{
 "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",
    "    The default heuristic is 0 and the default action cost is 1 for all states.\n",
    "    When yiou create an instance of a subclass, specify `initial`, and `goal` states \n",
    "    (or give an `is_goal` method) and perhaps other keyword args for the subclass.\"\"\"\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 action_cost(self, s, a, 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.action_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",
    "    node = Node(problem.initial)\n",
    "    frontier = PriorityQueue([node], key=f)\n",
    "    reached = {problem.initial: node}\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 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",
    "\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 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",
    "\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))\n",
    "\n",
    "\n",
    "def is_cycle(node, k=30):\n",
    "    \"Does this node form a cycle of length k or less?\"\n",
    "    def find_cycle(ancestor, k):\n",
    "        return (ancestor is not None and k > 0 and\n",
    "                (ancestor.state == node.state or find_cycle(ancestor.parent, k - 1)))\n",
    "    return find_cycle(node.parent, k)\n",
    "\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 = {problem.initial}\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",
    "        \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",
    "\n",
    "def depth_first_recursive_search(problem, node=None):\n",
    "    if node is None: \n",
    "        node = Node(problem.initial)\n",
    "    if problem.is_goal(node.state):\n",
    "        return node\n",
    "    elif is_cycle(node):\n",
    "        return failure\n",
    "    else:\n",
    "        for child in expand(problem, node):\n",
    "            result = depth_first_recursive_search(problem, child)\n",
    "            if result:\n",
    "                return result\n",
    "        return failure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'r2' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_1075091/2231190771.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mpath_states\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdepth_first_recursive_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'r2' is not defined"
     ]
    }
   ],
   "source": [
    "path_states(depth_first_recursive_search(r2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bidirectional Best-First Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bidirectional_best_first_search(problem_f, f_f, problem_b, f_b, terminated):\n",
    "    node_f = Node(problem_f.initial)\n",
    "    node_b = Node(problem_f.goal)\n",
    "    frontier_f, reached_f = PriorityQueue([node_f], key=f_f), {node_f.state: node_f}\n",
    "    frontier_b, reached_b = PriorityQueue([node_b], key=f_b), {node_b.state: node_b}\n",
    "    solution = failure\n",
    "    while frontier_f and frontier_b and not terminated(solution, frontier_f, frontier_b):\n",
    "        def S1(node, f):\n",
    "            return str(int(f(node))) + ' ' + str(path_states(node))\n",
    "        print('Bi:', S1(frontier_f.top(), f_f), S1(frontier_b.top(), f_b))\n",
    "        if f_f(frontier_f.top()) < f_b(frontier_b.top()):\n",
    "            solution = proceed('f', problem_f, frontier_f, reached_f, reached_b, solution)\n",
    "        else:\n",
    "            solution = proceed('b', problem_b, frontier_b, reached_b, reached_f, solution)\n",
    "    return solution\n",
    "\n",
    "def inverse_problem(problem):\n",
    "    if isinstance(problem, CountCalls):\n",
    "        return CountCalls(inverse_problem(problem._object))\n",
    "    else:\n",
    "        inv = copy.copy(problem)\n",
    "        inv.initial, inv.goal = inv.goal, inv.initial\n",
    "        return inv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bidirectional_uniform_cost_search(problem_f):\n",
    "    def terminated(solution, frontier_f, frontier_b):\n",
    "        n_f, n_b = frontier_f.top(), frontier_b.top()\n",
    "        return g(n_f) + g(n_b) > g(solution)\n",
    "    return bidirectional_best_first_search(problem_f, g, inverse_problem(problem_f), g, terminated)\n",
    "\n",
    "def bidirectional_astar_search(problem_f):\n",
    "    def terminated(solution, frontier_f, frontier_b):\n",
    "        nf, nb = frontier_f.top(), frontier_b.top()\n",
    "        return g(nf) + g(nb) > g(solution)\n",
    "    problem_f = inverse_problem(problem_f)\n",
    "    return bidirectional_best_first_search(problem_f, lambda n: g(n) + problem_f.h(n),\n",
    "                                           problem_b, lambda n: g(n) + problem_b.h(n), \n",
    "                                           terminated)\n",
    "   \n",
    "\n",
    "def proceed(direction, problem, frontier, reached, reached2, solution):\n",
    "    node = frontier.pop()\n",
    "    for child in expand(problem, node):\n",
    "        s = child.state\n",
    "        print('proceed', direction, S(child))\n",
    "        if s not in reached or child.path_cost < reached[s].path_cost:\n",
    "            frontier.add(child)\n",
    "            reached[s] = child\n",
    "            if s in reached2: # Frontiers collide; solution found\n",
    "                solution2 = (join_nodes(child, reached2[s]) if direction == 'f' else\n",
    "                             join_nodes(reached2[s], child))\n",
    "                #print('solution', path_states(solution2), solution2.path_cost, \n",
    "                # path_states(child), path_states(reached2[s]))\n",
    "                if solution2.path_cost < solution.path_cost:\n",
    "                    solution = solution2\n",
    "    return solution\n",
    "\n",
    "S = path_states\n",
    "\n",
    "#A-S-R + B-P-R => A-S-R-P + B-P\n",
    "def join_nodes(nf, nb):\n",
    "    \"\"\"Join the reverse of the backward node nb to the forward node nf.\"\"\"\n",
    "    #print('join', S(nf), S(nb))\n",
    "    join = nf\n",
    "    while nb.parent is not None:\n",
    "        cost = join.path_cost + nb.path_cost - nb.parent.path_cost\n",
    "        join = Node(nb.parent.state, join, nb.action, cost)\n",
    "        nb = nb.parent\n",
    "        #print('  now join', S(join), 'with nb', S(nb), 'parent', S(nb.parent))\n",
    "    return join\n",
    "    \n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#A , B = uniform_cost_search(r1), uniform_cost_search(r2)\n",
    "#path_states(A), path_states(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#path_states(append_nodes(A, B))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TODO: 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": 10,
   "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 action_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": 11,
   "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) link.\"\"\"\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.neighbors = multimap(links)\n",
    "        self.locations = locations or defaultdict(lambda: (0, 0))\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": 12,
   "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",
    "    {'A': ( 76, 497), 'B': (400, 327), 'C': (246, 285), 'D': (160, 296), 'E': (558, 294), \n",
    "     'F': (285, 460), 'G': (368, 257), 'H': (548, 355), 'I': (488, 535), 'L': (162, 379),\n",
    "     'M': (160, 343), 'N': (407, 561), 'O': (117, 580), 'P': (311, 372), 'R': (227, 412),\n",
