search4e.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Search for AIMA 4th edition\n",
    "\n",
    "Implementation of search algorithms and search problems for AIMA.\n",
    "\n",
    "# Problems and Nodes\n",
    "\n",
    "We start by defining the abstract class for a `Problem`; specific problem domains will subclass this. To make it easier for algorithms that use a heuristic evaluation function, `Problem` has a default `h` function (uniformly zero), and subclasses can define their own default `h` function.\n",
    "\n",
    "We also define a `Node` in a search tree, and some functions on nodes: `expand` to generate successors; `path_actions` and `path_states`  to recover aspects of the path from the node.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import heapq\n",
    "import math\n",
    "import sys\n",
    "from collections import defaultdict, deque, Counter\n",
    "from itertools import combinations\n",
    "\n",
    "\n",
    "class Problem(object):\n",
    "    \"\"\"The abstract class for a formal problem. A new domain subclasses this,\n",
    "    overriding `actions` and `results`, and perhaps other methods.\n",
    "    Specify `initial=<state>`, and `goal=<state>` (or give an `is_goal` method).\n",
    "    The default heuristic is 0 and the default step cost is 1 for all states.\"\"\"\n",
    "\n",
    "    def __init__(self, initial=None, goal=None, **kwds): \n",
    "        self.__dict__.update(initial=initial, goal=goal, **kwds) \n",
    "        \n",
    "    def actions(self, state):           raise NotImplementedError\n",
    "    def result(self, state, action):    raise NotImplementedError\n",
    "    def is_goal(self, state):           return state == self.goal\n",
    "    def step_cost(self, s, action, s1): return 1\n",
    "    def h(self, node):                  return 0\n",
    "    \n",
    "    def __str__(self):\n",
    "        return '{}({!r}, {!r})'.format(\n",
    "            type(self).__name__, self.initial, self.goal)\n",
    "    \n",
    "\n",
    "class Node:\n",
    "    \"A Node in a search tree.\"\n",
    "    def __init__(self, state, parent=None, action=None, path_cost=0):\n",
    "        self.__dict__.update(state=state, parent=parent, action=action, path_cost=path_cost)\n",
    "\n",
    "    def __repr__(self): return '<{}>'.format(self.state)\n",
    "    def __len__(self): return 0 if self.parent is None else (1 + len(self.parent))\n",
    "    def __lt__(self, other): return self.path_cost < other.path_cost\n",
    "    \n",
    "    \n",
    "failure = Node('failure', path_cost=math.inf) # Indicates an algorithm couldn't find a solution.\n",
    "cutoff  = Node('cutoff',  path_cost=math.inf) # Indicates iterative deepening search was cut off.\n",
    "    \n",
    "    \n",
    "def expand(problem, node):\n",
    "    \"Expand a node, generating the children nodes.\"\n",
    "    s = node.state\n",
    "    for action in problem.actions(s):\n",
    "        s1 = problem.result(s, action)\n",
    "        cost = node.path_cost + problem.step_cost(s, action, s1)\n",
    "        yield Node(s1, node, action, cost)\n",
    "        \n",
    "\n",
    "def path_actions(node):\n",
    "    \"The sequence of actions to get to this node.\"\n",
    "    if node.parent is None:\n",
    "        return []  \n",
    "    return path_actions(node.parent) + [node.action]\n",
    "\n",
    "\n",
    "def path_states(node):\n",
    "    \"The sequence of states to get to this node.\"\n",
    "    if node in (cutoff, failure, None): \n",
    "        return []\n",
    "    return path_states(node.parent) + [node.state]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Queues\n",
    "\n",
    "First-in-first-out and Last-in-first-out queues, and a `PriorityQueue`, which allows you to keep a collection of items, and continually remove from it the item with minimum `f(item)` score."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "FIFOQueue = deque\n",
    "\n",
    "LIFOQueue = list\n",
    "\n",
    "class PriorityQueue:\n",
    "    \"\"\"A queue in which the item with minimum f(item) is always popped first.\"\"\"\n",
    "\n",
    "    def __init__(self, items=(), key=lambda x: x): \n",
    "        self.key = key\n",
    "        self.items = [] # a heap of (score, item) pairs\n",
    "        for item in items:\n",
    "            self.add(item)\n",
    "         \n",
    "    def add(self, item):\n",
    "        \"\"\"Add item to the queuez.\"\"\"\n",
    "        pair = (self.key(item), item)\n",
    "        heapq.heappush(self.items, pair)\n",
    "\n",
    "    def pop(self):\n",
    "        \"\"\"Pop and return the item with min f(item) value.\"\"\"\n",
    "        return heapq.heappop(self.items)[1]\n",
    "    \n",
    "    def top(self): return self.items[0][1]\n",
    "\n",
    "    def __len__(self): return len(self.items)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Search Algorithms: Best-First\n",
    "\n",
    "Best-first search with various *f(n)* functions gives us different search algorithms. Note that A\\*, weighted A\\* and greedy search can be given a heuristic function, `h`, but if `h` is not supplied they use the problem's default `h` function (if the problem does not define one, it is taken as *h(n)* = 0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def best_first_search(problem, f):\n",
    "    \"Search nodes with minimum f(node) value first.\"\n",
    "    frontier = PriorityQueue([Node(problem.initial)], key=f)\n",
    "    reached = {}\n",
    "    while frontier:\n",
    "        node = frontier.pop()\n",
    "        if problem.is_goal(node.state):\n",
    "            return node\n",
    "        for child in expand(problem, node):\n",
    "            s = child.state\n",
    "            if s not in reached or child.path_cost < reached[s].path_cost:\n",
    "                reached[s] = child\n",
    "                frontier.add(child)\n",
    "    return failure\n",
    "\n",
    "\n",
    "def g(n): return n.path_cost\n",
    "\n",
    "\n",
    "def astar_search(problem, h=None):\n",
    "    \"\"\"Search nodes with minimum f(n) = g(n) + h(n).\"\"\"\n",
    "    h = h or problem.h\n",
    "    return best_first_search(problem, f=lambda n: g(n) + h(n))\n",
    "\n",
    "\n",
    "def weighted_astar_search(problem, h=None, weight=1.4):\n",
    "    \"\"\"Search nodes with minimum f(n) = g(n) + weight * h(n).\"\"\"\n",
    "    h = h or problem.h\n",
    "    return best_first_search(problem, f=lambda n: g(n) + weight * h(n))\n",
    "\n",
    "        \n",
    "def greedy_bfs(problem, h=None):\n",
    "    \"\"\"Search nodes with minimum h(n).\"\"\"\n",
    "    h = h or problem.h\n",
    "    return best_first_search(problem, f=h)\n",
    "\n",
    "\n",
    "def uniform_cost_search(problem):\n",
    "    \"Search nodes with minimum path cost first.\"\n",
    "    return best_first_search(problem, f=g)\n",
    "\n",
    "\n",
    "def breadth_first_bfs(problem):\n",
    "    \"Search shallowest nodes in the search tree first; using best-first.\"\n",
    "    return best_first_search(problem, f=len)\n",
    "\n",
    "\n",
    "def depth_first_bfs(problem):\n",
    "    \"Search deepest nodes in the search tree first; using best-first.\"\n",
    "    return best_first_search(problem, f=lambda n: -len(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Other Search Algorithms\n",
    "\n",
    "Here are the other search algorithms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def breadth_first_search(problem):\n",
    "    \"Search shallowest nodes in the search tree first.\"\n",
    "    node = Node(problem.initial)\n",
    "    if problem.is_goal(problem.initial):\n",
    "        return node\n",
    "    frontier = FIFOQueue([node])\n",
    "    reached = set()\n",
    "    while frontier:\n",
    "        node = frontier.pop()\n",
    "        for child in expand(problem, node):\n",
    "            s = child.state\n",
    "            if problem.is_goal(s):\n",
    "                return child\n",
    "            if s not in reached:\n",
    "                reached.add(s)\n",
    "                frontier.appendleft(child)\n",
    "    return failure\n",
    "\n",
    "\n",
    "def iterative_deepening_search(problem):\n",
    "    \"Do depth-limited search with increasing depth limits.\"\n",
    "    for limit in range(1, sys.maxsize):\n",
    "        result = depth_limited_search(problem, limit)\n",
    "        if result != cutoff:\n",
    "            return result\n",
    "        \n",
    "def depth_limited_search(problem, limit=10):\n",
    "    \"Search deepest nodes in the search tree first.\"\n",
    "    frontier = LIFOQueue([Node(problem.initial)])\n",
    "    result = failure\n",
    "    while frontier:\n",
    "        node = frontier.pop()\n",
    "        if problem.is_goal(node.state):\n",
    "            return node\n",
    "        elif len(node) >= limit:\n",
    "            result = cutoff\n",
    "        elif not is_cycle(node):\n",
    "            for child in expand(problem, node):\n",
    "                frontier.append(child)\n",
    "    return result\n",
    "\n",
    "def best_first_tree_search(problem, f):\n",
    "    \"A version of best_first_search without the `reached` table.\"\n",
    "    frontier = PriorityQueue([Node(problem.initial)], key=f)\n",
    "    while frontier:\n",
    "        node = frontier.pop()\n",
    "        if problem.is_goal(node.state):\n",
    "            return node\n",
    "        for child in expand(problem, node):\n",
    "            if not is_cycle(child):\n",
    "                frontier.add(child)\n",
    "    return failure\n",
    "\n",
    "def astar_tree_search(problem, h=None):\n",
    "    \"\"\"Search nodes with minimum f(n) = g(n) + h(n), with no `reached` table.\"\"\"\n",
