pop()\n",
    "\n",
    "            # goal test\n",
    "            if node.state == goal_state:\n",
    "                return self._solution(node)\n",
    "\n",
    "            # expand        \n",
    "            for successor, action, step_cost in node.state.successors():\n",
    "                self.num_generated += 1\n",
    "                path_cost = node.cost + step_cost\n",
    "\n",
    "                if successor not in self.reached or path_cost < self.reached[successor].cost:\n",
    "                    child_node = Node(successor, node, action, path_cost)\n",
    "                    self.reached[successor] = child_node\n",
    "                    self.frontier.push(child_node, path_cost)\n",
    "\n",
    "        return None  # if no solution found\n",
    "    \n",
    "    def __call__(self, start_state, goal_state):\n",
    "        return self.search(start_state, goal_state)\n",
    "   \n",
    "    @staticmethod\n",
    "    def _solution(node):\n",
    "        path = []\n",
    "        while node.parent is not None:\n",
    "            path = [(node.state, node.action)] + path\n",
    "            node = node.parent\n",
    "        return path"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "ucs = UCS()\n",
    "solution_path = ucs(start_state, goal_state)\n",
    "\n",
    "print(f\"Number of generated nodes: {ucs.num_generated}\")\n",
    "show_solution(start_state, solution_path, ncols=6)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of generated nodes: 122\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x216 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "**Note**: that because in this problem, the cost of all the actions are equal, the UCS strategy is exactly the same as BFS strategy (the unoptimized version)."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### DLS\n",
    "\n",
    "<img src='imgs/DLS_IDS.png' width='80%'>"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "class DLS:\n",
    "    '''Depth Limitted Search'''\n",
    "    \n",
    "    def __init__(self):\n",
    "        self._initialize()\n",
    "        \n",
    "    def _initialize(self):\n",
    "        self.frontier = Stack()\n",
    "        self.num_generated = 0\n",
    "        self.result = 'failure'\n",
    "\n",
    "    def search(self, start_state, goal_state, limit=30):\n",
    "\n",
    "        def is_cycle(node):\n",
    "            state = node.state\n",
    "            while node.parent is not None:\n",
    "                if state == node.parent.state:\n",
    "                    return True\n",
    "                node = node.parent\n",
    "            return False\n",
    "        \n",
    "        self._initialize()\n",
    "        self.frontier.push(Node(start_state, None, None, 0))  # 0 is the depth of the start node\n",
    "\n",
    "        while not self.frontier.is_empty():\n",
    "            # select a candidate node\n",
    "            node = self.frontier.pop()\n",
    "\n",
    "            # goal test\n",
    "            if node.state == goal_state: \n",
    "                return self._solution(node)\n",
    "\n",
    "            # before expansion, check the depth limit\n",
    "            if node.cost >= limit:\n",
    "                self.result = 'cutoff'\n",
    "            elif not is_cycle(node):\n",
    "                # expand                \n",
    "                for successor, action, step_cost in node.state.successors():\n",
    "                    self.frontier.push(Node(successor, node, action, node.cost + step_cost))\n",
    "                    self.num_generated += 1\n",
    "\n",
    "        return self.result\n",
    "    \n",
    "    def __call__(self, start_state, goal_state, limit=30):\n",
    "        return self.search(start_state, goal_state, limit)\n",
    "\n",
    "    @staticmethod\n",
    "    def _solution(node):\n",
    "        path = []\n",
    "        while node.parent is not None:\n",
    "            path = [(node.state, node.action)] + path\n",
    "            node = node.parent\n",
    "        return path"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Perform a depth limitted search with depth limit 15."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "source": [
    "dls = DLS()\n",
    "solution_path = dls(start_state, goal_state, limit=15)\n",
    "\n",
    "print(f\"Number of generated nodes: {dls.num_generated}\")\n",
    "show_solution(start_state, solution_path, ncols=6)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of generated nodes: 2347\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x648 with 18 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Perform a depth limitted search with depth limit 10."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "source": [
    "solution_path = dls(start_state, goal_state, limit=10)\n",
    "\n",
    "print(f\"Number of generated nodes: {dls.num_generated}\")\n",
    "show_solution(start_state, solution_path, ncols=6)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of generated nodes: 823\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x216 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Perform a depth limitted search with depth limit 5."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "source": [
