Solving Problems by Searching.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from IPython.display import clear_output\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.ticker as plticker\n",
    "import networkx as nx\n",
    "import random\n",
    "from collections import namedtuple\n",
    "import heapq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cities = {'Oradea'\n",
    "         , 'Zerind'\n",
    "         , 'Arad'\n",
    "         , 'Timisoara'\n",
    "         , 'Lugoj'\n",
    "         , 'Mehadia'\n",
    "         , 'Drobeta'\n",
    "         , 'Sibiu'\n",
    "         , 'Rimnicu Vilcea'\n",
    "         , 'Craiova'\n",
    "         , 'Fagaras'\n",
    "         , 'Pitesti'\n",
    "         , 'Bucharest'\n",
    "         , 'Giurgiu'\n",
    "         , 'Neamt'\n",
    "         , 'Iasi'\n",
    "         , 'Vaslui'\n",
    "         , 'Urziceni'\n",
    "         , 'Hirsova'\n",
    "         , 'Eforie'}\n",
    "\n",
    "assert len(cities) == 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "roads = {Road(('Oradea', 'Zerind'), 71)\n",
    "        ,Road(('Arad', 'Zerind'), 75)\n",
    "        ,Road(('Arad', 'Timisoara'), 118)\n",
    "        ,Road(('Timisoara', 'Lugoj'), 111)\n",
    "        ,Road(('Lugoj', 'Mehadia'), 70)\n",
    "        ,Road(('Mehadia', 'Drobeta'), 75)\n",
    "        ,Road(('Oradea', 'Sibiu'), 151)\n",
    "        ,Road(('Arad', 'Sibiu'), 140)\n",
    "        ,Road(('Sibiu', 'Rimnicu Vilcea'),80)\n",
    "        ,Road(('Rimnicu Vilcea', 'Craiova'), 146)\n",
    "        ,Road(('Drobeta', 'Craiova'), 120)\n",
    "        ,Road(('Sibiu', 'Fagaras'), 99)\n",
    "        ,Road(('Rimnicu Vilcea', 'Pitesti'), 97)\n",
    "        ,Road(('Pitesti', 'Craiova'), 138)\n",
    "        ,Road(('Fagaras', 'Bucharest'), 211)\n",
    "        ,Road(('Pitesti', 'Bucharest'), 101)\n",
    "        ,Road(('Bucharest', 'Giurgiu'), 90)\n",
    "        ,Road(('Bucharest', 'Urziceni'), 85)\n",
    "        ,Road(('Neamt', 'Iasi'), 87)\n",
    "        ,Road(('Iasi', 'Vaslui'), 92)\n",
    "        ,Road(('Vaslui', 'Urziceni'), 142)\n",
    "        ,Road(('Urziceni', 'Hirsova'), 98)\n",
    "        ,Road(('Hirsova', 'Eforie'), 86)}\n",
    "\n",
    "assert len(roads) == 23\n",
    "for r in roads:\n",
    "    assert r.cities[0] in cities\n",
    "    assert r.cities[1] in cities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def get_dest(road, city):\n",
    "    assert city in road.cities\n",
    "    for cc in road.cities:\n",
    "        if cc != city:\n",
    "            return cc\n",
    "\n",
    "def get_exits(city):\n",
    "    '''return list of tuples (city, cost) available when in state city'''\n",
    "    exits = []\n",
    "    for r in roads:\n",
    "        if city in r.cities:\n",
    "            dest = get_dest(r, city)\n",
    "            exits.append((dest, r.cost))\n",
    "    return exits\n",
    "\n",
    "roadmap = {}\n",
    "for city in cities:\n",
    "    roadmap[city] = get_exits(city)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Problem():\n",
    "    def __init__(self, problem_mapping):\n",
    "        self._problem = problem_mapping\n",
    "        self.states = self._problem.keys()\n",
    "    \n",
    "    def result(self, state, action):\n",
    "        abstract\n",
    "        \n",
    "    def cost(self, action):\n",
    "        abstract\n",
    "        \n",
    "    def available(self, state):\n",
    "        assert state in self._problem\n",
    "        return self._problem[state]\n",
    "    \n",
    "    def goal_test(self, state):\n",
    "        abstract"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Roadmap(Problem):\n",
    "    def result(self, state, action):\n",
    "        assert action in self._problem[state]\n",
    "        return action[0]\n",
    "    \n",
    "    def cost(self, action):\n",
    "        return action[1]\n",
    "    \n",
    "    def goal_test(self, state):\n",
    "        return state == 'Bucharest'\n",
    "    \n",
    "    def view_graph(self):\n",
    "        labels = {}\n",
    "        grid_graph = self.graph\n",
    "        pos=nx.graphviz_layout(grid_graph)\n",
    "\n",
    "        for state in self.states:\n",
    "            labels[state] = state\n",
    "            for action in self._problem[state]:\n",
    "                nx.draw_networkx_edges(grid_graph, pos, edgelist=[(state, action[0])], width=1, color='r')\n",
    "\n",
    "        nx.draw_networkx_nodes(grid_graph, pos, nodelist=self.states, node_color='w', node_size=3000)\n",
    "\n",