    "    h = h or problem.h\n",
    "    return best_first_tree_search(problem, f=lambda n: g(n) + h(n))\n",
    "\n",
    "def is_cycle(node, k=30):\n",
    "    \"Does this node form a cycle of length k or less?\"\n",
    "    ancestor = node.parent\n",
    "    for _ in range(k):\n",
    "        if ancestor is None:\n",
    "            return False\n",
    "        elif ancestor.state == node.state:\n",
    "            return True\n",
    "        ancestor = ancestor.parent\n",
    "    return False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TODO: bidirectional-search, RBFS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem Domains\n",
    "\n",
    "Now we turn our attention to defining some problem domains as subclasses of `Problem`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Route Finding Problems\n",
    "\n",
    "![](romania.png)\n",
    "\n",
    "In a `RouteProblem`, the states are names of \"cities\" (or other locations), like `'A'` for Arad. The actions are also city names; `'Z'` is the action to move to city `'Z'`. The layout of cities is given by a separate data structure, a `Map`, which is a graph where there are vertexes (cities), links between vertexes, distances (costs) of those links (if not specified, the default is 1 for every link), and optionally the 2D (x, y) location of each city can be specified. A `RouteProblem` takes this `Map` as input and allows actions to move between linked cities. The default heuristic is straight-line distance to the goal, or is uniformly zero if locations were not given."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class RouteProblem(Problem):\n",
    "    \"\"\"A problem to find a route between locations on a `Map`.\n",
    "    Create a problem with RouteProblem(start, goal, map=Map(...)}).\n",
    "    States are the vertexes in the Map graph; actions are destination states.\"\"\"\n",
    "    \n",
    "    def actions(self, state): \n",
    "        \"\"\"The places neighboring `state`.\"\"\"\n",
    "        return self.map.neighbors[state]\n",
    "    \n",
    "    def result(self, state, action):\n",
    "        \"\"\"Go to the `action` place, if the map says that is possible.\"\"\"\n",
    "        return action if action in self.map.neighbors[state] else state\n",
    "    \n",
    "    def step_cost(self, s, action, s1):\n",
    "        \"\"\"The distance (cost) to go from s to s1.\"\"\"\n",
    "        return self.map.distances[s, s1]\n",
    "    \n",
    "    def h(self, node):\n",
    "        \"Straight-line distance between state and the goal.\"\n",
    "        locs = self.map.locations\n",
    "        return straight_line_distance(locs[node.state], locs[self.goal])\n",
    "    \n",
    "    \n",
    "def straight_line_distance(A, B):\n",
    "    \"Straight-line distance between two points.\"\n",
    "    return sum(abs(a - b)**2 for (a, b) in zip(A, B)) ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Map:\n",
    "    \"\"\"A map of places in a 2D world: a graph with vertexes and links between them. \n",
    "    In `Map(links, locations)`, `links` can be either [(v1, v2)...] pairs, \n",
    "    or a {(v1, v2): distance...} dict. Optional `locations` can be {v1: (x, y)} \n",
    "    If `directed=False` then for every (v1, v2) link, we add a (v2, v1).\"\"\"\n",
    "\n",
    "    def __init__(self, links, locations=None, directed=False):\n",
    "        if not hasattr(links, 'items'): # Distances are 1 by default\n",
    "            links = {link: 1 for link in links}\n",
    "        if not directed:\n",
    "            for (v1, v2) in list(links):\n",
    "                links[v2, v1] = links[v1, v2]\n",
    "        self.distances = links\n",
    "        self.locations = locations or defaultdict(lambda: (0, 0))\n",
    "        self.neighbors = multimap(links)\n",
    "\n",
    "        \n",
    "def multimap(pairs) -> dict:\n",
    "    \"Given (key, val) pairs, make a dict of {key: [val,...]}.\"\n",
    "    result = defaultdict(list)\n",
    "    for key, val in pairs:\n",
    "        result[key].append(val)\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some specific RouteProblems\n",
    "\n",
    "romania = Map(\n",
    "    {('O', 'Z'): 71, ('O', 'S'): 151, ('A', 'Z'): 75, ('A', 'S'): 140, ('A', 'T'): 118, \n",
    "     ('L', 'T'): 111, ('L', 'M'): 70, ('D', 'M'): 75, ('C', 'D'): 120, ('C', 'R'): 146, \n",
    "     ('C', 'P'): 138, ('R', 'S'): 80, ('F', 'S'): 99, ('B', 'F'): 211, ('B', 'P'): 101, \n",
    "     ('B', 'G'): 90, ('B', 'U'): 85, ('H', 'U'): 98,  ('E', 'H'): 86, ('U', 'V'): 142, \n",
    "     ('I', 'V'): 92, ('I', 'N'): 87, ('P', 'R'): 97},\n",
    "    locations=dict(\n",
    "    A=(91, 492), B=(400, 327), C=(253, 288), D=(165, 299), E=(562, 293), F=(305, 449),\n",
    "    G=(375, 270), H=(534, 350), I=(473, 506), L=(165, 379), M=(168, 339), N=(406, 537),\n",
    "    O=(131, 571), P=(320, 368), R=(233, 410), S=(207, 457), T=(94, 410), U=(456, 350),\n",
    "    V=(509, 444), Z=(108, 531)))\n",
    "\n",
    "r0 = RouteProblem('A', 'A', map=romania)\n",
    "r1 = RouteProblem('A', 'B', map=romania)\n",
    "r2 = RouteProblem('N', 'L', map=romania)\n",
    "r3 = RouteProblem('E', 'T', map=romania)\n",
    "r4 = RouteProblem('O', 'M', map=romania)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['A', 'S', 'R', 'P', 'B']"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path_states(uniform_cost_search(r1)) # Lowest-cost path from Arab to Bucharest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['A', 'S', 'F', 'B']"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path_states(breadth_first_search(r1)) # Breadth-first: fewer steps, higher path cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Grid Problems\n",
    "\n",
    "A `GridProblem` involves navigating on a 2D grid, with some cells being impassible obstacles. By default you can move to any of the eight neighboring cells that are not obstacles (but in a problem instance you can supply a `directions=` keyword to change that). Again, the default heuristic is straight-line distance to the goal. States are `(x, y)` cell locations, such as `(4, 2)`, and actions are `(dx, dy)` cell movements, such as `(0, -1)`, which means leave the `x` coordinate alone, and decrement the `y` coordinate by 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GridProblem(Problem):\n",
    "    \"\"\"Finding a path on a 2D grid with obstacles. Obstacles are (x, y) cells.\"\"\"\n",
    "\n",
    "    def __init__(self, initial=(15, 30), goal=(130, 30), obstacles=(), **kwds):\n",
    "        Problem.__init__(self, initial=initial, goal=goal, \n",
    "                         obstacles=set(obstacles) - {initial, goal}, **kwds)\n",
    "\n",
    "    directions = [(-1, -1), (0, -1), (1, -1),\n",
    "                  (-1, 0),           (1,  0),\n",
    "                  (-1, +1), (0, +1), (1, +1)]\n",
    "    \n",
    "    def step_cost(self, s, action, s1): return straight_line_distance(s, s1)\n",
    "    \n",
    "    def h(self, node): return straight_line_distance(node.state, self.goal)\n",
    "                  \n",
    "    def result(self, state, action): \n",
    "        \"Both states and actions are represented by (x, y) pairs.\"\n",
    "        return action if action not in self.obstacles else state\n",
    "    \n",
    "    def actions(self, state):\n",
    "        \"\"\"You can move one cell in any of `directions` to a non-obstacle cell.\"\"\"\n",
    "        x, y = state\n",
    "        return {(x + dx, y + dy) for (dx, dy) in self.directions} - self.obstacles\n",
    "    \n",
    "class ErraticVacuum(Problem):\n",
    "    def actions(self, state): \n",
    "        return ['suck', 'forward', 'backward']\n",
    "    \n",
    "    def results(self, state, action): return self.table[action][state]\n",
    "    \n",
    "    table = dict(suck=    {1:{5,7}, 2:{4,8}, 3:{7}, 4:{2,4}, 5:{1,5}, 6:{8}, 7:{3,7}, 8:{6,8}},\n",
    "                 forward= {1:{2}, 2:{2}, 3:{4}, 4:{4}, 5:{6}, 6:{6}, 7:{8}, 8:{8}},\n",
    "                 backward={1:{1}, 2:{1}, 3:{3}, 4:{3}, 5:{5}, 6:{5}, 7:{7}, 8:{7}})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some grid routing problems\n",
    "\n",
    "# The following can be used to create obstacles:\n",
    "    \n",
    "def random_lines(X=range(15, 130), Y=range(60), N=150, lengths=range(6, 12)):\n",
    "    \"\"\"The set of cells in N random lines of the given lengths.\"\"\"\n",
    "    result = set()\n",
    "    for _ in range(N):\n",
    "        x, y = random.choice(X), random.choice(Y)\n",
    "        dx, dy = random.choice(((0, 1), (1, 0)))\n",
    "        result |= line(x, y, dx, dy, random.choice(lengths))\n",
    "    return result\n",
    "\n",
    "def line(x, y, dx, dy, length):\n",
    "    \"\"\"A line of `length` cells starting at (x, y) and going in (dx, dy) direction.\"\"\"\n",
    "    return {(x + i * dx, y + i * dy) for i in range(length)}\n",
    "\n",
    "random.seed(42) # To make this reproducible\n",
    "\n",
    "frame = line(-10, 20, 0, 1, 20) | line(150, 20, 0, 1, 20)\n",
    "cup = line(102, 44, -1, 0, 15) | line(102, 20, -1, 0, 20) | line(102, 44, 0, -1, 24)\n",
    "\n",
    "d1 = GridProblem(obstacles=random_lines(N=100) | frame)\n",
    "d2 = GridProblem(obstacles=random_lines(N=150) | frame)\n",
    "d3 = GridProblem(obstacles=random_lines(N=200) | frame)\n",
    "d4 = GridProblem(obstacles=random_lines(N=250) | frame)\n",
    "d5 = GridProblem(obstacles=random_lines(N=300) | frame)\n",
    "d6 = GridProblem(obstacles=cup | frame)\n",
    "d7 = GridProblem(obstacles=cup | frame | line(50, 35, 0, -1, 10) | line(60, 37, 0, -1, 17) | line(70, 31, 0, -1, 19))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 8 Puzzle Problems\n",
    "\n",
    "![](https://ece.uwaterloo.ca/~dwharder/aads/Algorithms/N_puzzles/images/puz3.png)\n",