    "     'S': (187, 463), 'T': ( 83, 414), 'U': (471, 363), 'V': (535, 473), 'Z': (92, 539)})\n",
    "\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": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['A', 'S', 'R', 'P', 'B']"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path_states(uniform_cost_search(r1)) # Lowest-cost path from Arab to Bucharest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['A', 'S', 'F', 'B']"
      ]
     },
     "execution_count": 14,
     "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": 15,
   "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 action_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": 16,
   "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 tile 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": 17,
   "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",
    "    def h(self, node): return h2(self, node)\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": 18,
   "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": 19,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'h2' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_1075091/1214029143.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Solve an 8 puzzle problem and print out each state\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mpath_states\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mastar_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0me1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mboard8\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36mastar_search\u001b[0;34m(problem, h)\u001b[0m\n\u001b[1;32m     35\u001b[0m     \u001b[0;34m\"\"\"Search nodes with minimum f(n) = g(n) + h(n).\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mh\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 37\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mbest_first_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36mbest_first_search\u001b[0;34m(problem, f)\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;34m\"Search nodes with minimum f(node) value first.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mnode\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0mfrontier\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPriorityQueue\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0mreached\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0;32mwhile\u001b[0m \u001b[0mfrontier\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/2092060460.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, items, key)\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m# a heap of (score, item) pairs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mitem\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mitems\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/2092060460.py\u001b[0m in \u001b[0;36madd\u001b[0;34m(self, item)\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m         \u001b[0;34m\"\"\"Add item to the queuez.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m         \u001b[0mpair\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     17\u001b[0m         \u001b[0mheapq\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mheappush\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpair\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m     35\u001b[0m     \u001b[0;34m\"\"\"Search nodes with minimum f(n) = g(n) + h(n).\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mh\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 37\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mbest_first_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/1915594217.py\u001b[0m in \u001b[0;36mh\u001b[0;34m(self, node)\u001b[0m\n\u001b[1;32m     39\u001b[0m                    for (s, g) in zip(node.state, self.goal) if s != 0)\n\u001b[1;32m     40\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 41\u001b[0;31m     \u001b[0;32mdef\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mh2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     42\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     43\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'h2' is not defined"
     ]
    }
   ],
   "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": 20,
   "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 instead of all actions costing 1, in these problems the cost of an action is the amount of water that flows from the tap. (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": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GreenPourProblem(PourProblem): \n",
    "    \"\"\"A PourProblem in which the cost is the amount of water used.\"\"\"\n",
    "    def action_cost(self, s, action, s1):\n",
    "        \"The cost is the amount of water used.\"\n",
    "        act, i, *_ = action\n",
    "        return self.sizes[i] - s[i] if act == 'Fill' else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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": 23,
   "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": 23,
     "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 (top) state in the diagram above is `(2, 1, 4, 6, 3, 5)`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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": 25,
   "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": 26,
   "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": 26,
     "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": 27,
   "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": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(1, 2), (3, 2)}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JumpingPuzzle(N=2).actions('LL.RR')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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": 29,
     "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": 30,
   "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(actions=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 |{:9,d} goal |{:5.0f} cost |{:8,d} actions | {}'.format(\n",
    "          counts['result'], counts['is_goal'], counts['cost'], counts['actions'], 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": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "uniform_cost_search:\n",
      "      948 nodes |      109 goal |    4 cost |     112 actions | PourProblem((1, 1, 1), 13)\n",
      "    3,499 nodes |      389 goal |    9 cost |     397 actions | PourProblem((0, 0, 0), 21)\n",
      "      124 nodes |       30 goal |   14 cost |      43 actions | PourProblem((0, 0), 8)\n",
      "    3,499 nodes |      389 goal |    9 cost |     397 actions | PourProblem((0, 0, 0), 21)\n",
      "       52 nodes |       14 goal |    6 cost |      19 actions | PourProblem((0, 0), 4)\n",
      "    8,122 nodes |      931 goal |   42 cost |     968 actions | TOTAL\n",
      "\n"
     ]
    }
   ],
   "source": [
    "report([uniform_cost_search], [p1, p2, p3, p4, p5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "uniform_cost_search:\n",
      "      948 nodes |      109 goal |    4 cost |     112 actions | PourProblem((1, 1, 1), 13)\n",
      "    1,696 nodes |      190 goal |   10 cost |     204 actions | GreenPourProblem((1, 1, 1), 13)\n",
      "    3,499 nodes |      389 goal |    9 cost |     397 actions | PourProblem((0, 0, 0), 21)\n",
      "    4,072 nodes |      454 goal |   21 cost |     463 actions | GreenPourProblem((0, 0, 0), 21)\n",
      "      124 nodes |       30 goal |   14 cost |      43 actions | PourProblem((0, 0), 8)\n",