    "solution_path = dls(start_state, goal_state, limit=5)\n",
    "\n",
    "print(f\"Number of generated nodes: {dls.num_generated}\")\n",
    "show_solution(start_state, solution_path, ncols=6)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of generated nodes: 56\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x216 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Perform a depth limitted search with depth limit 3."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "solution_path = dls(start_state, goal_state, limit=3)\n",
    "\n",
    "print(f\"Number of generated nodes: {dls.num_generated}\")\n",
    "show_solution(start_state, solution_path, ncols=6)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of generated nodes: 26\n",
      "No solution found!\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### IDS"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "source": [
    "class IDS:\n",
    "    '''Iterative Deepening Search'''\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.num_generated = 0\n",
    "        self.dls = DLS()\n",
    "    \n",
    "    def search(self, start_state, goal_state):\n",
    "        limit = 0\n",
    "\n",
    "        while True:\n",
    "            solution_path = self.dls(start_state, goal_state, limit)\n",
    "            print(f'DLS (limit={limit}), number of generated nodes = {self.dls.num_generated:3d}')\n",
    "            limit += 1\n",
    "            self.num_generated += dls.num_generated\n",
    "\n",
    "            if isinstance(solution_path, list):\n",
    "                return solution_path\n",
    "            \n",
    "    def __call__(self, start_state, goal_state):\n",
    "        return self.search(start_state, goal_state)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "source": [
    "ids = IDS()\n",
    "solution_path = ids(start_state, goal_state)\n",
    "\n",
    "print(f\"Total number of generated nodes: {ids.num_generated}\")\n",
    "show_solution(start_state, solution_path, ncols=6)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "DLS (limit=0), number of generated nodes =   0\n",
      "DLS (limit=1), number of generated nodes =   3\n",
      "DLS (limit=2), number of generated nodes =  11\n",
      "DLS (limit=3), number of generated nodes =  26\n",
      "DLS (limit=4), number of generated nodes =  50\n",
      "DLS (limit=5), number of generated nodes =  56\n",
      "Total number of generated nodes: 156\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x216 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Informed Search Strategies: OOP"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "source": [
    "def h1(state, goal):\n",
    "    ''' Number of misplaced tiles heuristic\n",
    "    '''\n",
    "    return sum([state.tiles.index(tile) != goal.tiles.index(tile) \n",
    "                for tile in range(1, state.N + 1)])\n",
    "\n",
    "\n",
    "def h2(state, goal):\n",
    "    ''' Sum of manhatan distance heuristic\n",
    "    '''\n",
    "    return sum([manhatan_distance(tile, state, goal)\n",
    "                for tile in range(1, state.N + 1)])"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "source": [
    "class Greedy:\n",
    "    '''Greedy Search'''\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.num_generated = 0\n",
    "        self.frontier = PriorityQueue()\n",
    "        self.reached = dict()  # a dictionary of (state, node)\n",
    "\n",
    "        \n",
    "    def search(self, start_state, goal_state, heuristic):\n",
    "\n",
    "        node = Node(start_state, None, None, 0) \n",
    "        self.frontier.push(node, heuristic(start_state, goal_state))\n",
    "        self.reached[start_state] = node\n",
    "\n",
    "        while not self.frontier.is_empty():\n",
    "            # select a node\n",
    "            node = self.frontier.pop()\n",
    "\n",
    "            # goal test\n",
    "            if node.state == goal_state:\n",
    "                return self._solution(node)\n",
    "\n",
    "            # expand\n",
    "            for successor, action, step_cost in node.state.successors():\n",
    "                self.num_generated += 1\n",
    "                path_cost = node.cost + step_cost\n",
    "\n",
    "                if successor not in self.reached or path_cost < self.reached[successor].cost:\n",
    "                    child_node = Node(successor, node, action, path_cost)\n",
    "                    self.reached[successor] = child_node\n",
    "                    self.frontier.push(child_node, heuristic(successor, goal_state))\n",
    "\n",
    "        return None  # no solution found\n",
    "    \n",
    "    def __call__(self, start_state, goal_state, heuristic):\n",
    "        return self.search(start_state, goal_state, heuristic)\n",
    "\n",
    "    @staticmethod\n",
    "    def _solution(node):\n",
    "        path = []\n",
    "        while node.parent is not None:\n",