    "\n",
    "A sliding block puzzle where you can swap the blank with an adjacent piece, trying to reach a goal configuration. The cells are numbered 0 to 8, starting at the top left and going row by row left to right. The pieces are numebred 1 to 8, with 0 representing the blank. An action is the cell index number that is to be swapped with the blank (*not* the actual number to be swapped but the index into the state). So the diagram above left is the state `(5, 2, 7, 8, 4, 0, 1, 3, 6)`, and the action is `8`, because the cell number 8 (the 9th or last cell, the `6` in the bottom right) is swapped with the blank.\n",
    "\n",
    "There are two disjoint sets of states that cannot be reached from each other. One set has an even number of \"inversions\"; the other has an odd number. An inversion is when a piece in the state is larger than a piece that follows it.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "class EightPuzzle(Problem):\n",
    "    \"\"\" The problem of sliding tiles numbered from 1 to 8 on a 3x3 board,\n",
    "    where one of the squares is a blank, trying to reach a goal configuration.\n",
    "    A board state is represented as a tuple of length 9, where the element at index i \n",
    "    represents the tile number at index i, or 0 if for the empty square, e.g. the goal:\n",
    "        1 2 3\n",
    "        4 5 6 ==> (1, 2, 3, 4, 5, 6, 7, 8, 0)\n",
    "        7 8 _\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, initial, goal=(0, 1, 2, 3, 4, 5, 6, 7, 8)):\n",
    "        assert inversions(initial) % 2 == inversions(goal) % 2 # Parity check\n",
    "        self.initial, self.goal = initial, goal\n",
    "    \n",
    "    def actions(self, state):\n",
    "        \"\"\"The indexes of the squares that the blank can move to.\"\"\"\n",
    "        moves = ((1, 3),    (0, 2, 4),    (1, 5),\n",
    "                 (0, 4, 6), (1, 3, 5, 7), (2, 4, 8),\n",
    "                 (3, 7),    (4, 6, 8),    (7, 5))\n",
    "        blank = state.index(0)\n",
    "        return moves[blank]\n",
    "    \n",
    "    def result(self, state, action):\n",
    "        \"\"\"Swap the blank with the square numbered `action`.\"\"\"\n",
    "        s = list(state)\n",
    "        blank = state.index(0)\n",
    "        s[action], s[blank] = s[blank], s[action]\n",
    "        return tuple(s)\n",
    "    \n",
    "    def h1(self, node):\n",
    "        \"\"\"The misplaced tiles heuristic.\"\"\"\n",
    "        return hamming_distance(node.state, self.goal)\n",
    "    \n",
    "    def h2(self, node):\n",
    "        \"\"\"The Manhattan heuristic.\"\"\"\n",
    "        X = (0, 1, 2, 0, 1, 2, 0, 1, 2)\n",
    "        Y = (0, 0, 0, 1, 1, 1, 2, 2, 2)\n",
    "        return sum(abs(X[s] - X[g]) + abs(Y[s] - Y[g])\n",
    "                   for (s, g) in zip(node.state, self.goal) if s != 0)\n",
    "    \n",
    "    h = h2\n",
    "    \n",
    "    \n",
    "def hamming_distance(A, B):\n",
    "    \"Number of positions where vectors A and B are different.\"\n",
    "    return sum(a != b for a, b in zip(A, B))\n",
    "    \n",
    "\n",
    "def inversions(board):\n",
    "    \"The number of times a piece is a smaller number than a following piece.\"\n",
    "    return sum((a > b and a != 0 and b != 0) for (a, b) in combinations(board, 2))\n",
    "    \n",
    "    \n",
    "def board8(board, fmt=(3 * '{} {} {}\\n')):\n",
    "    \"A string representing an 8-puzzle board\"\n",
    "    return fmt.format(*board).replace('0', '_')\n",
    "\n",
    "class Board(defaultdict):\n",
    "    empty = '.'\n",
    "    off = '#'\n",
    "    def __init__(self, board=None, width=8, height=8, to_move=None, **kwds):\n",
    "        if board is not None:\n",
    "            self.update(board)\n",
    "            self.width, self.height = (board.width, board.height) \n",
    "        else:\n",
    "            self.width, self.height = (width, height)\n",
    "        self.to_move = to_move\n",
    "\n",
    "    def __missing__(self, key):\n",
    "        x, y = key\n",
    "        if x < 0 or x >= self.width or y < 0 or y >= self.height:\n",
    "            return self.off\n",
    "        else:\n",
    "            return self.empty\n",
    "        \n",
    "    def __repr__(self):\n",
    "        def row(y): return ' '.join(self[x, y] for x in range(self.width))\n",
    "        return '\\n'.join(row(y) for y in range(self.height))\n",
    "            \n",
    "    def __hash__(self): \n",
    "        return hash(tuple(sorted(self.items()))) + hash(self.to_move)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some specific EightPuzzle problems\n",
    "\n",
    "e1 = EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8))\n",
    "e2 = EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0))\n",
    "e3 = EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6))\n",
    "e4 = EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1))\n",
    "e5 = EightPuzzle((8, 6, 7, 2, 5, 4, 3, 0, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 4 2\n",
      "_ 7 5\n",
      "3 6 8\n",
      "\n",
      "1 4 2\n",
      "3 7 5\n",
      "_ 6 8\n",
      "\n",
      "1 4 2\n",
      "3 7 5\n",
      "6 _ 8\n",
      "\n",
      "1 4 2\n",
      "3 _ 5\n",
      "6 7 8\n",
      "\n",
      "1 _ 2\n",
      "3 4 5\n",
      "6 7 8\n",
      "\n",
      "_ 1 2\n",
      "3 4 5\n",
      "6 7 8\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Solve an 8 puzzle problem and print out each state\n",
    "\n",
    "for s in path_states(astar_search(e1)):\n",
    "    print(board8(s))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Water Pouring Problems\n",
    "\n",
    "![](http://puzzles.nigelcoldwell.co.uk/images/water22.png)\n",
    "\n",
    "In a [water pouring problem](https://en.wikipedia.org/wiki/Water_pouring_puzzle) you are given a collection of jugs, each of which has a size (capacity) in, say, litres, and a current level of water (in litres). The goal is to measure out a certain level of water; it can appear in any of the jugs. For example, in the movie *Die Hard 3*, the heroes were faced with the task of making exactly 4 gallons from jugs of size 5 gallons and 3 gallons.) A state is represented by a tuple of current water levels, and the available actions are:\n",
    "- `(Fill, i)`: fill the `i`th jug all the way to the top (from a tap with unlimited water).\n",
    "- `(Dump, i)`: dump all the water out of the `i`th jug.\n",
    "- `(Pour, i, j)`: pour water from the `i`th jug into the `j`th jug until either the jug `i` is empty, or jug `j` is full, whichever comes first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PourProblem(Problem):\n",
    "    \"\"\"Problem about pouring water between jugs to achieve some water level.\n",
    "    Each state is a tuples of water levels. In the initialization, also provide a tuple of \n",
    "    jug sizes, e.g. PourProblem(initial=(0, 0), goal=4, sizes=(5, 3)), \n",
    "    which means two jugs of sizes 5 and 3, initially both empty, with the goal\n",
    "    of getting a level of 4 in either jug.\"\"\"\n",
    "    \n",
    "    def actions(self, state):\n",
    "        \"\"\"The actions executable in this state.\"\"\"\n",
    "        jugs = range(len(state))\n",
    "        return ([('Fill', i)    for i in jugs if state[i] < self.sizes[i]] +\n",
    "                [('Dump', i)    for i in jugs if state[i]] +\n",
    "                [('Pour', i, j) for i in jugs if state[i] for j in jugs if i != j])\n",
    "\n",
    "    def result(self, state, action):\n",
    "        \"\"\"The state that results from executing this action in this state.\"\"\"\n",
    "        result = list(state)\n",
    "        act, i, *_ = action\n",
    "        if act == 'Fill':   # Fill i to capacity\n",
    "            result[i] = self.sizes[i]\n",
    "        elif act == 'Dump': # Empty i\n",
    "            result[i] = 0\n",
    "        elif act == 'Pour': # Pour from i into j\n",
    "            j = action[2]\n",
    "            amount = min(state[i], self.sizes[j] - state[j])\n",
    "            result[i] -= amount\n",
    "            result[j] += amount\n",
    "        return tuple(result)\n",
    "\n",
    "    def is_goal(self, state):\n",
    "        \"\"\"True if the goal level is in any one of the jugs.\"\"\"\n",
    "        return self.goal in state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a `GreenPourProblem`, the states and actions are the same, but the path cost is not the number of steps, but rather the total amount of water that flows from the tap during *Fill* actions. (There is an issue that non-*Fill* actions have 0 cost, which in general can lead to indefinitely long solutions, but in this problem there is a finite number of states, so we're ok.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GreenPourProblem(PourProblem): \n",
    "    \"\"\"A PourProblem in which we count not the steps, but the amount of water used.\"\"\"\n",
    "    def step_cost(self, s, action, s1):\n",
    "        \"The cost is the amount of water used in a fill.\"\n",
    "        act, i, *_ = action\n",
    "        return self.sizes[i] - s[i] if act == 'Fill' else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some specific PourProblems\n",
    "\n",
    "p1 = PourProblem((1, 1, 1), 13, sizes=(2, 16, 32))\n",
    "p2 = PourProblem((0, 0, 0), 21, sizes=(8, 11, 31))\n",
    "p3 = PourProblem((0, 0),     8, sizes=(7,9))\n",
    "p4 = PourProblem((0, 0, 0), 21, sizes=(8, 11, 31))\n",
    "p5 = PourProblem((0, 0),     4, sizes=(3, 5))\n",
    "\n",
    "g1 = GreenPourProblem((1, 1, 1), 13, sizes=(2, 16, 32))\n",
    "g2 = GreenPourProblem((0, 0, 0), 21, sizes=(8, 11, 31))\n",
    "g3 = GreenPourProblem((0, 0),     8, sizes=(7,9))\n",