      "      124 nodes |       30 goal |   35 cost |      45 actions | GreenPourProblem((0, 0), 8)\n",
      "    3,499 nodes |      389 goal |    9 cost |     397 actions | PourProblem((0, 0, 0), 21)\n",
      "    4,072 nodes |      454 goal |   21 cost |     463 actions | GreenPourProblem((0, 0, 0), 21)\n",
      "    3,499 nodes |      389 goal |    9 cost |     397 actions | PourProblem((0, 0, 0), 21)\n",
      "    4,072 nodes |      454 goal |   21 cost |     463 actions | GreenPourProblem((0, 0, 0), 21)\n",
      "    3,590 nodes |      719 goal |    7 cost |     725 actions | PancakeProblem((4, 6, 2, 5, 1, 3), (1, 2\n",
      "   30,204 nodes |    5,035 goal |    8 cost |   5,042 actions | PancakeProblem((1, 3, 7, 5, 2, 6, 4), (1\n",
      "   22,068 nodes |    3,679 goal |    6 cost |   3,684 actions | PancakeProblem((1, 7, 2, 6, 3, 5, 4), (1\n",
      "   81,467 nodes |   12,321 goal |  174 cost |  12,435 actions | TOTAL\n",
      "\n",
      "breadth_first_search:\n",
      "      596 nodes |      597 goal |    4 cost |      73 actions | PourProblem((1, 1, 1), 13)\n",
      "      596 nodes |      597 goal |   15 cost |      73 actions | GreenPourProblem((1, 1, 1), 13)\n",
      "    2,618 nodes |    2,619 goal |    9 cost |     302 actions | PourProblem((0, 0, 0), 21)\n",
      "    2,618 nodes |    2,619 goal |   32 cost |     302 actions | GreenPourProblem((0, 0, 0), 21)\n",
      "      120 nodes |      121 goal |   14 cost |      42 actions | PourProblem((0, 0), 8)\n",
      "      120 nodes |      121 goal |   36 cost |      42 actions | GreenPourProblem((0, 0), 8)\n",
      "    2,618 nodes |    2,619 goal |    9 cost |     302 actions | PourProblem((0, 0, 0), 21)\n",
      "    2,618 nodes |    2,619 goal |   32 cost |     302 actions | GreenPourProblem((0, 0, 0), 21)\n",
      "    2,618 nodes |    2,619 goal |    9 cost |     302 actions | PourProblem((0, 0, 0), 21)\n",
      "    2,618 nodes |    2,619 goal |   32 cost |     302 actions | GreenPourProblem((0, 0, 0), 21)\n",
      "    2,951 nodes |    2,952 goal |    7 cost |     598 actions | PancakeProblem((4, 6, 2, 5, 1, 3), (1, 2\n",
      "   25,945 nodes |   25,946 goal |    8 cost |   4,333 actions | PancakeProblem((1, 3, 7, 5, 2, 6, 4), (1\n",
      "    5,975 nodes |    5,976 goal |    6 cost |   1,002 actions | PancakeProblem((1, 7, 2, 6, 3, 5, 4), (1\n",
      "   52,011 nodes |   52,024 goal |  213 cost |   7,975 actions | 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 uninformed (i.e. *h* = 0) breadth-first search:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "breadth_first_search:\n",
      "       81 nodes |       82 goal |    5 cost |      35 actions | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "  160,948 nodes |  160,949 goal |   22 cost |  59,960 actions | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "  218,263 nodes |  218,264 goal |   23 cost |  81,829 actions | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "  418,771 nodes |  418,772 goal |   26 cost | 156,533 actions | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "  448,667 nodes |  448,668 goal |   27 cost | 167,799 actions | EightPuzzle((8, 6, 7, 2, 5, 4, 3, 0, 1),\n",
      "1,246,730 nodes |1,246,735 goal |  103 cost | 466,156 actions | TOTAL\n",
      "\n",
      "astar_misplaced_tiles:\n",
      "       17 nodes |        7 goal |    5 cost |      11 actions | EightPuzzle((1, 4, 2, 0, 7, 5, 3, 6, 8),\n",
      "   23,407 nodes |    8,726 goal |   22 cost |   8,747 actions | EightPuzzle((1, 2, 3, 4, 5, 6, 7, 8, 0),\n",
      "   38,632 nodes |   14,433 goal |   23 cost |  14,455 actions | EightPuzzle((4, 0, 2, 5, 1, 3, 7, 8, 6),\n",
      "  124,324 nodes |   46,553 goal |   26 cost |  46,578 actions | EightPuzzle((7, 2, 4, 5, 0, 6, 8, 3, 1),\n",
      "  156,111 nodes |   58,475 goal |   27 cost |  58,501 actions | EightPuzzle((8, 6, 7, 2, 5, 4, 3, 0, 1),\n",
      "  342,491 nodes |  128,194 goal |  103 cost | 128,292 actions | TOTAL\n",
      "\n",
      "astar_search:\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'h2' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_1075091/1501421569.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mastar_misplaced_tiles\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mastar_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mh1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m report([breadth_first_search, astar_misplaced_tiles, astar_search], \n\u001b[0m\u001b[1;32m      4\u001b[0m        [e1, e2, e3, e4, e5])\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/1959091182.py\u001b[0m in \u001b[0;36mreport\u001b[0;34m(searchers, problems, verbose)\u001b[0m\n\u001b[1;32m     18\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mp\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mproblems\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m             \u001b[0mprob\u001b[0m   \u001b[0;34m=\u001b[0m \u001b[0mCountCalls\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m             \u001b[0msoln\u001b[0m   \u001b[0;34m=\u001b[0m \u001b[0msearcher\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprob\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     21\u001b[0m             \u001b[0mcounts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprob\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_counts\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m             \u001b[0mcounts\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mactions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msoln\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcost\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msoln\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath_cost\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36mastar_search\u001b[0;34m(problem, h)\u001b[0m\n\u001b[1;32m     35\u001b[0m     \u001b[0;34m\"\"\"Search nodes with minimum f(n) = g(n) + h(n).\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mh\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 37\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mbest_first_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36mbest_first_search\u001b[0;34m(problem, f)\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;34m\"Search nodes with minimum f(node) value first.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mnode\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0mfrontier\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPriorityQueue\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0mreached\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0;32mwhile\u001b[0m \u001b[0mfrontier\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/2092060460.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, items, key)\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m# a heap of (score, item) pairs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mitem\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mitems\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/2092060460.py\u001b[0m in \u001b[0;36madd\u001b[0;34m(self, item)\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m         \u001b[0;34m\"\"\"Add item to the queuez.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m         \u001b[0mpair\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     17\u001b[0m         \u001b[0mheapq\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mheappush\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpair\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m     35\u001b[0m     \u001b[0;34m\"\"\"Search nodes with minimum f(n) = g(n) + h(n).\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mh\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 37\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mbest_first_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/1915594217.py\u001b[0m in \u001b[0;36mh\u001b[0;34m(self, node)\u001b[0m\n\u001b[1;32m     39\u001b[0m                    for (s, g) in zip(node.state, self.goal) if s != 0)\n\u001b[1;32m     40\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 41\u001b[0;31m     \u001b[0;32mdef\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mh2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     42\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     43\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'h2' is not defined"