    "            path = [(node.state, node.action)] + path\n",
    "            node = node.parent\n",
    "        return path"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "source": [
    "greedy = Greedy()\n",
    "solution_path = greedy(start_state, goal_state, h1)\n",
    "\n",
    "print(f\"Number of generated nodes: {greedy.num_generated}\")\n",
    "show_solution(start_state, solution_path, ncols=6)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of generated nodes: 18\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x216 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {
    "scrolled": true
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### A-Star"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "source": [
    "class AStar:\n",
    "    '''A-Star Search'''\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.num_generated = 0\n",
    "        self.frontier = PriorityQueue()\n",
    "        self.reached = dict()  # a dictionary of (state, node)\n",
    "\n",
    "    def search(self, start_state, goal_state, heuristic):\n",
    "        node = Node(start_state, None, None, 0) \n",
    "        self.frontier.push(node, 0 + heuristic(start_state, goal_state))\n",
    "        self.reached[start_state] = node\n",
    "\n",
    "        while not self.frontier.is_empty():\n",
    "            # select a node\n",
    "            node = self.frontier.pop()\n",
    "\n",
    "            # goal test\n",
    "            if node.state == goal_state:\n",
    "                return self._solution(node)\n",
    "\n",
    "            # expand\n",
    "            for successor, action, step_cost in node.state.successors():\n",
    "                self.num_generated += 1\n",
    "                path_cost = node.cost + step_cost\n",
    "\n",
    "                if successor not in self.reached or path_cost < self.reached[successor].cost:\n",
    "                    child_node = Node(successor, node, action, path_cost)\n",
    "                    self.reached[successor] = child_node\n",
    "                    self.frontier.push(child_node, path_cost + heuristic(successor, goal_state))\n",
    "\n",
    "        return None  # no solution found\n",
    "    \n",
    "    def __call__(self, start_state, goal_state, heuristic):\n",
    "        return self.search(start_state, goal_state, heuristic)\n",
    "\n",
    "    @staticmethod\n",
    "    def _solution(node):\n",
    "        path = []\n",
    "        while node.parent is not None:\n",
    "            path = [(node.state, node.action)] + path\n",
    "            node = node.parent\n",
    "        return path"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "source": [
    "a_star = AStar()\n",
    "path = a_star(start_state, goal_state, h2)\n",
    "\n",
    "print(f\"Number of generated nodes = {a_star.num_generated}\")\n",
    "show_solution(start_state, path, ncols=6)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of generated nodes = 15\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x216 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Solving a hard case\n",
    "- Solving a typical instance of the 8-puzzle. \n",
    "- The shortest solution is 26 actions long."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "source": [
    "start_state_tiles = [\n",
    "    7, 2, 4, \n",
    "    5, 0, 6, \n",
    "    8, 3, 1]\n",
    "\n",
    "goal_state_tiles = [\n",
    "    0, 1, 2, \n",
    "    3, 4, 5, \n",
    "    6, 7, 8] \n",
    "\n",
    "# define start state and goal state\n",
    "start_state = NPuzzleState(tiles=start_state_tiles)\n",
    "goal_state = NPuzzleState(tiles=goal_state_tiles)\n",
    "\n",
    "# plot the start state and the goal state\n",
    "fig, axes = plt.subplots(1, 2, figsize=(6, 3))\n",
    "start_state.plot(axes[0], 'Start')\n",
    "goal_state.plot(axes[1], 'Goal')\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "source": [
    "a_star = AStar()\n",
    "path = a_star(start_state, goal_state, h2)\n",
    "\n",
    "print(f\"Number of generated nodes = {a_star.num_generated}\")\n",
    "show_solution(start_state, path, ncols=8)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Number of generated nodes = 10644\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1728x864 with 32 Axes>"
      ]
     },
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   "source": [
    "## What is next?\n",
    "- So far, we have solved problems in which the aim is to find a path from an initial state to a goal state. \n",
    "- However, in many real world problems, the aim is to find a single state (not a solution path) which is an optimal (or good) state, in terms of some criteria.\n",
    "- For example in schedling problem, the goal is to find a schedule which satisfies some certain criteria. Here the import thing is the schedule itself not the path which leads to that schedule.\n",
    "- In the next lesson, we will explore some local search strategies which are used to solve these kinds of problems."
   ],
   "metadata": {}
  }
 ],
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