    "g4 = GreenPourProblem((0, 0, 0), 21, sizes=(8, 11, 31))\n",
    "g5 = GreenPourProblem((0, 0),     4, sizes=(3, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([('Fill', 1), ('Pour', 1, 0), ('Dump', 0), ('Pour', 1, 0)],\n",
       " [(1, 1, 1), (1, 16, 1), (2, 15, 1), (0, 15, 1), (2, 13, 1)])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solve the PourProblem of getting 13 in some jug, and show the actions and states\n",
    "soln = breadth_first_search(p1)\n",
    "path_actions(soln), path_states(soln)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pancake Sorting Problems\n",
    "\n",
    "Given a stack of pancakes of various sizes, can you sort them into a stack of decreasing sizes, largest on bottom to smallest on top? You have a spatula with which you can flip the top `i` pancakes. This is shown below for `i = 3`; on the top the spatula grabs the first three pancakes; on the bottom we see them flipped:\n",
    "\n",
    "\n",
    "![](https://upload.wikimedia.org/wikipedia/commons/0/0f/Pancake_sort_operation.png)\n",
    "\n",
    "How many flips will it take to get the whole stack sorted? This is an interesting [problem](https://en.wikipedia.org/wiki/Pancake_sorting) that Bill Gates has [written about](https://people.eecs.berkeley.edu/~christos/papers/Bounds%20For%20Sorting%20By%20Prefix%20Reversal.pdf). A reasonable heuristic for this problem is the *gap heuristic*: if we look at neighboring pancakes, if, say, the 2nd smallest is next to the 3rd smallest, that's good; they should stay next to each other. But if the 2nd smallest is next to the 4th smallest, that's bad: we will require at least one move to separate them and insert the 3rd smallest between them. The gap heuristic counts the number of neighbors that have a gap like this. In our specification of the problem, pancakes are ranked by size: the smallest is `1`, the 2nd smallest `2`, and so on, and the representation of a state is a tuple of these rankings, from the top to the bottom pancake. Thus the goal state is always `(1, 2, ..., `*n*`)` and the initial state in the diagram above is `(2, 1, 4, 6, 3, 5)`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PancakeProblem(Problem):\n",
    "    \"\"\"A PancakeProblem the goal is always `tuple(range(1, n+1))`, where the\n",
    "    initial state is a permutation of `range(1, n+1)`. An act is the index `i` \n",
    "    of the top `i` pancakes that will be flipped.\"\"\"\n",
    "    \n",
    "    def __init__(self, initial): \n",
    "        self.initial, self.goal = tuple(initial), tuple(sorted(initial))\n",
    "    \n",
    "    def actions(self, state): return range(2, len(state) + 1)\n",
    "\n",
    "    def result(self, state, i): return state[:i][::-1] + state[i:]\n",
    "    \n",
    "    def h(self, node):\n",
    "        \"The gap heuristic.\"\n",
    "        s = node.state\n",
    "        return sum(abs(s[i] - s[i - 1]) > 1 for i in range(1, len(s)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "c0 = PancakeProblem((2, 1, 4, 6, 3, 5))\n",
    "c1 = PancakeProblem((4, 6, 2, 5, 1, 3))\n",
    "c2 = PancakeProblem((1, 3, 7, 5, 2, 6, 4))\n",
    "c3 = PancakeProblem((1, 7, 2, 6, 3, 5, 4))\n",
    "c4 = PancakeProblem((1, 3, 5, 7, 9, 2, 4, 6, 8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(2, 1, 4, 6, 3, 5),\n",
       " (6, 4, 1, 2, 3, 5),\n",
       " (5, 3, 2, 1, 4, 6),\n",
       " (4, 1, 2, 3, 5, 6),\n",
       " (3, 2, 1, 4, 5, 6),\n",
       " (1, 2, 3, 4, 5, 6)]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solve a pancake problem\n",
    "path_states(astar_search(c0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Jumping Frogs Puzzle\n",
    "\n",
    "In this puzzle (which also can be played as a two-player game), the initial state is a line of squares, with N pieces of one kind on the left, then one empty square, then N pieces of another kind on the right. The diagram below uses 2 blue toads and 2 red frogs; we will represent this as the string `'LL.RR'`. The goal is to swap the pieces, arriving at `'RR.LL'`. An `'L'` piece moves left-to-right, either sliding one space ahead to an empty space, or two spaces ahead if that space is empty and if there is an `'R'` in between to hop over. The `'R'` pieces move right-to-left analogously. An action will be an `(i, j)` pair meaning to swap the pieces at those indexes. The set of actions for the N = 2 position below is `{(1, 2), (3, 2)}`, meaning either the blue toad in position 1 or the red frog in position 3 can swap places with the blank in position 2.\n",
    "\n",
    "![](https://upload.wikimedia.org/wikipedia/commons/2/2f/ToadsAndFrogs.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "class JumpingPuzzle(Problem):\n",
    "    \"\"\"Try to exchange L and R by moving one ahead or hopping two ahead.\"\"\"\n",
    "    def __init__(self, N=2):\n",
    "        self.initial = N*'L' + '.' + N*'R'\n",
    "        self.goal = self.initial[::-1]\n",
    "        \n",
    "    def actions(self, state):\n",
    "        \"\"\"Find all possible move or hop moves.\"\"\"\n",
    "        idxs = range(len(state))\n",
    "        return ({(i, i + 1) for i in idxs if state[i:i+2] == 'L.'}   # Slide\n",
    "               |{(i, i + 2) for i in idxs if state[i:i+3] == 'LR.'}  # Hop\n",
    "               |{(i + 1, i) for i in idxs if state[i:i+2] == '.R'}   # Slide\n",
    "               |{(i + 2, i) for i in idxs if state[i:i+3] == '.LR'}) # Hop\n",
    "\n",
    "    def result(self, state, action):\n",
    "        \"\"\"An action (i, j) means swap the pieces at positions i and j.\"\"\"\n",
    "        i, j = action\n",
    "        result = list(state)\n",
    "        result[i], result[j] = state[j], state[i]\n",
    "        return ''.join(result)\n",
    "    \n",
    "    def h(self, node): return hamming_distance(node.state, self.goal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(1, 2), (3, 2)}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JumpingPuzzle(N=2).actions('LL.RR')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['LLL.RRR',\n",
       " 'LLLR.RR',\n",
       " 'LL.RLRR',\n",
       " 'L.LRLRR',\n",
       " 'LRL.LRR',\n",
       " 'LRLRL.R',\n",
       " 'LRLRLR.',\n",
       " 'LRLR.RL',\n",
       " 'LR.RLRL',\n",
       " '.RLRLRL',\n",
       " 'R.LRLRL',\n",
       " 'RRL.LRL',\n",
       " 'RRLRL.L',\n",
       " 'RRLR.LL',\n",
       " 'RR.RLLL',\n",
       " 'RRR.LLL']"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "j3 = JumpingPuzzle(N=3)\n",
    "j9 = JumpingPuzzle(N=9)\n",
    "path_states(astar_search(j3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reporting Summary Statistics on Search Algorithms\n",
    "\n",
    "Now let's gather some metrics on how well each algorithm does.  We'll use `CountCalls` to wrap a `Problem` object in such a way that calls to its methods are delegated to the original problem, but each call increments a counter. Once we've solved the problem, we print out summary statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "class CountCalls:\n",
    "    \"\"\"Delegate all attribute gets to the object, and count them in ._counts\"\"\"\n",
    "    def __init__(self, obj):\n",
    "        self._object = obj\n",
    "        self._counts = Counter()\n",
    "        \n",
    "    def __getattr__(self, attr):\n",
    "        \"Delegate to the original object, after incrementing a counter.\"\n",
    "        self._counts[attr] += 1\n",
    "        return getattr(self._object, attr)\n",
    "\n",
    "        \n",
    "def report(searchers, problems, verbose=True):\n",
    "    \"\"\"Show summary statistics for each searcher (and on each problem unless verbose is false).\"\"\"\n",
    "    for searcher in searchers:\n",
    "        print(searcher.__name__ + ':')\n",
    "        total_counts = Counter()\n",
    "        for p in problems:\n",
    "            prob   = CountCalls(p)\n",
    "            soln   = searcher(prob)\n",
    "            counts = prob._counts; \n",
    "            counts.update(steps=len(soln), cost=soln.path_cost)\n",
    "            total_counts += counts\n",
    "            if verbose: report_counts(counts, str(p)[:40])\n",
    "        report_counts(total_counts, 'TOTAL\\n')\n",
    "        \n",
    "def report_counts(counts, name):\n",
    "    \"\"\"Print one line of the counts report.\"\"\"\n",
    "    print('{:9,d} nodes |{:7,d} goal |{:5.0f} cost |{:3d} steps | {}'.format(\n",
    "          counts['result'], counts['is_goal'], counts['cost'], counts['steps'], name))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a tiny report for uniform-cost search on the jug pouring problems:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "uniform_cost_search:\n",
      "      948 nodes |    109 goal |    4 cost |  4 steps | PourProblem((1, 1, 1), 13)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "      126 nodes |     31 goal |   14 cost | 14 steps | PourProblem((0, 0), 8)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "       54 nodes |     15 goal |    6 cost |  6 steps | PourProblem((0, 0), 4)\n",
      "    8,142 nodes |    935 goal |   42 cost | 42 steps | TOTAL\n",
      "\n"
     ]
    }
   ],
   "source": [
    "report([uniform_cost_search], [p1, p2, p3, p4, p5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "uniform_cost_search:\n",
      "      948 nodes |    109 goal |    4 cost |  4 steps | PourProblem((1, 1, 1), 13)\n",
      "    1,696 nodes |    190 goal |   10 cost | 15 steps | GreenPourProblem((1, 1, 1), 13)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "      126 nodes |     31 goal |   14 cost | 14 steps | PourProblem((0, 0), 8)\n",
      "      126 nodes |     31 goal |   35 cost | 16 steps | GreenPourProblem((0, 0), 8)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "    3,600 nodes |    721 goal |    7 cost |  7 steps | PancakeProblem((4, 6, 2, 5, 1, 3), (1, 2\n",