    "        nx.draw_networkx_labels(grid_graph, pos, labels, font_size=10, font_color='red', font_weight='bold')\n",
    "\n",
    "        fig = plt.gcf()\n",
    "        fig.set_size_inches(20,10)\n",
    "        \n",
    "    @property\n",
    "    def graph(self):\n",
    "        g = nx.DiGraph()\n",
    "        for state in self.states:\n",
    "            g.add_node(state, color='blue')\n",
    "        for state in self.states:\n",
    "            for action in self._problem[state]:\n",
    "                g.add_edge(state, action[0])\n",
    "        return g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "this_problem = Roadmap(roadmap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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9qOnBBAAAAHKAp/MWTxcPAF3EiQcccECl6bCnvdauXeuEQqG0pLjpAQUAAAA8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\nkiRJKiP/HyB/wjP9JXUDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f211268abd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "this_problem.view_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Node():\n",
    "    def __init__(self, state, parent, action, path_cost):\n",
    "        self.state = state\n",
    "        self.parent = parent\n",
    "        self.action = action\n",
    "        self.path_cost = path_cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "start_node = Node('Sibiu', None, None, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def child_node(problem, parent, action):\n",
    "    '''return a node that is a child of given node'''\n",
    "    new_state = problem.result(parent.state, action)\n",
    "    this_cost = parent.path_cost + problem.cost(action)\n",
    "    return Node(new_state, parent, action, this_cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('Rimnicu Vilcea', 80), ('Oradea', 151), ('Fagaras', 99), ('Arad', 140)]\n",
      "Rimnicu Vilcea\n"
     ]
    }
   ],
   "source": [
    "available_actions = this_problem.available(start_node.state)\n",
    "print available_actions\n",
    "\n",
    "first_child = child_node(this_problem, start_node, available_actions[0])\n",
    "print first_child.state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def breadth_first_search(problem, start_node):\n",
    "    if problem.goal_test(start_node.state):\n",
    "        return start_node\n",
    "    frontier = [start_node]\n",
    "    frontier_states = {start_node.state}\n",
    "    explored = set([])\n",
    "    while(1):\n",
    "        if len(frontier) == 0:\n",
    "            return 'FAILURE'\n",
    "        this_node = frontier.pop(0)\n",
    "        frontier_states.remove(this_node.state)\n",
    "        explored.add(this_node.state)\n",
    "        #print explored\n",
    "        for action in problem.available(this_node.state):\n",
    "            this_child = child_node(problem, this_node, action)\n",
    "            if (this_child.state not in explored) and (this_child.state not in frontier_states):\n",
    "                if problem.goal_test(this_child.state):\n",
    "                    return this_child\n",
    "                frontier.append(this_child)\n",
    "                frontier_states.add(this_child.state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def uniform_cost_search(problem, start_node):\n",
    "    if problem.goal_test(start_node.state):\n",
    "        return start_node\n",
    "\n",
    "    frontier = []\n",
    "    heapq.heappush(frontier, (0, start_node))\n",
    "    \n",
    "    frontier_states = {start_node.state:start_node.path_cost}\n",
    "    explored = set([])\n",
    "    \n",
    "    while(1):\n",
    "        try:\n",
    "            this_node = heapq.heappop(frontier)[1]\n",
    "        except IndexError:\n",
    "            return 'FAILURE' #heap was empty\n",
    "                \n",
    "        del frontier_states[this_node.state]\n",
    "        if problem.goal_test(this_node.state):\n",
    "            print this_node\n",
    "            return this_node\n",
    "        explored.add(this_node.state)\n",
    "        for action in problem.available(this_node.state):\n",
    "            this_child = child_node(problem, this_node, action)\n",
    "            if (this_child.state not in explored) and (this_child.state not in frontier_states.keys()):\n",
    "                heapq.heappush(frontier, (this_child.path_cost, this_child))\n",
    "                frontier_states[this_child.state] = this_child.path_cost\n",
    "            elif (this_child.state in frontier_states.keys()):\n",
    "                if frontier_states[this_child.state] > this_child.path_cost:\n",