     ]
    }
   ],
   "source": [
    "def astar_misplaced_tiles(problem): return astar_search(problem, h=problem.h1)\n",
    "\n",
    "report([breadth_first_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": null,
   "metadata": {},
   "outputs": [],
   "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": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "astar_search:\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'h2' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_1075091/1052081939.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mreport\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mastar_search\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mastar_tree_search\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0me1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0me2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0me3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0me4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/tmp/ipykernel_1075091/1959091182.py\u001b[0m in \u001b[0;36mreport\u001b[0;34m(searchers, problems, verbose)\u001b[0m\n\u001b[1;32m     18\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mp\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mproblems\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m             \u001b[0mprob\u001b[0m   \u001b[0;34m=\u001b[0m \u001b[0mCountCalls\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m             \u001b[0msoln\u001b[0m   \u001b[0;34m=\u001b[0m \u001b[0msearcher\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprob\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     21\u001b[0m             \u001b[0mcounts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprob\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_counts\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m             \u001b[0mcounts\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mactions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msoln\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcost\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msoln\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath_cost\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36mastar_search\u001b[0;34m(problem, h)\u001b[0m\n\u001b[1;32m     35\u001b[0m     \u001b[0;34m\"\"\"Search nodes with minimum f(n) = g(n) + h(n).\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mh\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 37\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mbest_first_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36mbest_first_search\u001b[0;34m(problem, f)\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;34m\"Search nodes with minimum f(node) value first.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mnode\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0mfrontier\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPriorityQueue\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0mreached\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0;32mwhile\u001b[0m \u001b[0mfrontier\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/2092060460.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, items, key)\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m# a heap of (score, item) pairs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mitem\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mitems\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/2092060460.py\u001b[0m in \u001b[0;36madd\u001b[0;34m(self, item)\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m         \u001b[0;34m\"\"\"Add item to the queuez.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m         \u001b[0mpair\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     17\u001b[0m         \u001b[0mheapq\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mheappush\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpair\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m     35\u001b[0m     \u001b[0;34m\"\"\"Search nodes with minimum f(n) = g(n) + h(n).\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mh\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 37\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mbest_first_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/1915594217.py\u001b[0m in \u001b[0;36mh\u001b[0;34m(self, node)\u001b[0m\n\u001b[1;32m     39\u001b[0m                    for (s, g) in zip(node.state, self.goal) if s != 0)\n\u001b[1;32m     40\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 41\u001b[0;31m     \u001b[0;32mdef\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mh2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     42\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     43\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'h2' is not defined"
     ]
    }
   ],
   "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": 35,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "greedy_bfs:\n",
      "        0 nodes |        1 goal |    0 cost |       0 actions | RouteProblem('A', 'A')\n",
      "        9 nodes |        4 goal |  450 cost |       6 actions | RouteProblem('A', 'B')\n",
      "       28 nodes |       12 goal | 1207 cost |      22 actions | RouteProblem('N', 'L')\n",
      "       19 nodes |        8 goal |  837 cost |      14 actions | RouteProblem('E', 'T')\n",
      "       14 nodes |        6 goal |  572 cost |      10 actions | RouteProblem('O', 'M')\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'h2' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_1075091/3931949981.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mextra_weighted_astar_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mweighted_astar_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mweight\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m report((greedy_bfs, extra_weighted_astar_search, weighted_astar_search, astar_search, uniform_cost_search), \n\u001b[0m\u001b[1;32m      4\u001b[0m        (r0, r1, r2, r3, r4, e1, d1, d2, j9, e2, d3, d4, d6, d7, e3, e4))\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/1959091182.py\u001b[0m in \u001b[0;36mreport\u001b[0;34m(searchers, problems, verbose)\u001b[0m\n\u001b[1;32m     18\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mp\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mproblems\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m             \u001b[0mprob\u001b[0m   \u001b[0;34m=\u001b[0m \u001b[0mCountCalls\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m             \u001b[0msoln\u001b[0m   \u001b[0;34m=\u001b[0m \u001b[0msearcher\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprob\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     21\u001b[0m             \u001b[0mcounts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprob\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_counts\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m             \u001b[0mcounts\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mactions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msoln\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcost\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msoln\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath_cost\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36mgreedy_bfs\u001b[0;34m(problem, h)\u001b[0m\n\u001b[1;32m     53\u001b[0m     \u001b[0;34m\"\"\"Search nodes with minimum h(n).