      "   30,234 nodes |  5,040 goal |    8 cost |  8 steps | PancakeProblem((1, 3, 7, 5, 2, 6, 4), (1\n",
      "   19,608 nodes |  3,269 goal |    6 cost |  6 steps | PancakeProblem((1, 7, 2, 6, 3, 5, 4), (1\n",
      "   79,084 nodes | 11,926 goal |  174 cost |127 steps | TOTAL\n",
      "\n",
      "breadth_first_search:\n",
      "      596 nodes |    597 goal |    4 cost |  4 steps | PourProblem((1, 1, 1), 13)\n",
      "      596 nodes |    597 goal |   15 cost |  4 steps | GreenPourProblem((1, 1, 1), 13)\n",
      "    2,621 nodes |  2,622 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    2,621 nodes |  2,622 goal |   32 cost |  9 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "      122 nodes |    123 goal |   14 cost | 14 steps | PourProblem((0, 0), 8)\n",
      "      122 nodes |    123 goal |   36 cost | 14 steps | GreenPourProblem((0, 0), 8)\n",
      "    2,621 nodes |  2,622 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    2,621 nodes |  2,622 goal |   32 cost |  9 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "    2,621 nodes |  2,622 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    2,621 nodes |  2,622 goal |   32 cost |  9 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "    2,956 nodes |  2,957 goal |    7 cost |  7 steps | PancakeProblem((4, 6, 2, 5, 1, 3), (1, 2\n",
      "   25,951 nodes | 25,952 goal |    8 cost |  8 steps | PancakeProblem((1, 3, 7, 5, 2, 6, 4), (1\n",
      "    5,981 nodes |  5,982 goal |    6 cost |  6 steps | PancakeProblem((1, 7, 2, 6, 3, 5, 4), (1\n",
      "   52,050 nodes | 52,063 goal |  213 cost |111 steps | TOTAL\n",
      "\n"
     ]
    }
   ],
   "source": [
    "report((uniform_cost_search, breadth_first_search), \n",
    "       (p1, g1, p2, g2, p3, g3, p4, g4, p4, g4, c1, c2, c3)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparing heuristics\n",
    "\n",
    "First, let's look at the eight puzzle problems, and compare three different heuristics the Manhattan heuristic, the less informative misplaced tiles heuristic, and the uninformative *h* = 0 heuristic used by uniform-cost search:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "uniform_cost_search:\n",
      "      143 nodes |     53 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "  217,902 nodes | 80,379 goal |   22 cost | 22 steps | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "  307,346 nodes |114,678 goal |   23 cost | 23 steps | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "  440,722 nodes |164,234 goal |   26 cost | 26 steps | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "  461,018 nodes |172,126 goal |   27 cost | 27 steps | EightPuzzle((8, 6, 7, 2, 5, 4, 3, 0, 1),\n",
      "1,427,131 nodes |531,470 goal |  103 cost |103 steps | TOTAL\n",
      "\n",
      "astar_misplaced_tiles:\n",
      "       17 nodes |      7 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "   23,409 nodes |  8,727 goal |   22 cost | 22 steps | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "   38,635 nodes | 14,434 goal |   23 cost | 23 steps | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "  124,328 nodes | 46,554 goal |   26 cost | 26 steps | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "  156,114 nodes | 58,476 goal |   27 cost | 27 steps | EightPuzzle((8, 6, 7, 2, 5, 4, 3, 0, 1),\n",
      "  342,503 nodes |128,198 goal |  103 cost |103 steps | TOTAL\n",
      "\n",
      "astar_search:\n",
      "       15 nodes |      6 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "    3,616 nodes |  1,350 goal |   22 cost | 22 steps | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "    5,376 nodes |  2,011 goal |   23 cost | 23 steps | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "   10,836 nodes |  4,087 goal |   26 cost | 26 steps | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "   11,672 nodes |  4,418 goal |   27 cost | 27 steps | EightPuzzle((8, 6, 7, 2, 5, 4, 3, 0, 1),\n",
      "   31,515 nodes | 11,872 goal |  103 cost |103 steps | TOTAL\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def astar_misplaced_tiles(problem): return astar_search(problem, h=problem.h1)\n",
    "\n",
    "report([uniform_cost_search, astar_misplaced_tiles, astar_search], \n",
    "       [e1, e2, e3, e4, e5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that all three algorithms get cost-optimal solutions, but the better the heuristic, the fewer nodes explored. \n",
    "Compared to the uninformed search, the misplaced tiles heuristic explores about 1/4 the number of nodes, and the Manhattan heuristic needs just 2%.\n",
    "\n",
    "Next, we can show the value of the gap heuristic for pancake sorting problems:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "astar_search:\n",
      "    1,290 nodes |    259 goal |    7 cost |  7 steps | PancakeProblem((4, 6, 2, 5, 1, 3), (1, 2\n",
      "    3,810 nodes |    636 goal |    8 cost |  8 steps | PancakeProblem((1, 3, 7, 5, 2, 6, 4), (1\n",
      "      300 nodes |     51 goal |    6 cost |  6 steps | PancakeProblem((1, 7, 2, 6, 3, 5, 4), (1\n",
      "    2,256 nodes |    283 goal |    9 cost |  9 steps | PancakeProblem((1, 3, 5, 7, 9, 2, 4, 6, \n",
      "    7,656 nodes |  1,229 goal |   30 cost | 30 steps | TOTAL\n",
      "\n",
      "uniform_cost_search:\n",
      "    3,600 nodes |    721 goal |    7 cost |  7 steps | PancakeProblem((4, 6, 2, 5, 1, 3), (1, 2\n",
      "   30,234 nodes |  5,040 goal |    8 cost |  8 steps | PancakeProblem((1, 3, 7, 5, 2, 6, 4), (1\n",
      "   19,608 nodes |  3,269 goal |    6 cost |  6 steps | PancakeProblem((1, 7, 2, 6, 3, 5, 4), (1\n",
      "2,470,560 nodes |308,821 goal |    9 cost |  9 steps | PancakeProblem((1, 3, 5, 7, 9, 2, 4, 6, \n",
      "2,524,002 nodes |317,851 goal |   30 cost | 30 steps | TOTAL\n",
      "\n"
     ]
    }
   ],
   "source": [
    "report([astar_search, uniform_cost_search], [c1, c2, c3, c4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to explore 300 times more nodes without the heuristic.\n",
    "\n",
    "# Comparing graph search and tree search\n",
    "\n",
    "Keeping the *reached* table in `best_first_search` allows us to do a graph search, where we notice when we reach a state by two different paths, rather than a tree search, where we have duplicated effort. The *reached* table consumes space and also saves time. How much time? In part it depends on how good the heuristics are at focusing the search.  Below we show that on some pancake and eight puzzle problems, the tree search expands roughly twice as many nodes (and thus takes roughly twice as much time):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "astar_search:\n",
      "       15 nodes |      6 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "    3,616 nodes |  1,350 goal |   22 cost | 22 steps | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "    5,376 nodes |  2,011 goal |   23 cost | 23 steps | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "   10,836 nodes |  4,087 goal |   26 cost | 26 steps | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "       15 nodes |      6 goal |  418 cost |  4 steps | RouteProblem('A', 'B')\n",
      "       35 nodes |     16 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       34 nodes |     15 goal |  805 cost |  8 steps | RouteProblem('E', 'T')\n",
      "       22 nodes |     10 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "   19,949 nodes |  7,501 goal | 2654 cost |102 steps | TOTAL\n",
      "\n",
      "astar_tree_search:\n",
      "       15 nodes |      6 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "    5,384 nodes |  2,000 goal |   22 cost | 22 steps | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "    9,116 nodes |  3,404 goal |   23 cost | 23 steps | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "   19,084 nodes |  7,185 goal |   26 cost | 26 steps | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "       15 nodes |      6 goal |  418 cost |  4 steps | RouteProblem('A', 'B')\n",
      "       47 nodes |     19 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       46 nodes |     18 goal |  805 cost |  8 steps | RouteProblem('E', 'T')\n",
      "       24 nodes |     10 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "   33,731 nodes | 12,648 goal | 2654 cost |102 steps | TOTAL\n",
      "\n"
     ]
    }
   ],
   "source": [
    "report([astar_search, astar_tree_search], [e1, e2, e3, e4, r1, r2, r3, r4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparing different weighted search values\n",
    "\n",
    "Below we report on problems using these four algorithms:\n",
    "\n",
    "|Algorithm|*f*|Optimality|\n",
    "|:---------|---:|:----------:|\n",
    "|Greedy best-first search | *f = h*|nonoptimal|\n",
    "|Extra weighted A* search | *f = g + 2 &times; h*|nonoptimal|\n",
    "|Weighted A* search | *f = g + 1.4 &times; h*|nonoptimal|\n",
    "|A* search | *f = g + h*|optimal|\n",
    "|Uniform-cost search | *f = g*|optimal|\n",
    "\n",
    "We will see that greedy best-first search (which ranks nodes solely by the heuristic) explores the fewest number of nodes, but has the highest path costs. Weighted A* search explores twice as many nodes (on this problem set) but gets 10% better path costs. A* is optimal, but explores more nodes, and uniform-cost is also optimal, but explores an order of magnitude more nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "greedy_bfs:\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "        9 nodes |      4 goal |  450 cost |  3 steps | RouteProblem('A', 'B')\n",
      "       30 nodes |     13 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       19 nodes |      8 goal |  837 cost |  7 steps | RouteProblem('E', 'T')\n",
      "       14 nodes |      6 goal |  572 cost |  5 steps | RouteProblem('O', 'M')\n",