    "                    frontier_states[this_child.state] = this_child.path_cost\n",
    "                    heapq.heappush(frontier, (this_child.path_cost, this_child))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def solution(node):\n",
    "    if node == 'FAILURE':\n",
    "        print node\n",
    "    else:\n",
    "        path = []\n",
    "        this_node = node\n",
    "        while(this_node is not None):\n",
    "            path.append(this_node.state)\n",
    "            this_node = this_node.parent\n",
    "        path.reverse()\n",
    "        print path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Sibiu', 'Fagaras', 'Bucharest']\n"
     ]
    }
   ],
   "source": [
    "solution(breadth_first_search(this_problem, start_node))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sibiu\n",
      "Rimnicu Vilcea\n",
      "Fagaras\n",
      "Arad\n",
      "Oradea\n",
      "Pitesti\n",
      "Zerind\n",
      "Craiova\n",
      "Timisoara\n",
      "Bucharest\n",
      "<__main__.Node instance at 0x7f21133dda28>\n",
      "['Sibiu', 'Rimnicu Vilcea', 'Pitesti', 'Bucharest']\n"
     ]
    }
   ],
   "source": [
    "solution(uniform_cost_search(this_problem, start_node))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def recursive_dls(this_node, problem, limit):\n",
    "    if problem.goal_test(this_node.state):\n",
    "        return this_node\n",
    "    if limit == 0:\n",
    "        return 'CUTOFF'\n",
    "    cutoffp = False\n",
    "    for action in problem.available(this_node.state):\n",
    "        this_child = child_node(problem, this_node, action)\n",
    "        result = recursive_dls(this_child, problem, limit-1)\n",
    "        if result == 'CUTOFF':\n",
    "            cutoffp = True\n",
    "        elif result != 'FAILURE':\n",
    "            return result\n",
    "    if cutoffp:\n",
    "        return 'CUTOFF'\n",
    "    else:\n",
    "        return 'FAILURE'\n",
    "    \n",
    "def depth_limited_search(problem, limit, start_node):\n",
    "    return recursive_dls(start_node, problem, limit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Sibiu', 'Rimnicu Vilcea', 'Sibiu', 'Rimnicu Vilcea', 'Sibiu', 'Rimnicu Vilcea', 'Sibiu', 'Rimnicu Vilcea', 'Pitesti', 'Bucharest']\n"
     ]
    }
   ],
   "source": [
    "solution(depth_limited_search(this_problem, 9, start_node))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def iterative_deepening_search(this_problem, start_node):\n",
    "    depth = 0\n",
    "    while(1):\n",
    "        result = depth_limited_search(this_problem, depth, start_node)\n",
    "        if result != 'CUTOFF':\n",
    "            return result\n",
    "        depth += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Sibiu', 'Fagaras', 'Bucharest']\n"
     ]
    }
   ],
   "source": [
    "solution(iterative_deepening_search(this_problem, start_node))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Sliding Block Puzzle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#map blank index to available moves\n",
    "allowed_actions = {0:('R','D')\n",
    "                  ,1:('L','D','R')\n",
    "                  ,2:('L','D')\n",
    "                  ,3:('U','R','D')\n",
    "                  ,4:('U','R','D','L')\n",
    "                  ,5:('U','L','D')\n",
    "                  ,6:('U','R')\n",
    "                  ,7:('U','R','L')\n",
    "                  ,8:('U','L')}\n",
    "\n",
    "class SlidingBlock3(Problem):\n",
    "    def __init__(self):\n",
    "        pass\n",
    "    \n",
    "    def result(self, state, action):\n",
    "        assert action in self.available(state)\n",
    "        new_state = list(state)\n",
    "        blank_index = state.index(0)\n",
    "        if action == 'R':\n",
    "            moved_block_loc = blank_index+1\n",
    "        elif action == 'L':\n",
    "            moved_block_loc = blank_index-1\n",
    "        elif action == 'U':\n",
    "            moved_block_loc = blank_index-3\n",
    "        elif action == 'D':\n",
    "            moved_block_loc = blank_index+3\n",
    "            \n",
    "        \n",
    "        moved_block = state[moved_block_loc]\n",
    "        new_state[blank_index] = moved_block\n",
    "        new_state[moved_block_loc] = 0\n",
    "        \n",
    "        return tuple(new_state)\n",
    "    \n",
    "    def available(self, state):\n",
    "        blank_index = state.index(0)\n",
    "        return allowed_actions[blank_index]\n",
    "    \n",
    "    def cost(self, action):\n",
    "        return 1\n",
    "    \n",