\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     54\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mh\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 55\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mbest_first_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     56\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     57\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36mbest_first_search\u001b[0;34m(problem, f)\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;34m\"Search nodes with minimum f(node) value first.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mnode\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0mfrontier\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPriorityQueue\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0mreached\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0;32mwhile\u001b[0m \u001b[0mfrontier\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/2092060460.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, items, key)\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m# a heap of (score, item) pairs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mitem\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mitems\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/2092060460.py\u001b[0m in \u001b[0;36madd\u001b[0;34m(self, item)\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m         \u001b[0;34m\"\"\"Add item to the queuez.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m         \u001b[0mpair\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     17\u001b[0m         \u001b[0mheapq\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mheappush\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpair\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/1915594217.py\u001b[0m in \u001b[0;36mh\u001b[0;34m(self, node)\u001b[0m\n\u001b[1;32m     39\u001b[0m                    for (s, g) in zip(node.state, self.goal) if s != 0)\n\u001b[1;32m     40\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 41\u001b[0;31m     \u001b[0;32mdef\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mh2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     42\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     43\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'h2' is not defined"
     ]
    }
   ],
   "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": 36,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "astar_search:\n",
      "      948 nodes |      109 goal |    4 cost |     112 actions | PourProblem((1, 1, 1), 13)\n",
      "    1,696 nodes |      190 goal |   10 cost |     204 actions | GreenPourProblem((1, 1, 1), 13)\n",
      "    3,499 nodes |      389 goal |    9 cost |     397 actions | PourProblem((0, 0, 0), 21)\n",
      "    4,072 nodes |      454 goal |   21 cost |     463 actions | GreenPourProblem((0, 0, 0), 21)\n",
      "      124 nodes |       30 goal |   14 cost |      43 actions | PourProblem((0, 0), 8)\n",
      "      124 nodes |       30 goal |   35 cost |      45 actions | GreenPourProblem((0, 0), 8)\n",
      "    3,499 nodes |      389 goal |    9 cost |     397 actions | PourProblem((0, 0, 0), 21)\n",
      "    4,072 nodes |      454 goal |   21 cost |     463 actions | GreenPourProblem((0, 0, 0), 21)\n",
      "        0 nodes |        1 goal |    0 cost |       0 actions | RouteProblem('A', 'A')\n",
      "       15 nodes |        6 goal |  418 cost |       9 actions | RouteProblem('A', 'B')\n",
      "       34 nodes |       15 goal |  910 cost |      23 actions | RouteProblem('N', 'L')\n",
      "       33 nodes |       14 goal |  805 cost |      21 actions | RouteProblem('E', 'T')\n",
      "       20 nodes |        9 goal |  445 cost |      13 actions | RouteProblem('O', 'M')\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'h2' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_1075091/4164331635.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m report((astar_search, uniform_cost_search,  breadth_first_search, breadth_first_bfs, \n\u001b[0m\u001b[1;32m      2\u001b[0m         \u001b[0miterative_deepening_search\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdepth_limited_search\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgreedy_bfs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m         weighted_astar_search, extra_weighted_astar_search), \n\u001b[1;32m      4\u001b[0m        (p1, g1, p2, g2, p3, g3, p4, g4, r0, r1, r2, r3, r4, e1))\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/1959091182.py\u001b[0m in \u001b[0;36mreport\u001b[0;34m(searchers, problems, verbose)\u001b[0m\n\u001b[1;32m     18\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mp\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mproblems\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m             \u001b[0mprob\u001b[0m   \u001b[0;34m=\u001b[0m \u001b[0mCountCalls\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m             \u001b[0msoln\u001b[0m   \u001b[0;34m=\u001b[0m \u001b[0msearcher\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprob\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     21\u001b[0m             \u001b[0mcounts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprob\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_counts\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m             \u001b[0mcounts\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mactions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msoln\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcost\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msoln\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath_cost\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36mastar_search\u001b[0;34m(problem, h)\u001b[0m\n\u001b[1;32m     35\u001b[0m     \u001b[0;34m\"\"\"Search nodes with minimum f(n) = g(n) + h(n).\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mh\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 37\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mbest_first_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36mbest_first_search\u001b[0;34m(problem, f)\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;34m\"Search nodes with minimum f(node) value first.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mnode\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0mfrontier\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPriorityQueue\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0mreached\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0;32mwhile\u001b[0m \u001b[0mfrontier\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/2092060460.