      "       15 nodes |      6 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "      909 nodes |    138 goal |  136 cost |121 steps | GridProblem((15, 30), (130, 30))\n",
      "      974 nodes |    147 goal |  152 cost |131 steps | GridProblem((15, 30), (130, 30))\n",
      "    5,146 nodes |  4,984 goal |   99 cost | 99 steps | JumpingPuzzle('LLLLLLLLL.RRRRRRRRR', 'RR\n",
      "    1,176 nodes |    426 goal |   38 cost | 38 steps | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "    1,429 nodes |    258 goal |  164 cost |150 steps | GridProblem((15, 30), (130, 30))\n",
      "    1,899 nodes |    342 goal |  153 cost |129 steps | GridProblem((15, 30), (130, 30))\n",
      "   18,239 nodes |  2,439 goal |  134 cost |126 steps | GridProblem((15, 30), (130, 30))\n",
      "   18,329 nodes |  2,460 goal |  152 cost |135 steps | GridProblem((15, 30), (130, 30))\n",
      "      280 nodes |    106 goal |   33 cost | 33 steps | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "    1,000 nodes |    363 goal |   42 cost | 42 steps | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "   49,468 nodes | 11,701 goal | 3877 cost |1033 steps | TOTAL\n",
      "\n",
      "extra_weighted_astar_search:\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "        9 nodes |      4 goal |  450 cost |  3 steps | RouteProblem('A', 'B')\n",
      "       30 nodes |     13 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       23 nodes |      9 goal |  805 cost |  8 steps | RouteProblem('E', 'T')\n",
      "       18 nodes |      8 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "       15 nodes |      6 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "    1,575 nodes |    239 goal |  136 cost |119 steps | GridProblem((15, 30), (130, 30))\n",
      "    1,384 nodes |    231 goal |  133 cost |119 steps | GridProblem((15, 30), (130, 30))\n",
      "   10,990 nodes | 10,660 goal |   99 cost | 99 steps | JumpingPuzzle('LLLLLLLLL.RRRRRRRRR', 'RR\n",
      "    1,778 nodes |    655 goal |   24 cost | 24 steps | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "    9,287 nodes |  1,413 goal |  163 cost |140 steps | GridProblem((15, 30), (130, 30))\n",
      "    1,354 nodes |    228 goal |  134 cost |118 steps | GridProblem((15, 30), (130, 30))\n",
      "   16,024 nodes |  2,098 goal |  129 cost |117 steps | GridProblem((15, 30), (130, 30))\n",
      "   16,950 nodes |  2,237 goal |  140 cost |123 steps | GridProblem((15, 30), (130, 30))\n",
      "    1,883 nodes |    700 goal |   25 cost | 25 steps | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "    1,323 nodes |    494 goal |   30 cost | 30 steps | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "   62,643 nodes | 18,996 goal | 3628 cost |944 steps | TOTAL\n",
      "\n",
      "weighted_astar_search:\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "        9 nodes |      4 goal |  450 cost |  3 steps | RouteProblem('A', 'B')\n",
      "       33 nodes |     15 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       29 nodes |     12 goal |  805 cost |  8 steps | RouteProblem('E', 'T')\n",
      "       18 nodes |      8 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "       15 nodes |      6 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "    1,631 nodes |    236 goal |  128 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "    1,706 nodes |    275 goal |  131 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "   10,990 nodes | 10,660 goal |   99 cost | 99 steps | JumpingPuzzle('LLLLLLLLL.RRRRRRRRR', 'RR\n",
      "    2,372 nodes |    881 goal |   22 cost | 22 steps | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "    8,390 nodes |  1,267 goal |  154 cost |131 steps | GridProblem((15, 30), (130, 30))\n",
      "    1,400 nodes |    229 goal |  133 cost |116 steps | GridProblem((15, 30), (130, 30))\n",
      "   12,122 nodes |  1,572 goal |  124 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "   24,129 nodes |  3,141 goal |  127 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "    3,981 nodes |  1,483 goal |   25 cost | 25 steps | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "    1,996 nodes |    749 goal |   26 cost | 26 steps | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "   68,821 nodes | 20,539 goal | 3585 cost |909 steps | TOTAL\n",
      "\n",
      "astar_search:\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "       15 nodes |      6 goal |  418 cost |  4 steps | RouteProblem('A', 'B')\n",
      "       35 nodes |     16 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       34 nodes |     15 goal |  805 cost |  8 steps | RouteProblem('E', 'T')\n",
      "       22 nodes |     10 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "       15 nodes |      6 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "   26,719 nodes |  3,621 goal |  127 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "   12,938 nodes |  1,823 goal |  124 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "   10,991 nodes | 10,661 goal |   99 cost | 99 steps | JumpingPuzzle('LLLLLLLLL.RRRRRRRRR', 'RR\n",
      "    3,616 nodes |  1,350 goal |   22 cost | 22 steps | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "   62,514 nodes |  8,730 goal |  154 cost |131 steps | GridProblem((15, 30), (130, 30))\n",
      "   15,198 nodes |  2,277 goal |  133 cost |116 steps | GridProblem((15, 30), (130, 30))\n",
      "   25,311 nodes |  3,197 goal |  124 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "   32,580 nodes |  4,150 goal |  127 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "    5,376 nodes |  2,011 goal |   23 cost | 23 steps | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "   10,836 nodes |  4,087 goal |   26 cost | 26 steps | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "  206,200 nodes | 41,961 goal | 3543 cost |908 steps | TOTAL\n",
      "\n",
      "uniform_cost_search:\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "       33 nodes |     14 goal |  418 cost |  4 steps | RouteProblem('A', 'B')\n",
      "       43 nodes |     20 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       45 nodes |     21 goal |  805 cost |  8 steps | RouteProblem('E', 'T')\n",
      "       32 nodes |     13 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "      143 nodes |     53 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "  355,476 nodes | 44,987 goal |  127 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "  326,947 nodes | 41,648 goal |  124 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "   10,992 nodes | 10,662 goal |   99 cost | 99 steps | JumpingPuzzle('LLLLLLLLL.RRRRRRRRR', 'RR\n",
      "  217,902 nodes | 80,379 goal |   22 cost | 22 steps | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "  558,081 nodes | 70,738 goal |  154 cost |131 steps | GridProblem((15, 30), (130, 30))\n",
      "  370,375 nodes | 47,243 goal |  133 cost |116 steps | GridProblem((15, 30), (130, 30))\n",
      "  349,054 nodes | 43,692 goal |  124 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "  367,028 nodes | 45,974 goal |  127 cost |115 steps | GridProblem((15, 30), (130, 30))\n",
      "  307,346 nodes |114,678 goal |   23 cost | 23 steps | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "  440,722 nodes |164,234 goal |   26 cost | 26 steps | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "3,304,219 nodes |664,357 goal | 3543 cost |908 steps | TOTAL\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def extra_weighted_astar_search(problem): return weighted_astar_search(problem, weight=2)\n",
    "    \n",
    "report((greedy_bfs, extra_weighted_astar_search, weighted_astar_search, astar_search, uniform_cost_search), \n",
    "       (r0, r1, r2, r3, r4, e1, d1, d2, j9, e2, d3, d4, d6, d7, e3, e4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that greedy search expands the fewest nodes, but has the highest path costs. In contrast, A\\* gets optimal path costs, but expands 4 or 5 times more nodes. Weighted A* is a good compromise, using half the compute time as A\\*, and achieving path costs within  1% or 2% of optimal. Uniform-cost is optimal, but is an order of magnitude slower than A\\*.\n",
    "\n",
    "# Comparing  many search algorithms\n",
    "\n",
    "Finally, we compare a host of algorihms (even the slow ones) on some of the easier problems:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "astar_search:\n",
      "      948 nodes |    109 goal |    4 cost |  4 steps | PourProblem((1, 1, 1), 13)\n",
      "    1,696 nodes |    190 goal |   10 cost | 15 steps | GreenPourProblem((1, 1, 1), 13)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "      126 nodes |     31 goal |   14 cost | 14 steps | PourProblem((0, 0), 8)\n",
      "      126 nodes |     31 goal |   35 cost | 16 steps | GreenPourProblem((0, 0), 8)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "       15 nodes |      6 goal |  418 cost |  4 steps | RouteProblem('A', 'B')\n",
      "       35 nodes |     16 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       34 nodes |     15 goal |  805 cost |  8 steps | RouteProblem('E', 'T')\n",
      "       22 nodes |     10 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "       15 nodes |      6 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "   18,181 nodes |  2,105 goal | 2706 cost |118 steps | TOTAL\n",
      "\n",
      "uniform_cost_search:\n",
      "      948 nodes |    109 goal |    4 cost |  4 steps | PourProblem((1, 1, 1), 13)\n",
      "    1,696 nodes |    190 goal |   10 cost | 15 steps | GreenPourProblem((1, 1, 1), 13)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "      126 nodes |     31 goal |   14 cost | 14 steps | PourProblem((0, 0), 8)\n",