    "    def goal_test(self, state):\n",
    "        return state == tuple(range(9))\n",
    "    \n",
    "def solution_sbp(node):\n",
    "    if node == 'FAILURE':\n",
    "        print node\n",
    "    else:\n",
    "        path = []\n",
    "        this_node = node\n",
    "        while(this_node is not None):\n",
    "            path.append(this_node.action)\n",
    "            this_node = this_node.parent\n",
    "        path.reverse()\n",
    "        print path[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['L']\n"
     ]
    }
   ],
   "source": [
    "start_sbp = Node((1,0,2,3,4,5,6,7,8), None, None, 0)\n",
    "\n",
    "this_sbp = SlidingBlock3()\n",
    "\n",
    "solution_sbp(iterative_deepening_search(this_sbp, start_sbp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from random import choice\n",
    "\n",
    "#generate random problem instance\n",
    "def random_sbp(num_moves):\n",
    "    start = tuple(range(9))\n",
    "\n",
    "    this_state = tuple(range(9))\n",
    "    for ii in range(num_moves):\n",
    "        next_move = choice(this_sbp.available(this_state))\n",
    "        this_state = this_sbp.result(this_state, next_move)\n",
    "\n",
    "    return this_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['L', 'L', 'U', 'U']\n"
     ]
    }
   ],
   "source": [
    "random_sbp_node = Node(random_sbp(20), None, None, 0)\n",
    "solution_sbp(breadth_first_search(this_sbp, random_sbp_node))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Heuristics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def h_1(state):\n",
    "    '''returns the number of misplaced tiles in the nine-puzzle'''\n",
    "    matches = 0\n",
    "    for b1, b2 in zip(state, range(9)):\n",
    "        if b1 == b2 and b1!=0:\n",
    "            matches += 1\n",
    "    return (8-matches)\n",
    "\n",
    "test_h_state = tuple([7, 2, 4, 5, 0, 6, 8, 3, 1])\n",
    "assert h_1(test_h_state) == 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def h_2(state):\n",
    "    '''returns sum of manhattan distances of tiles from correct place'''\n",
    "    hh = 0\n",
    "    for bb, pp in zip(state, range(9)):\n",
    "        hh += manhattan_distance(bb, pp)\n",
    "    return hh\n",
    "\n",
    "def manhattan_distance(bb, pp):\n",
    "    if bb == 0:\n",
    "        return 0\n",
    "    md = abs(bb % 3- pp%3) + abs(bb/3 - pp/3)\n",
    "    return md\n",
    "\n",
    "assert h_2(test_h_state)  == 18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def a_star_search(problem, start_node):\n",
    "    if problem.goal_test(start_node.state):\n",
    "        return start_node\n",
    "\n",
    "    frontier = []\n",
    "    heapq.heappush(frontier, (0, start_node))\n",
    "    \n",
    "    eval_cost = start_node.path_cost + h_2(start_node.state)\n",
    "    \n",
    "    frontier_states = {start_node.state:eval_cost}\n",
    "    explored = set([])\n",
    "    \n",
    "    while(1):\n",
    "        try:\n",
    "            this_node = heapq.heappop(frontier)[1]\n",
    "        except IndexError:\n",
    "            return 'FAILURE' #heap was empty\n",
    "                \n",
    "        del frontier_states[this_node.state]\n",
    "        if problem.goal_test(this_node.state):\n",
    "            print this_node\n",
    "            return this_node\n",
    "        explored.add(this_node.state)\n",
    "        for action in problem.available(this_node.state):\n",
    "            this_child = child_node(problem, this_node, action)\n",
    "            eval_cost = this_child.path_cost + h_2(this_child.state)\n",
    "            if (this_child.state not in explored) and (this_child.state not in frontier_states.keys()):\n",
    "                heapq.heappush(frontier, (eval_cost, this_child))\n",
    "                frontier_states[this_child.state] = eval_cost\n",
    "            elif (this_child.state in frontier_states.keys()):\n",
    "                if frontier_states[this_child.state] > eval_cost:\n",
    "                    frontier_states[this_child.state] = eval_cost\n",
    "                    heapq.heappush(frontier, (eval_cost, this_child))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<__main__.Node instance at 0x7f21095554d0>\n",
      "['U', 'R', 'D', 'L', 'D', 'R', 'U', 'U', 'L', 'D', 'R', 'D', 'L', 'U', 'L', 'U']\n"
     ]
    }
   ],
   "source": [
    "random_sbp_node = Node(random_sbp(100), None, None, 0)\n",
    "solution_sbp(a_star_search(this_sbp, random_sbp_node))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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