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, items, key)\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m# a heap of (score, item) pairs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mitem\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mitems\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/2092060460.py\u001b[0m in \u001b[0;36madd\u001b[0;34m(self, item)\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m         \u001b[0;34m\"\"\"Add item to the queuez.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m         \u001b[0mpair\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     17\u001b[0m         \u001b[0mheapq\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mheappush\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpair\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/94729273.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m     35\u001b[0m     \u001b[0;34m\"\"\"Search nodes with minimum f(n) = g(n) + h(n).\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mh\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 37\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mbest_first_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     38\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_1075091/1915594217.py\u001b[0m in \u001b[0;36mh\u001b[0;34m(self, node)\u001b[0m\n\u001b[1;32m     39\u001b[0m                    for (s, g) in zip(node.state, self.goal) if s != 0)\n\u001b[1;32m     40\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 41\u001b[0;31m     \u001b[0;32mdef\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mh2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     42\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     43\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'h2' is not defined"
     ]
    }
   ],
   "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": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def best_first_search(problem, f):\n",
    "    \"Search nodes with minimum f(node) value first.\"\n",
    "    global reached # <<<<<<<<<<< Only change here\n",
    "    node = Node(problem.initial)\n",
    "    frontier = PriorityQueue([node], key=f)\n",
    "    reached = {problem.initial: node}\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 plot_grid_problem(grid, solution, reached=(), title='Search', show=True):\n",
    "    \"Use matplotlib to plot the grid, obstacles, solution, and reached.\"\n",
    "    reached = list(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": 35,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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N7VHKUSnmldoxBQDuLdfrdXQOAOz4ds6U20hL37/xeXtFGj4poFB7v6V65KPW5tp6FioZJcI4tVAyt0ffkq4yph77IWfcc9vn6bybug+BcySFjNANVxYBHXsPnY96GJ3iIPNijHEGRTs+oh/iG32OHL1/TIQCNwEoFUbQLtChHssrIHIbn7WoQk6Bjh6FUzTmUtnxM8tcUhorpdj5PvRXBKnNMXW+H0YVKgOAPVxZjOHBdAoj1I6p5aMUO4rPJKcPWoxB632MPH6iUxorpVgOpbw9HFMcewBcYbEYg1JhhJHFBGaLHcVnktMHLcag9T5GHj/RKY2VUiyHUt4ejimOPQCucBtqAM+3svw8YkwtH6XYbfzp6fZ/ncNe32x5fYvXc399eL5l7JP33xuDo75WniOpsVnmktJYKcVyKOT9Umzk9e3TL3O4dizjtdXPLQAwAlcWAUSTU+CBIgHbKJIBTxSPY8WcjqgVWFM3ul9G7x8T4cqiM0oP+usUE5gzdhufoShJSt+8lBNPLRpBgZuxBTpa9sNRLr3GwGPMW3+pnvs8tYU/w5CH/sJMuLLoz4PpPOjfI6aWj1LsKB5Vi74pHYOanxfp+Ek1MhelsVKK7VHK0cO5L1JbAEyKxaI/Sg/6Ryom4DF2FI+qRd+UjkHNz4t0/KQamYvSWCnF9ijl6OHcF6ktACbFbajOKBQT6Bmr+ZkHRRBOFSIYHVu37/Z/jadF39QuAKM8R3rEcufhyFyUxkoptqf/XEo7Z6ue+3ocPwDQGlcWMZO9ggPeChFgPIpBAO2lnrMVjzvFnAAgG1cWhSkUDhgdq/mZXoqSUODmo15907sAjNfjx+Nxdu+YUBorpZhKf6XPpX7Ho06b+449gHlxZVHbg+kUDhgVa/WZt5TaXNo3UfTqG6Ux9XD8eDzO1PJRj+1Ryif6MbVl5NgDmNRyvV5H54AdSr80R7gyclRG//Hx8kalzeevnuX9yYJ7np6edk8Orz8v9XW5evWNx7FXuQqifpzdOyaUxkoldnQ8K43fqOM2eptTHM2RLSXfA6n79bQPwBsWi5hG9C+B3C9wcR9q/h0rpbF/KdrRc58nnRoDsb6unouj8UuxGuPo46fOQ5tZLB6+f+T5oer3JvCC21ABKIryj/EtXtrmJc/eIvVLpLZEQfEs30YeUxzPaILFoohlsWVZ7LPn20KINeybLUptLu2bKHr1zcjxUxflOOvVPo969VekudRyP5fL5d3lclkeHy9vHh8v3398vLy5XC7L5XJ5p9T/AObBYlHHg+kUN1CKtfrMW0ptLu2bKHr1zcjxUxflOGuRTxS9+ivSXFL6HuBcBaApFos6vjSzHz3/l9inWnzmLaU2l/ZNFL36ZuT4qYtynLXIJ4pe/RVpLil9D3CuAtAUi0UR16tdr1f7+euKZMTafeYtpTaX9k0Uvfpm5Pipi3Kc9WqfR736K9JcGrVvpf4HMI/vjE4AADZELubwwXwUIog8BiW8jF8KxhjNbVQYjVy1c+T5geMZTbBYBCag8HcWPZSE7yHwP5KmwPgBxaL82LLC+QERcRuqiFFVztRjrT7zllKbS/umdvtSP6/26zz0jXps9L5V+lotH/WYWn+p5aI0VkpjAiAmFos6lCqfKcVafeYtpTaX9s2WHv1V+3Ue+kY9Nnrft5RyGZmPemyPUj4zHlNKMQCTWK7X6+gcYB9/ubOPJ+IvXx4sJ1a3b96/f/rlXv8/Pl7eqLT5bN/Ubl/q59V+nYe+8RIbsW+lvj7K5XK5LEpjpRI7ul1cafxGHbdKYzUqdjRHUrV8NKIEj0sAaywWMY3oXwK12xfpmcXoY7/l6enpKwv8bJAlFMmYcdxLKfVZjUWJmBCFXVgsAnPhNlQApfYqsFGZbazIC0Wz+O1DPMxZfXyfATdYLHa296C40oPrSrFWn3lLqc2lfVO7ffc+73K5vLtcLsvj4+XN4+Pl+4+PlzeXy2W5XC7vRvV/r75Rj0VX2g9KY6UUU+uvSJTGmTFZe/k+29jcXxEGzmKx2N+D8cB8TqzVZ95SanNp32xR6q/anzeyb9Rj0ZX2g9JYKcX2qOXjkdI4MyYA7uKZxc6ef5l7MB6Y715MQLFYQs2+GVXgRrH/R+5bJRbwea+Ve2NHgZu680apwI1XEc43kZ9ZBLDGYhHTUPqiOSg+croAwqgCN6M+z8u+U0xQjKaJe2OnPu6KlPos4g8eEeYdi0VgLtyGCoyxtzAoWTDUfjCfB/37YaGYj3kIb5izANz5zugEIhtxq2W0WM3PfP++fKyUclnHP16RrJd33c/r2f8j9127byLpfxvjcT4KY68YU+mvo/HzcCVJaUx7zREA8XBlsa0HG1fEJUqs1WfeGtm+s7mMzFu9/0fuu3bfRKLWr0pjrxTbo5aPOqUxZUwAnMIziw1xZVHtyqJOkZMauaiNlVL/j9x37b6JROk4o8DNdsxLgRuuLGrOkVQ8swj4wWIR7qUWi8n8gjtdaCbFjF96FLjZF7GQxxalAikK465Iqc965BKwuFTT7y4zCtwAs+E2VETQolhMpH88QN8MhS9GtJEiTbgn2rm+R3s4foCJUOCmIW5D7XMbamrxktwiIqMKN0SdNxS4OYrVLk7kc4707FedHPVie5TOGdjXepxerlxyez0wB64stvVgsQuV9IjlvvZW6utS39uifWf32ytHpTaX9k2PfSvF1PJRiqnloxTbo5YPtqkdPwAc45nFhvj1v9eVxbTiJbm/crYs5kCBm7Z9PXLfSjG1fJRiavmoxGYrcBPxeeEe45Ty2trjxzOLwBgsFuFe6hdI7j8KWn75tPjSSy3008PgohGr9nr8R4ZA4Y3u86aEQH/1MLR4SdACN+H+EaRyTqs9fmJzU+b7FmiN21CBOFoU+jlr5D/aoywYRrdj9P5zecv3jJHFS6IWNYnWrmjtUaX0fQs0RYGbhrgdqtetLmljEL3AjVIRF4XCFKp947UPlfpGtb96aN2vqcVLooxpy6tACn2o+t18pg9zz+MA6uDKYlsPRqGF0ljua2+lvi71vS3ad3a/LT6zR/t6Ue8br32oHotO7bzLmO5T6kO17+ZUPb7rARxgsdjWl2b2o+f/HsVyXjtbLPe1t1Jfl/reFu07u98Wn9mjfb2o943XPlSPRad23mVM9yn1odp3c6oe3/UADlDgBu5R4KbdZ27sw0URkdv2KhVGSKVQeGO2eeOB6nxtYeJzWogiKcEL3CTnIjrHzgoxN5GHK4sAcnj4wotS4GF0O2ru38O88WD0nIhIcW4q5qTAa/GlSOMZqS1IRIGbhihwM/4hegrc1G3L6CIiZ/8GpccCN9dreaERlbaMnjctpP4NV49/x1Mln4jzJpVC//f6bu55TixtMzAjriy29WA+iwkoxXJfeyv1danvbdG+s/tt8ZkleffgoW+UYor5RBF5finmMxul/u/13aweA6bEM4sNefsVVzGW8trUX/WPXnfvvfV/MS+/EtHiM0vy7kG5bxRjKvmMnjctcGVx7Lyp+Mzi9f6r+lOfNymvjXhcvMh8ZlFyjp0103PT+IjFItyjwE27z8zZRw/ifbNXxGD6ggCj500LqeeW2f9hFay4RzcR5o3H44L5ep/q2KEdbkMFkGNkIQGvRQz4h4f+2OWK1p6WmP/5mF/jMF+PMTcnRIGbSiLc8qMYS3ktBW7qfWbLAgM9b0ka0TeKRXRG7lt93tRsn+LYq8wbz0VqtuaXmdZYKc8Rj8eFp/nKFT70wpXFeh4sTjEBpVjua2+lvi71vS3ad3a/LT5Tvc0e+qbHPmY8t2xR65vaOUaaNx5FP6Z6zZEtSm2JMl+BJnhmsRKVX3GjxVJeS4Gbep/Z9hfbkVcWxxb/GdX/vfbjcd54yFH5vFujb9RxZbHPd/Potnidr1xZRC8sFuGeeoGb3AfmlYu4lBiZ3+jiPwr975WHfvWQ4yieixvNPnZ7Uot5lRwXowqGeZqvzE/0wm2oQHs8MA9gVl4LYnjNu4cexbxGFQzzMu5e8kQAFLipROWWn2ixlNeqF7hptd+c/SiMac/8Ruxbsf9H7lu9Xz3kGGPenC9upBhTy2dkP2ypdVyMO6bS5muPvwEKqODKYj0PplVMIEos97W3Ul+X+t7SttTcb85+1Ma0dX6j9916HzOeW7ao9U3tHJk3ejG1fJSOx5zXRjmmgPB4ZrESfqnUf4h+VIGbVvvN2Y9CMQEK3GgeP+oxCtwwb5RiavmMiB0915f6nXvvuFA/priyiJlwZbGS69Wu16v9/PUXSmqs9P2RY7mvvZX6utT3lral5n5z9qM2pq3zG73v1vtocfyox2r3q4ccmTd6MbV8RvbDltrHRcl7R/YDEAmLRQAAAADACovFSpbFlmWxz55vU8iKlb4/ciz3tbdSX5f63tK21Nxvzn7UxrR1fqP33XofLY4f9VjtfvWQI/NGL6aWz8h+2FL7uCh578h+ACJhsVjPg/HAfItY7mtvpb4u9b2lbam535z9qI1p6/xG77v1PmY8t2xR65vaOTJv9GJq+SgdjzmvjXJMAeFR4KaS51+aHowH5qvGUl5LgZu8fhg1phS40Tx+1GMUuGHeKMXU8hkRo8ANBW4wF5eLxaenp69s+w+zfrhcPv6NHMzj6Ivr9Un76HX33lui135T+2GUkfn12Ld6/+c4OMdGUfW7ItLYox+v/5ap8Z1777jI2Ef0c5WZ+HzANq/H9xavt6HunRiinzBQ5sPoBAAnop9Lo7cPPkT/t8zed27N7+IofXVkhjZGFOb49rpYlFP6gPSoh7PVY7mvvfX6dZfL5d3lclkeHy9vHh8v33++lSXpvbXakqK0b3q0pXY/9Jo3vfbdeh8tjp+SOetV5LEfOW8ix1p95i2lNuecG16/dus793K5LJfL5V3tvgHQDovFeh6MB+ZbxHJfe6vHe0v2UZrzqLbU7ode86bXvlvvo9e5JbrIY893UptYq8+8pdTmnHPDqL4B0AiLxXq+NLMfPf83N1b6/six3Nfe6vHekn2U5jyqLbX7ode86bXv1vvodW6JLvLY853UJtbqM28ptTnn3DCqbwA04rXAzW7SFBOYT4+H6EtQ4OYjCtz4kTtnPao5JqPGXqC4x6lCDZEKP5Twes5QOp/OcK4y054P2Ob1+N7ClUXMrscD+BiPcc4TvV+itG90oYSz+w9T+AHDRTmWj8zQRgj7zugEPHp+qPrBjL/b1DqW8tr370vG6uOv2C3bcpTfuZz3/pZg+WeO6of282bsOCsfP6OOi9F/w7BujnsZap1bWvDUX2rf1977oWXe6X2Tdq6q/XcRc64aRbrChDlxZfGcB9N/YD5KLPe1t9TakqK0b0o+c1Q/RDqmtng4ftRjW9T6pnaOtc8tLXjsL+ZNm5x77cfrsQK4xGLxnNQHs1NjLT4zSiz3tbfU2pKitG9KPnNUP0Q6prZ4OH7UY1vU+qZ2jrXPLS147C/mTZuce+3H67ECuESBG7inPh8ocPPRLIUItij0v1fq89psaIGb4cdU61v4IlMYv9pUC4aN/Dzm+5wijTtXFgEtkR9kj9w2tENxon2j+2D0/gEAjVHg5gTlB+ajxVJeq14k4Ci/mgU61PthqxDBUdGBSJSPH/1Ym2I7NT+zVRGrCH3j8ZytOm88UJ0jEfsa6IUri+c8mP4D81Fiua+9pdaWmvn12s+ovonEw/EzW6zVZ6ZQ6oeR82aLUj+ozRsP1OcIgEw8s3iC8i+V0WIpr21VWr/eL6R9Sv+r90Nu30Qyqv977cdjrOZn5pblV+qHMVcW/Z2res8br2qNX+05wp/OQG+Rxp3FItzLLBLw4XL5eOtWL73mq8fjImKBh8q6z9denp6evrIJ/gi76rE3ksdzVQuc/1z55Fxca+xez/cJzolhv8+2RDrPcRsqZhP5ROwRBTKORZ6vkdsGIJYe56vo58To7QuLAjcnKN/WEi2W8tpxxSXGFnPotZ+2Ma0CHYq3hUU9t8xccEKh/8fehkrf3OsH5dtxuSIKzIUri+c8mP4D81Fiua9NMbItNXPptR+PsRrvVxH93DIjpf4fOW+2KPVDr77ZotRmjltgYjyzeILyL5XRYimvzb0a1PsXWwrcaM4bL1cWa86R0eOi3tctUOCm3znRW9947YdZryzePF9YpQ9afKYyb8/qlRi9VqmJxSLcyz3B9p4jFLjxQ/HLuvXYTVBUYSiOvbXo56qDYyq5SIpyPyieJ3tgsVhOeV7X5vX43sJtqIiAIimoRW0u9ciHhSJQ194xxbHmV49zsdr3T23R2xcWBW5OUL6tJVos7bXrIilHt/f0v91uL5O6feO5aITOMXW+4I7iLWVpee9lrU/lFt0at9TGOH7GnhNV+ia1fd77YUutKya1r8p4uMoz05+VgC9cWTznwfQfmI8Sq/H+WyPbUjOXXvvxGBu971se+sEjtTlSYsbjZ4tSP7Q4piL1A4AJsFg850sz+9Hzf2vEWnxmlFiN998a2ZaaufTaj8fY6H3f8tAPHqnNkRIzHj9blPqhxTEVqR8ATIDF4gnXq12vV/v569sxSmItPjNKrMb7b41sS81cPLTZ67xRGude/eCR2hwZ1Ravx496P7Q4piL1A4A58MwiAMztg/ksvDGkWEJu9dhBFQ4/8PwTRtiY71HnYpXzJucHeMBiEQAmxj8asnlYWHvIEXMIORf3zptO/vxFyDFBO9yGesKy2LIs9tlzhbDiWIvPjBKr8f5bI9tSMxcPbfY6b5TG2Ws/qMdqvF+Zh3lTO2+1eZPaPq/9AGAOLBbPaVFVTKnKmVKsxvtvjWxLzVx67cdjbPS+b83YD+qxGu9X5mHe1M5bbd5sidQPACawXK/X0TlkG/33cp5/XXsw8/E3rTzHzr5f6W/etcpFuc2jYyP2rdj/auOiFGsxzkpU/gall2OlZt+kts9rP+TeaqnwdxF7/bvRyW2oMn9bMrLRa5WaWCwiJKU5ovAlxXFxXm5BEwcoblDAyz8GCzSfHyXnKu/H4+v2eT1ns1g8tx8lyvMrCq/H9xZuQwXi2KsOOaRqZCBu/2G6I1p7eot+PKnPD/X8cnDOxgjML2ShGuodKre1zBo7+/7378eOaY9c1vGPVwOUxs/bvMkdP6+UxsrfHDl/nHm5hdVM95zo/XiMcs5GHd6uMGFOXFm878G0HpifLVbj/bdGtqVmLiPboh5r9ZlRKI1VpDkSaS6pnxO9UjoGos9hABXwzOId2r9wx4+dfb9S4YBeBW5Gj5VSrNf4eaVcPKNXbMS+vcyly+WyqJ4TvfThngjHHs8snttP631DS6RnFlksIiSlOaKUC/J5KViQg3k3hpe51Hp+FBa4cdGHeyIce6MXix2cLvLEYhEvIv3bj9tQAeBYtGIA0drjiYe+V89RPb8ZRB+DSEWUgGIUuLkj6u1QXmJn3z9ngRu98fM2b7ZjvotQKOWjFBuzbx9zqfV+ys6JY/swrX37t8oqjfPZ2MtVt0i3BwPYx5XF+x4sdqEF9ViN998a2ZaauYxsi3pMLR/6QS+mlo9SrOd+bin1Q2nfbFFqS4t+ABAMzyzeofJL5ayxs++nwM3cMbV86Ae9mFo+SrHW+1E6P/e+sqjevrP9cNRmh88snv63JM8s4kWkZxZZLMK9p6enryzjGYMIBW5y21zZ6Yf/AQWDj58SIY696N/hE7TP6/GTjMUiSkU6D3AbKlxafrIsy0+WHyw/WRbT/9LaKwZQUiRgZJvV+xu4x+sc9pr3rRbnRPQTZR7uYR4Cr1Dg5g6V21pmjW3Fl58si13tj83sD83sT6/Xqy1L+o80/dvSpiDDSEpzhGOKfjjbNx7FmDc+Cv2cvw117PjNePyU/MmV1FuDgVlxZfG+B9N6YH622Cfx5yuJf2zXN39giy12ffMHf/r//Kll3k6t1L7SvhlFqR84pvZjavkoxbxi3oyN5b72llJbZjx+tsRo87L8li3L33+1/dbolBADzyzeofJL5ayxT+I/+PGX9oOf/LGZ/b6Z/fsv//uvL79uv/ubv2t/+B/9YdIVxggFBkY//K/eh2r50A9asdHHT4kex16Lz4wSS3lt9AI3isePypXFYc8sLsvvmNlfmtmvvYr+f2b2n9r1+n9W2QeyRHpmkcUiXPj2iuLf/sY/sr/zi/UL/vY37B/+B/9J0oIxwhwZ/WUdoQ8xr9HHT4nZjz0Pxb2i/xtF8fgpWSy+fq9o8Z7jebcsv/PX9u6vvmdffXK74C/N7IO9s9+0r/4BC8b+Ip0HuA0V8r5dKJr9/uZC0czs7/zCfvbXP7MTt6R6NfIBfB7+h3de57DXvGuiuNd4avMwJZ/UokqKY7yf08dbTf/ydqFo9vEf+N+zr8zM/pJbUlGCAjd3qNzWMm3spZjN9c0f2Jtf/ntHY/U317+xn/31z8zMDq8wSrXvZOzlV0aVfNRiavnQD1oxjh+/8+aoeEwvJTkq9GGL46f2rbe5f7fxft5px7zC/Mr0H5rZr+1d+XljZlezX/ux/fj3/uli/2PpbbaYE1cW73swrQfmZ4v9npn94b2F4ou/uf6N/cW//Qv7l7/4l0cvU2of86ZNTC0f+kEvppaPUkwtn70cRynJUakPW8yRLT3GOdL8quqX9ubNT+2H/51N1GbUxTOLd8z+K+7wWMaVRbO0YjcRCgy8tEUpH6WYWj70g15MLR+lmFo+qVecerhcLktJjlG/f/SvLPqYX3t2/227LH/fzP53O7hV9Wr24cf24//yn9ofcWWxo0jPLLJYhLxPnll8VQX1VmpV1JnmiOjD+jUlFZyobYJ+NRvUtzWJjpP7fh1pdHGVlO+PGf+NUrvNPfpQ9PyQ5bv/7t/Zf/5P/ol95xe/2LxV8Jdm9pX9pv09+9f2b+23XsIfrlfjHNRYpPMAt6FC3vWPrlcz+8dm9i/sb39j+0V/+xtZfz5jIq6/CBOMal/0fjWL0UbFNijm5AnFvVCL+2Pxm7/7d+0vfvIT+2Dv7PaS6MtC8XftZ68XimYB2o2+KHBzx+y3/IyO/Sp+fbAf/Pgf2/f+739k/+Bf2CdVUf/2N8z+6vftD3//HyYtFJXa13reOHxYP9uIY2qGfjXTmu+Rxkmhb/x+J40tTpTy2ugFbrbaUrvNPfpQ9fyQ66vf/m373/7b/8b+sz/6I1t++asl4//79a/b79rP7P+y31m9h9tQkYMri/c9GMUERsZ+Ff9ffvxgf/4nZn/1+/btFcbnhaL9+Z/kXFFUal+veRPZyGMqOqX5HmmclPqG76S8WO5rbym1pUU/bKl97EY/P2T76rd/2/6nf/7P7X/+Z//s2+3v2b/eXCg+C9kPaINnFu9Q+aVy1tht3Mx+aXY1+y/+a7Pv//dm/8d/Zfbnf2Jmi71//5Q0plELDHh6WL+mrfE0a33FKn6/mvk/VlTHSb1f1fJRiqW8lgI35W3u0Yeq54daHh8vR//z5vcm6on0zCKLRbiyLC8ntavZf/y/mv2b3zOzj0OeulicaY6MLgbRw4jxnKFfzfwfK6rj5L1fcWzGf6M4LXBz+vzw+ec/tK+//u7G/3K1l3+TKLteHSTpXKTzALehwqnF7N/8wE6clGcrUBC9vaPaF71fzWK0UbENijkBMzp9LG4vFM08LBSNcxAyUeDmDpXbWmaN3cZzxs4szi0/5+dN+2IQirdctd/P2CIbOv2gHtsfJ50c9WJq+SjFUl5LgZvyNvfpw/PncbNV8VFlSd/DwB6uLN73YFoPzM8WO4qnUGpL9Hmzhb4ZG1PLRymmlo9STC0fpVjua28ptaVFP2wp3U/Nz2vRD+oitQUD8MziHSq/VM4au43bwa95W88scmWxfWzOK4s+Ymr5KMXU8lGKqeWjFEt5reI5sf2VRX8FbkpixpVF3BHpmUUWi3BlWfZPaluLxZMP1n9l23+09sPl8vG2FfxK9OPxYD54FXIec9z6EfCYShbhnLjFY4GbVMtirufrlWI2QyjN4VLchgqs7X0puP2yQJFo4x6tPS84bv1gTOBJxnyVuwBDMRsUY7F4x7LYsiz22fMl+yaxXvvxGDuKpyjdd83Piz5vlPqrV/u8Upo3o+ahWt5KsZ77mY3SOLeYI7XbrNSHW96/f7rZ/oeXK3lvzOz7ZvbmerVlYOwdxx5KsVi878G0HpifLXYUT1G675qfF33ebInUN5EozZtR81Atb6VYz/3MRmmcW8yRLZG+V1IpjRXHHorwzOIdz7/EPBjFBIbEbuPWocCN+oP1avNGsb96tc8rpXk8ah6q5K0YGzlW0UU59m7jkQvcWOa/Oy6Xy6I0Vnvjh7YiPbPIYhGylsyHyrdO2g5VLcYxQSGJ5sVLjs43XlUu/CSP7wUtEY+pytwVZdoa088//+HeH6//cL3aYftG/Tuvxr87ON/ALNZahdtQoSz5hP327Tct8+ip9j/GXf7jPkOP9kUrEHC2PdHnEvqJdkzV5vFYW43pzkLRTLt9M/67Azj0ndEJeOTtlh/PsT1BriJuqjlv3r/vnX1/7Y+pj7/wKx0XY27HPTM6Gjjvqn0naR9TCrfJKvRD3hxZj6kd3L5Zcr5pfMvpkW9vf703R9TGCijBlcVzHsxnMQGPsRm1mDeRcUztx1p9pjfMkbyYWj4zfv8o9UOL758e76099jlzRG2sgNN4ZvEEf7/i+owty/6vYpGvLKY+vL8XV/uFvDWKl/S6suh3LjFH+E7KiSnMdfVCOCmvtYMri/bqKl3uGLTsm9Scj/JTK3CDMUavVWpisQhZR4vFW2/ffmNffPHTlunAD3fFITzwXJSE7wXkUJjr3ubsklkYZsMnRW9K/p1XIZdN149/x9DMNOZIB3yXFoi0VuE2VChLLoJw8CA95qNcPMEzipJgFqPn+uj9n1F63q153m7xHeBxTErxXQozo8DNKdzy0yf28itjxi0iK6p/30nhNqceWt4u5KnAgPKtYukxv0VJOO/ynZQX25/rKe/PPb+r33Ka0g9H7Xv92Mjj42X3dZ/24f7nJdxKWsOd22Qr7QVwgCuL5zwYxQR6xY7iKUr3XfPzStrhVa85Mmrf6jG1fEbNB/omL6aWj1Is97UplNpX2g8lSo7nHrnU3gfgAs8snsCvuEN/vdz9xXar6A1XFscadWVRrcCAyvEzOp9RVxYpcMO86dk3k15ZTPpuPrqyaIkFZO7111EuGU4X4InE27N1SkavVWpisQhXlswKqWfmQ4/5NcnD8U2PR84DeI35ABW553dv83PJLCCTsVj8xF7hutf9lZtLqsgV13N4m5tKIn0ncRsqAABAPdGLoSQvzt6+/ebw/z+SWLiu+kIxJ8fgos9jJKLAzQnc8qP5EH2tsSp5sL7GPrYo/wp19OtZ29sOj/NSmscqx8/ofEbNh9n7hnnTu2/WBXJyCzCpxw4c3kr6cqXw9a2klnnbaOq/CaJfHexx+zJgxpXFsx6MYgK9YkfxFKX7rvl5Je3wqtccGbVv9ZhaPqPmA32TF1PLRylW4/23lNpX0o6c1+Z8Zs33RjJynDERnlk8gV9x9R+ifxGlwI3XK4sUuNE6fkbn0/bKIgVuasXU8lGKnX1/j++VXrHloHaAnShSYwXf67nvjYQri9pGr1VqYrEIV46+pCYrcPPhcvl4q9Noo45HzgPjPT09NSkuUVvr+eClHxLJnFsiST1fDZ5Ln4z9cqJ4zPVqr9uS1OaS7/Xc90bC95y2SP9G4TZUwKco/zCFb8zDjyL1Q6S2eDSy/2/3nZsLBVH6oa/RDQVuTlC5rWWG2G28x1gpFrjxqu1th+P27SU2egxUtO4bL/2QQ2keK8XOvj/1e2X0XEr9vr1e7e6t/qltbpXjvds0S24NnuUxCMCMK4tnPZjWA/ORY0fxFKX7rvl5Je3wqtccGbVv9VjP/Sjr1TeRKM1jpViN999SmkstzrGl+zn73h7f9aXvV48BLBZP+tLMfmSf/qpVEmvxmVFiR/EUpfuu+Xkl7fCq1xwZtW/1WM/9KOvVN5EozWOlWI3331KaSy3OsaX7OfveHt/1pe9XjwHchnrG8+X5n9eKtfjMKLHb+LLc/q/Hzuz76eCZ+FrtO9pHJC3nyL0+VJrHKsdP7ZiXeXy2b16Kjby+ne6lzaNvF2xNaR4rxc6+P/V7ZdQx9fnnP7Svv/6uWcbfPKzV5pLv9aP3tvyun+X7BzDjyiIA4LzoRRZmLPYSfUzVDen/54ViKuYIMBGuLJ6g8sD8DLHbeI+xosBNPRS40Tp+6u/nY5n9tuN8XEji5f8+KlN+tm9mOE75G5R9jqn075X2x9RWzI6vKJ6aI6ML3LT8ro/4/QPs4criOQ+m9cB85NhRPEXpvmt+Xkk7vOo1R0btWz2mls+oY6W0byKLPm/Ujqktau1Lya/VZ6ao3a+135vzfqUYsInF4jktHiBWeqBZKXYUT1G675qfV9IOr3rNkVH7Vo+p5TPqWCntm8iizxu1Y2qLWvtS8mv1mSlq92vt9+a8XykGbGKxeML1atfr1X7++tJ9SazFZ0aJHcVTlO675ueVtMOrXnNk1L7VY2r5jDpWSvsmsujzRu2Y2qLWvpT8Wn1mitr9Wvu9Oe9XigF7eGYR3nywnaITj4+XT/7/t2+/sctl65UAkGT3fBMEhUomtCz2laXP64Fz5NN1zEvF1sfHpAUOcxuohMUiXLle7d1