      "      126 nodes |     31 goal |   35 cost | 16 steps | GreenPourProblem((0, 0), 8)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "       33 nodes |     14 goal |  418 cost |  4 steps | RouteProblem('A', 'B')\n",
      "       43 nodes |     20 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       45 nodes |     21 goal |  805 cost |  8 steps | RouteProblem('E', 'T')\n",
      "       32 nodes |     13 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "      143 nodes |     53 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "   18,356 nodes |  2,173 goal | 2706 cost |118 steps | TOTAL\n",
      "\n",
      "breadth_first_search:\n",
      "      596 nodes |    597 goal |    4 cost |  4 steps | PourProblem((1, 1, 1), 13)\n",
      "      596 nodes |    597 goal |   15 cost |  4 steps | GreenPourProblem((1, 1, 1), 13)\n",
      "    2,621 nodes |  2,622 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    2,621 nodes |  2,622 goal |   32 cost |  9 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "      122 nodes |    123 goal |   14 cost | 14 steps | PourProblem((0, 0), 8)\n",
      "      122 nodes |    123 goal |   36 cost | 14 steps | GreenPourProblem((0, 0), 8)\n",
      "    2,621 nodes |  2,622 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    2,621 nodes |  2,622 goal |   32 cost |  9 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "       21 nodes |     22 goal |  450 cost |  3 steps | RouteProblem('A', 'B')\n",
      "       43 nodes |     44 goal | 1085 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       37 nodes |     38 goal |  837 cost |  7 steps | RouteProblem('E', 'T')\n",
      "       32 nodes |     33 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "       84 nodes |     85 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "   12,137 nodes | 12,151 goal | 2973 cost |101 steps | TOTAL\n",
      "\n",
      "breadth_first_bfs:\n",
      "      948 nodes |    109 goal |    4 cost |  4 steps | PourProblem((1, 1, 1), 13)\n",
      "    1,062 nodes |    124 goal |   15 cost |  4 steps | GreenPourProblem((1, 1, 1), 13)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    3,799 nodes |    425 goal |   24 cost |  9 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "      126 nodes |     31 goal |   14 cost | 14 steps | PourProblem((0, 0), 8)\n",
      "      126 nodes |     31 goal |   36 cost | 14 steps | GreenPourProblem((0, 0), 8)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    3,799 nodes |    425 goal |   24 cost |  9 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "       31 nodes |     13 goal |  450 cost |  3 steps | RouteProblem('A', 'B')\n",
      "       56 nodes |     25 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       52 nodes |     23 goal |  837 cost |  7 steps | RouteProblem('E', 'T')\n",
      "       42 nodes |     17 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "      143 nodes |     53 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "   17,198 nodes |  2,057 goal | 2782 cost |101 steps | TOTAL\n",
      "\n",
      "iterative_deepening_search:\n",
      "    6,133 nodes |  6,118 goal |    4 cost |  4 steps | PourProblem((1, 1, 1), 13)\n",
      "    6,133 nodes |  6,118 goal |   15 cost |  4 steps | GreenPourProblem((1, 1, 1), 13)\n",
      "  288,706 nodes |288,675 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "  288,706 nodes |288,675 goal |   62 cost |  9 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "    3,840 nodes |  3,824 goal |   14 cost | 14 steps | PourProblem((0, 0), 8)\n",
      "    3,840 nodes |  3,824 goal |   36 cost | 14 steps | GreenPourProblem((0, 0), 8)\n",
      "  288,706 nodes |288,675 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "  288,706 nodes |288,675 goal |   62 cost |  9 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "       27 nodes |     25 goal |  450 cost |  3 steps | RouteProblem('A', 'B')\n",
      "      167 nodes |    173 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "      117 nodes |    120 goal |  837 cost |  7 steps | RouteProblem('E', 'T')\n",
      "      108 nodes |    109 goal |  572 cost |  5 steps | RouteProblem('O', 'M')\n",
      "      116 nodes |    118 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "1,175,305 nodes |1,175,130 goal | 2985 cost |101 steps | TOTAL\n",
      "\n",
      "depth_limited_search:\n",
      "    4,433 nodes |  4,374 goal |   10 cost | 10 steps | PourProblem((1, 1, 1), 13)\n",
      "    4,433 nodes |  4,374 goal |   30 cost | 10 steps | GreenPourProblem((1, 1, 1), 13)\n",
      "   37,149 nodes | 37,106 goal |   10 cost | 10 steps | PourProblem((0, 0, 0), 21)\n",
      "   37,149 nodes | 37,106 goal |   54 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "      452 nodes |    453 goal |  inf cost |  0 steps | PourProblem((0, 0), 8)\n",
      "      452 nodes |    453 goal |  inf cost |  0 steps | GreenPourProblem((0, 0), 8)\n",
      "   37,149 nodes | 37,106 goal |   10 cost | 10 steps | PourProblem((0, 0, 0), 21)\n",
      "   37,149 nodes | 37,106 goal |   54 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "       17 nodes |      8 goal |  733 cost |  7 steps | RouteProblem('A', 'B')\n",
      "       40 nodes |     38 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       29 nodes |     23 goal |  992 cost |  9 steps | RouteProblem('E', 'T')\n",
      "       35 nodes |     29 goal |  895 cost |  7 steps | RouteProblem('O', 'M')\n",
      "      351 nodes |    349 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "  158,838 nodes |158,526 goal |  inf cost | 97 steps | TOTAL\n",
      "\n",
      "greedy_bfs:\n",
      "      948 nodes |    109 goal |    4 cost |  4 steps | PourProblem((1, 1, 1), 13)\n",
      "    1,696 nodes |    190 goal |   10 cost | 15 steps | GreenPourProblem((1, 1, 1), 13)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "      126 nodes |     31 goal |   14 cost | 14 steps | PourProblem((0, 0), 8)\n",
      "      126 nodes |     31 goal |   35 cost | 16 steps | GreenPourProblem((0, 0), 8)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "        9 nodes |      4 goal |  450 cost |  3 steps | RouteProblem('A', 'B')\n",
      "       30 nodes |     13 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       19 nodes |      8 goal |  837 cost |  7 steps | RouteProblem('E', 'T')\n",
      "       14 nodes |      6 goal |  572 cost |  5 steps | RouteProblem('O', 'M')\n",
      "       15 nodes |      6 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "   18,147 nodes |  2,089 goal | 2897 cost |116 steps | TOTAL\n",
      "\n",
      "weighted_astar_search:\n",
      "      948 nodes |    109 goal |    4 cost |  4 steps | PourProblem((1, 1, 1), 13)\n",
      "    1,696 nodes |    190 goal |   10 cost | 15 steps | GreenPourProblem((1, 1, 1), 13)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "      126 nodes |     31 goal |   14 cost | 14 steps | PourProblem((0, 0), 8)\n",
      "      126 nodes |     31 goal |   35 cost | 16 steps | GreenPourProblem((0, 0), 8)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "        9 nodes |      4 goal |  450 cost |  3 steps | RouteProblem('A', 'B')\n",
      "       33 nodes |     15 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       29 nodes |     12 goal |  805 cost |  8 steps | RouteProblem('E', 'T')\n",
      "       18 nodes |      8 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "       15 nodes |      6 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "   18,164 nodes |  2,097 goal | 2738 cost |117 steps | TOTAL\n",
      "\n",
      "extra_weighted_astar_search:\n",
      "      948 nodes |    109 goal |    4 cost |  4 steps | PourProblem((1, 1, 1), 13)\n",
      "    1,696 nodes |    190 goal |   10 cost | 15 steps | GreenPourProblem((1, 1, 1), 13)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "      126 nodes |     31 goal |   14 cost | 14 steps | PourProblem((0, 0), 8)\n",
      "      126 nodes |     31 goal |   35 cost | 16 steps | GreenPourProblem((0, 0), 8)\n",
      "    3,507 nodes |    390 goal |    9 cost |  9 steps | PourProblem((0, 0, 0), 21)\n",
      "    4,075 nodes |    455 goal |   21 cost | 10 steps | GreenPourProblem((0, 0, 0), 21)\n",
      "        0 nodes |      1 goal |    0 cost |  0 steps | RouteProblem('A', 'A')\n",
      "        9 nodes |      4 goal |  450 cost |  3 steps | RouteProblem('A', 'B')\n",
      "       30 nodes |     13 goal |  910 cost |  9 steps | RouteProblem('N', 'L')\n",
      "       23 nodes |      9 goal |  805 cost |  8 steps | RouteProblem('E', 'T')\n",
      "       18 nodes |      8 goal |  445 cost |  5 steps | RouteProblem('O', 'M')\n",
      "       15 nodes |      6 goal |    5 cost |  5 steps | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "   18,155 nodes |  2,092 goal | 2738 cost |117 steps | TOTAL\n",
      "\n"
     ]
    }
   ],
   "source": [
    "report((astar_search, uniform_cost_search,  breadth_first_search, breadth_first_bfs, \n",
    "        iterative_deepening_search, depth_limited_search, greedy_bfs, \n",
    "        weighted_astar_search, extra_weighted_astar_search), \n",
    "       (p1, g1, p2, g2, p3, g3, p4, g4, r0, r1, r2, r3, r4, e1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This confirms some of the things we already knew: A* and uniform-cost search are optimal, but the others are not. A* explores fewer nodes than uniform-cost. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizing Reached States\n",
    "\n",
    "I would like to draw a picture of the state space, marking the states that have been reached by the search.\n",
    "Unfortunately, the *reached* variable is inaccessible inside `best_first_search`, so I will define a new version of `best_first_search` that is identical except that it declares *reached* to be `global`. I can then define `plot_grid_problem` to plot the obstacles of a `GridProblem`, along with the initial and goal states, the solution path, and the states reached during a search."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def best_first_search(problem, f):\n",
    "    \"Search nodes with minimum f(node) value first; make `reached` global.\"\n",
    "    global reached # <<<<<<<<<<< Only change here\n",
    "    frontier = PriorityQueue([Node(problem.initial)], key=f)\n",
    "    reached = {}\n",
    "    while frontier:\n",
    "        node = frontier.pop()\n",
    "        if problem.is_goal(node.state):\n",
    "            return node\n",
    "        for child in expand(problem, node):\n",
    "            s = child.state\n",
    "            if s not in reached or child.path_cost < reached[s].path_cost:\n",
    "                reached[s] = child\n",
    "                frontier.add(child)\n",
    "    return failure\n",
    "\n",
    "def plot_grid_problem(grid, solution, reached=(), title='Search', show=True):\n",
    "    \"Use matplotlib to plot the grid, obstacles, solution, and reached.\"\n",
    "    plt.figure(figsize=(16, 10))\n",
    "    plt.axis('off'); plt.axis('equal')\n",
    "    plt.scatter(*transpose(grid.obstacles), marker='s', color='darkgrey')\n",
    "    plt.scatter(*transpose(reached), 1**2, marker='.', c='blue')\n",
    "    plt.scatter(*transpose(path_states(solution)), marker='s', c='blue')\n",
    "    plt.scatter(*transpose([grid.initial]), 9**2, marker='D', c='green')\n",
    "    plt.scatter(*transpose([grid.goal]), 9**2, marker='8', c='red')\n",
    "    if show: plt.show()\n",
    "    print('{} {} search: {:.1f} path cost, {:,d} states reached'\n",
    "          .format(' ' * 10, title, solution.path_cost, len(reached)))\n",
    "    \n",
    "def plots(grid, weights=(1.4, 2)): \n",
    "    \"\"\"Plot the results of 4 heuristic search algorithms for this grid.\"\"\"\n",
    "    solution = astar_search(grid)\n",
    "    plot_grid_problem(grid, solution, reached, 'A* search')\n",
    "    for weight in weights:\n",
    "        solution = weighted_astar_search(grid, weight=weight)\n",
    "        plot_grid_problem(grid, solution, reached, '(b) Weighted ({}) A* search'.format(weight))\n",
    "    solution = greedy_bfs(grid)\n",
    "    plot_grid_problem(grid, solution, reached, 'Greedy best-first search')\n",
    "    \n",
    "def transpose(matrix): return list(zip(*matrix))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           A* search search: 154.2 path cost, 7,418 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           (b) Weighted (1.4) A* search search: 154.2 path cost, 944 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           (b) Weighted (2) A* search search: 162.8 path cost, 782 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Greedy best-first search search: 164.5 path cost, 448 states reached\n"
     ]
    }
   ],
   "source": [
    "plots(d3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           A* search search: 133.0 path cost, 2,196 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           (b) Weighted (1.4) A* search search: 133.0 path cost, 440 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           (b) Weighted (2) A* search search: 134.2 path cost, 418 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Greedy best-first search search: 153.0 path cost, 502 states reached\n"
     ]
    }
   ],
   "source": [
    "plots(d4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The cost of weighted A* search\n",
    "\n",
    "Now I want to try a much simpler grid problem, `d6`, with only a few obstacles. We see that A* finds the optimal path, skirting below the obstacles. Weighterd A* with a weight of 1.4 finds the same optimal path while exploring only 1/3 the number of states. But weighted A* with weight 2 takes the slightly longer path above the obstacles, because that path allowed it to stay closer to the goal in straight-line distance, which it over-weights. And greedy best-first search has a bad showing, not deviating from its path towards the goal until it is almost inside the cup made by the obstacles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           A* search search: 124.1 path cost, 3,305 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           (b) Weighted (1.4) A* search search: 124.1 path cost, 975 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           (b) Weighted (2) A* search search: 128.6 path cost, 879 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Greedy best-first search search: 133.9 path cost, 758 states reached\n"
     ]
    }
   ],
   "source": [
    "plots(d6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next problem, `d7`, we see a similar story. the optimal path found by A*, and we see that again weighted A* with weight 1.4 does great and with weight 2 ends up erroneously going below the first two barriers, and then makes another mistake by reversing direction back towards the goal and passing above the third barrier. Again, greedy best-first makes bad decisions all around."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           A* search search: 127.4 path cost, 4,058 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           (b) Weighted (1.4) A* search search: 127.4 path cost, 1,289 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           (b) Weighted (2) A* search search: 140.4 path cost, 982 states reached\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Greedy best-first search search: 151.6 path cost, 826 states reached\n"
     ]
    }
   ],
   "source": [
    "plots(d7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Nondeterministic Actions\n",
    "\n",
    "To handle problems with nondeterministic problems, we'll replace the `result` method with `results`, which returns a collection of possible result states. We'll represent the solution to a problem not with a `Node`, but with a plan that consist of two types of component: sequences of actions, like `['forward', 'suck']`, and condition actions, like\n",
    "`{5: ['forward', 'suck'], 7: []}`, which says that if we end up in state 5, then do `['forward', 'suck']`, but if we end up in state 7, then do the empty sequence of actions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def and_or_search(problem):\n",
    "    \"Find a plan for a problem that has nondterministic actions.\"\n",
    "    return or_search(problem, problem.initial, [])\n",
    "    \n",
    "def or_search(problem, state, path):\n",
    "    \"Find a sequence of actions to reach goal from state, without repeating states on path.\"\n",
    "    if problem.is_goal(state): return []\n",
    "    if state in path: return failure # check for loops\n",
    "    for action in problem.actions(state):\n",
    "        plan = and_search(problem, problem.results(state, action), [state] + path)\n",
    "        if plan != failure:\n",
    "            return [action] + plan\n",
    "    return failure\n",
    "\n",
    "def and_search(problem, states, path):\n",
    "    \"Plan for each of the possible states we might end up in.\"\n",
    "    if len(states) == 1: \n",
    "        return or_search(problem, next(iter(states)), path)\n",
    "    plan = {}\n",
    "    for s in states:\n",
    "        plan[s] = or_search(problem, s, path)\n",
    "        if plan[s] == failure: return failure\n",
    "    return [plan]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MultiGoalProblem(Problem):\n",
    "    \"\"\"A version of `Problem` with a colllection of `goals` instead of one `goal`.\"\"\"\n",
    "    \n",
    "    def __init__(self, initial=None, goals=(), **kwds): \n",
    "        self.__dict__.update(initial=initial, goals=goals, **kwds)\n",
    "        \n",
    "    def is_goal(self, state): return state in self.goals\n",
    "    \n",
    "class ErraticVacuum(MultiGoalProblem):\n",
    "    \"\"\"In this 2-location vacuum problem, the suck action in a dirty square will either clean up that square,\n",
    "    or clean up both squares. A suck action in a clean square will either do nothing, or\n",
    "    will deposit dirt in that square. Forward and backward actions are deterministic.\"\"\"\n",
    "    \n",
    "    def actions(self, state): \n",
    "        return ['suck', 'forward', 'backward']\n",
    "    \n",
    "    def results(self, state, action): return self.table[action][state]\n",
    "    \n",
    "    table = {'suck':{1:{5,7}, 2:{4,8}, 3:{7}, 4:{2,4}, 5:{1,5}, 6:{8}, 7:{3,7}, 8:{6,8}},\n",
    "             'forward': {1:{2}, 2:{2}, 3:{4}, 4:{4}, 5:{6}, 6:{6}, 7:{8}, 8:{8}},\n",
    "             'backward': {1:{1}, 2:{1}, 3:{3}, 4:{3}, 5:{5}, 6:{5}, 7:{7}, 8:{7}}}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find a plan to get from state 1 to the goal of no dirt (states 7 or 8):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['suck', {5: ['forward', 'suck'], 7: []}]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "and_or_search(ErraticVacuum(1, {7, 8}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plan says \"First suck, and if we end up in state 5, go forward and suck again; if we end up in state 7, do nothing because that is a goal.\"\n",
    "\n",
    "Here are the plans to get to a goal state starting from any one of the 8 states:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: ['suck', {5: ['forward', 'suck'], 7: []}],\n",
       " 2: ['suck', {8: [], 4: ['backward', 'suck']}],\n",
       " 3: ['suck'],\n",
       " 4: ['backward', 'suck'],\n",
       " 5: ['forward', 'suck'],\n",
       " 6: ['suck'],\n",
       " 7: [],\n",
       " 8: []}"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{s: and_or_search(ErraticVacuum(s, {7,8})) \n",
    " for s in range(1, 9)}"
   ]
  }
 ],
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