tbFm2vzgyq7sBwCcul8vqfAMEsLtQvF5t6ZnIsU9TOfpO18obiIXbUCtZFluWxT57rjCVFSt9f+RY7mtvle675uel7iO6Xn2oNI89HD/qsRLR+4Z546dvtigdUy36IXU/JUb2Q+18lOYDYMZisabSClRKFbGUYrmvvVW675qfl7qP6Hr1odI89nD8qMdKRO8b5k2/WI3331I6plr0Q+p+Sozsh9r5KM0HwJbr9To6h2xHf0/r9d/d6un515kHM8W/heY3lvJay/z7UPc+7+jvum39TbIz7TvaR6pRc/1W7vFYa47c+/t7SvNY+fhRj9X4O4v8LcH55o1a3/T4XkmNWYXvzJptPsrn/fun1+85SLvvd33E7x/UpbhWOYvFItxbdp5Z3PFh67nH13rMr6N9OPDh9bNco45HD+eBp6envUISH+49D3fw3pHu5l1b6jjnzAfRvr3Vva/Rzqjz1ZJXzOaTZ/96HSd3FoFJzjyzWDImHr5/MFakOcJtqIggp+qZ+j8QPaAP0+31VUofKvazYk5neGiHhxyhL2ce3X6XdpmDb99+U/oRVD4FGmKxWEnpQ8U9Hl72GEt57fVq755/VXxjZt+3O/M6Z99n31uyjxm16EO1eXw2PzVKfViSswfK591ZYzXef2vg8fPtd+b1+vG7dMSx8sUXP7X3758+2e5Iynvk+Vlpzno9/0EHi8V6HoxiAi1iNd5/q8d7S/YxoxZ9qDaPz+anRqkPS3L2wOt5N3KsxvtvcQ7K46FvlOashzGFMBaL9XxpZj96/m9urPT9kWM13n+rx3tL9jGjFn2oNo/P5qdGqQ9LcvbA63k3cqzG+29xDsrjoW+U5qyHMYUwCtwgpCWj6M3bt9/YF1/8tGU64ZwtLFKTh/NAqwIKI53pWycFZeSozGMlg+dSUtGhZaeozN53Ta1x3tvvnntFYUaeg46K3pwpZrOFAjdoKdIc8Xplce9hZh5yxovkufD1199tmUdEHGd9KPbz2ZxYKOZTHH8FI+dS6r43X9fhu6akmM3Z1zRxUPSG4wJehFmrfGd0AmcolhN/fnD4wYy/aVUzVvD+d7cxO/7bUkO8/ltOuX970dsvU0fOjPH79/U/s/7fCCzJ77Kaw17PLffGyqPefxvPyXl3irl0L8fan5fx9xOPnJiv++eglPcr/W3J2udnD98//E3FsRTXKmd5vbKo6MEoJtAi1uozVajn10uL8VSbxyPy67Ufj8deKaV+jT5v1OZS7Rw9nm/U8hnVX6XvV2ozsMnlM4uKov6KOzpW8zPt4MpiQqnuJiJcWaxxX/65X4X3++tyuSwK83j0L+sj2pzbD14pXBmJPm8U51LKucUyv2tqzaWj/dqpK4tlc2T0+a9lfh6+f7iyiFpYLGIaS0bRmy0tCuGkFoq5996RvBa4maDoSlIxjh5Ui/WUUDn+ZjN6Lt2O+5JZVGaUUT+IFmp6DutcgEzmfAzk4jZUzKTooeIGxQncPeS8w+tD3PL/wCuk1D71uZArWns8Gdn3W/tWOs42HRSLUafct7nzULktwCGXBW4URb3lZ3Ss8mcWF71peeuMQuGGM1r9Wtq6wIDX/s6lcTyfL9Zz73avl/+7wpXm3fcr3DLn+LwrM5da9M3tXHnt9dW8oz8F0cDpxxvUtL0NtWS/2/Pw6DzCLafwiiuL9TxY7GICo2I995NCKZfoSvuL/v5I6Xj2elwo9UOk867H2FFchXp+OUadW1qcq2Y8dyIAnlmsJO6vuLF/4bb8P6fR8MqizwI3rZRecard3x55KLTAlUW9mFo+SrHbuCUWs+HK4jlt7+apX4BH8TwClGKxiKkthUVvdny4Pt/yumeC4ioQEOEHhdEFTRqg0IVTS2Yxm1GLxevVkn5E8UC5SFqvzwRG4zZUzK5FsYSUf0ywUERrFGHRxLHvV/LY3RaV6Vhk5va493we8Jw7EAYFbhrilh8Xt0MlFUuwzNtVSx6sh6YztxCN/jtjLT6z/22oKaPji0K/Rp83A27pO7z18+XPLvW/FbFNQaCU16beQp76eT3PLS3mCLeXwiuuLLb1YBQTKI0p5pOi9udhvNrzZsbjp8ex54FSv0afN73modJxrzZHUimNaa85wjkR8nhmsSF+xY3zC7dVLoTjvejAjLiyOOrKYrxjRb1gjlo+KrHl+Bn3pKIy6mM/15VF3wVugF5YLAIJ7vwjIcUnRW+8Fx2Y0ZniBBQ7KBfxWGHstS2ZhWzM0ovKzDT2no9dCtwAv8JtqECa0gftb//hwYP7QJpox0q09kSUW4SIMY2F8QReocBNQ9zyE+p2qOJCOJ++d1104MzfWRTpG7nY2fcfjcG5z9sfP+V+0Ir1KdAxw62Dc82b87G9eWD28Qqi+nGvMke8FKfqdXsot5zCK64stvVgFBMojanlk5P3rZL3ln7mbLEa77+l9HnRj5+RfbNFKW/mTb/YHvXjXm2OqFObNx77EIHxzGJD/Io73y/cdlwIp2rRG64s9r2ySIGbWDG1sVKKqeWjdB5Pu7IYfy6lvNZLcaqaY9KqwA0wEotFoKIlrxBOUdEbHpavr3ZxAood+NFg7PeKpHy4XC7vNuIYYMksZnN9VchmT8lcOpg3aKTmuZhzPiLiNlSgrpwH4/kHARDX3vHNca8lZzx6FD5hfvRFMRvgDgrcNMQtP1PeDrUqxmGJRW/OFAMQabNc7Oz7axemGF3oQm1clGKtx2r02DNvkm85PbK6bTDlM0vG3ktRmBz3br+MdtvunhafCfTAlcW2HoxiAqUxtXxK23Ir9XU57ydW5/23lD5vxuOnV99s8Tj2zJu82JbSvkn9zNT3ehX5WMkZuxafCTTHM4sN8Ssuv3DbnSuL9uqXawrcjJ83FLiZJ9Z6rEaPPfOm7vk578ri+bH3UhQmx0xXFilwg4hYLAKNLRlFb96+/ca++OKnSa9t/bD8JIUWPik2QoGbjwTHvnlRGMY+vqVBMZstqWMveJw1kVDUJ8yxEqktwAtuQwXaS36A/uuvv1v9MwuE/0eMzdHGM9T6RS0f+EQxm/4oIAM4R4Gbhrjlh9uhnmNZRW+2bN2+0jrviIUWtqS2uXYfKh8/imPf/jbUuvsePfacdzdvOT2SdItgyn5Sx370cVZ6W2SP7xqFeVPrltEWnwn0wJXFth6MYgKlMbV8WrQvxci+iS61zbX70MPxo6RX39Ted+3P8zBv1GNbWvRN6n5GUZsjtXNUml+tPhNojmcWG5r9V1x+4d6P2cGVxffvn1axMVcW4xVa2PK6b6MVOTn7fsWxr91ft/FoY895N++8a1WvLKaN/ejjTOfKot9j5TZGgRtExGIRGGDJKHqDXFczW1bRveJBNwUndsdlpiInR3nPaKax92jJLFyz5XqymM0WL8ePyjyMdKxEagvwgttQgTF46L+Z7e/jneJBjMM2+gWelBaKmXG+z9hmACdQ4KazmW754Xaow1hx0Rvku//3vvbfe+72qrqf1+/4uazm58y3NHsc+5nOu/s9vavp7Ze5hWu83WqZ2g8zHCs5t4y2+EygB64s9vdg8xUTKImp5dOrzWijZAxqj+mMx49XHsc+0rypPb969U2PfCLNkS1KbS4d9xnPnQiAZxY7i/ArrtdfL9VjxpXFHu5cWYxV5KTFZ854ZdHj2EeYNw3PnY2vLObNd/X50P7Kot9j5TZGgRtExGIRSPD09FRcQOGex8dLy4/Htg/X51uCzShw04qXgh97PI19j3NVJR8ul8u7oxcsFQrXbLneKWbjqA9L3O3/XiKdJyO1BXjBbahAmub/cHj79puMV7v+t7eS1uO6V0RituISs7V3JC+LnJQ8W7QlZS566cMSM7QRQAUUuBGhcguFWkwln9yCBWds/VmHlrzd3pMTu43bwW1qqeN8Lp+6hWK8Hj89+iH3Vrac99c+Z3g/V9WScHtprirnNE99WELl3EKBG25DhTauLOp4MJ2Hs5ViivlEodSvvebNlpLXqcfU8hl1jLaYI7XzmfFcVbstM/ZhCbVzS+0clc5BrT4TaI5nFkUo/SqmFFPJx3uBji1cWfzWt/0QqdDCVj+MzsfrlUVPBW48navu9YN1LFzjtQ9LlBZcGXXsKpxv9mIUuEFELBaBBN4LdBSQKYJQYlnSv3Dfvv1m85ZgihNoKy0sEaW4kYdz1eef/9C+/vq71T/3eqdwTSoPfViDyjktUlGYSG0BXnAbKpBm1gIdUYogJI9fi3/EAh3Jn6taHGN5BcLuku/DCmZoI4AKKHAjQuUWCrWYTj7nC3R4v6VJo/+L581q/CzzFjel9vk7fnrchpo3dqXvr52Pwrmq17yxgttLjwsRXZr34dnPPMp764qTwjHV7zbUvZ7RanPpLaMtPhPogSuLOh5M5+FspZhaPqVt8UipD1vMm1RK7Zvx+CkZz5y+SX1/7XyUYj33k0KpX2u8P4XSfOg1R7Yotbl0jHvMG6A6nlkUofSrmFJMLZ8Zryx6KzDwknfJ1Y3375+m6YcoMQrc+Jk31ujKYo9+Pft+rizGPFZuYxS4QUQsFoHGvBdLiPpQ/pJR9GYCH67Pt+p6RYGbvpbFvrJOzzRfXxWu8dqvXvPuIVLfRGoL8ILbUAEciVwEIXLbckUpZFRibz4wT7b1mjP0PwAMRIEbYSq3VYyMqeVz7hab/TFW+TtX0WKJry0uehOJ0vjVPs7S5kh5YZiSfJRiKa/db12WE7f37n+YSt/k5j2qLSrfzaPHtEXf1G4LMBJXFrU9mM4D26NiavmUtuUWfdMmVuP9s1Eavx7HmVo+SrHc157lsV9b5L1FaT70On62KLW5dIz5ToJLPLMoTOmXsgi/Xo674tHm4X2V9inGzr7fJr6yaCeu8ijFSgvcjM5HoQ8zryzWOFbcFQ46+34K3OiOac0YBW4QEYtFoLEWD7w/PT11Ky6R6MPlcnFdIMXMbKHozWuuit6oFZZQyyfVMqhwTaqR/Xpw3r17/lOaD4LfHy0M+U5SGmegFm5DBXxS+6JXy+csimn8SpQxRR4K1+zb6xtvx4q3fM+YoY1AFywWnVkWW5bFPnu+TSF8TC2f0rbcqv15I6n19Zn3X6/27vlqxxsz+76ZvblebfEaS3mtlzGtfZyp5aMUy3R2fr7z2K+l+y4xeJzdUTt+GCt4xWLRnwfTeYi7R0wtn9K23Kr9eSOp9bVSPh76YYtSW2q3Qy0fpVgOpRxH9k2P8/bIcfZIaW62+kygOZ5ZdOb5l6YHE3ywu0VMLZ8zsRYP7x89FzGKUiGCkftWiqW81o4LlciMae3jTC0fhT68Xu265D+327UtI/u1pHhJboGbLT36MJIRxxkFbhARi0VMbZIH/bto+fB+wHEaVXxh1Y+Pj5ecj5AteqNWWEItn1tLpUI2Z4rUlBhc4Ob0vpXmg+KPjS1w3AN1cBsqZhdpATJS62IV0cZpVHtW+3379pui98OtGmPpsUgN5hi3UW3c2+8MfY6gvjM6AZRTuX2pRaz1ft6/L+19v5RvhbuNRRynEcfPVj9+8cVPzezT+WAHt6YqzIfcOaJ2blHor/3sPl4tVMhRsV/P7rvGOaxeWz7e1aD83ew19nLHSIs5BozClcUYHkynMELtWM/9zEZpnGccp5HHT2o+o/KuPUfUzi3q/aWWo1K/lu67hFr/K+WjFKvxfkAGzywGoPKLWotY6/3M8qD/Fl9XFuONU4/+v42nFgcxh0VvKHCTF7ODMda+skiBm1bty4mp5aMUq/F+QAmLRUxtlgf9t3h62D7iOCkXX1gOKmJeOxc0SaVWWEItn1sex9iMAjcA0BvPLGJ2H2zOoh3eHraPNk7q/b/b3xuLDNkKqTl6Vtzt/ePH55//0L7++rupL1efmwCAjlgsYmo9/nwBvyiXG/FnJma2tfg7uBIVZREfpR0rRwtF5auIAIDxKHAT1LLYsiz22fP98G5javmUtuUWfdOur5XyUeuHLaPm8ajjLOf9kXk9flLb0mO/Nd6fQq3/lfJRiuW+FlDHYjGuB9OpDFYSU8untC236Js2MbV81Pphy6h5POo4y3l/ZF6Pn9S29NhvjfenUOt/pXyUYrmvBaRR4Cao51+uHkygMlhJTC2fM7FW1ftU2qcYU8tHpR9K5qKJV0gtrYYaseLui8fHy9H/3L1SrOL5NCVGNVQfc2R0LPe1gDoWi0BjPLMIFSVzcTmonrmhe9Gb0uNMqeJuZkGaIsrPLPYsOgQzM/vA8+EAbnEbKgDgrrdvv8l5Of/AL9BroWj6lU+ZR33R3wBWWCxOROkB8BYPiqvHttA37fpaKR+1fthy7zO/+OKn9v790ydbyee1bHNKLjnvD+SNmX3fzN5cr7Zcr/bOw/GDfjjHlseO4oBHLBbn8mA6D4CnxtTyKW3LLfqmTUwtH7V+2FIyj0s+b9RxlvP+KLweP+jH6xxRih3FAXd4ZnEiz79wPZjAA+CpMbV8zsQocMO8UemHkrm49d7cwilKx1nO+3u7068lksZkL6507kQbqd9Je3Fi+30DeMViEWiMAjcfBSxW4a4YRMlc3Hrv0aLm3m2qPSkXuKGYzT6lokOzSDxWRp7L3Z13Ae+4DRVAL5EWimbx2jO7IcVeKGZzyGPOnqX298hzH+ddoLPvjE4A/SjdpjHT7YTv37cZE5X21egHrxT6Ne821PNt8Tx+acfPx6sVvW+LNcG/X9lrP/dj6zHx+ncWo8VGUuoHbkPFDLiyOJcH03kAPDWmlk9pW27N2DeRKPVrzhwpaYtHI4+fnHxSXsd5d9/I85dS30Q/jyv1Q+l5F5DHM4sTUfrlzd8v3P0Kb0Ttm4jFKtSvJtzGexa4UXpmMaXAzajj3riyKHE+5cpinX7oQb2vj+KARywWgcYiFbgJWKSmiMPxOz0XcwvcwOzt22/siy9++u3/n1vM5uqsIE0PI8+nkc7lJUYvFmfqa0ABt6ECyMFC8VemL77x9u03o1OQdrswzCxmM/382rHXL/RXPyP7mnEGOqPAzeSUbt3wdjtU+m1TbfpfrS1KLpfLojD2o2O38doFbl6ummXcVol9MrfWjdz3/VjdQkRn+maLRt/0ib386QqVfNRiQDRcWcSD6TwUvhVTy6e0Lbe89o0HSmOvdvxsqT2PkcfDvCG2TylH5sjYGBAKzyxOTunXOH+/cI8tyKDWFiVcWdy7sli3wM3We40ri594XejnzjOeXFkUj1HghjmS2jdAJCwWgcYiFUUYXdgglbd+7aV2gZut9y4L/2A64xqgmM3MBbA45wCIittQAeTwUFzAQ46R0f/5ovTZlAtFAIiMAjdYUbudQymfc7dutunrMe3zUdhALR+Vfqhd4GbnvcyR+7fjSt+yePb9XgpgtaA0fspzJFoMmAFXFrHlwbQeFFfKp7Qtt+ibNjG1fNT6YcuoeazWN+rHvYe+mZHS+HmYI1FiQHg8s4gVtV/tlPI592t7nAI3XmJq+aj0Q48CN6PbrDJHbMoriz4KYLXg8RhQPn68xIAZsFgEGotU4Aa+9Shwg4+Wg0I/1wDFbLZ4KYDVAscAgKi4DRVob694RZSiFgDWZjzuI7cNAKZEgRsk4VaXklibojA67dOLqeWj0g+dCtzI9cOgOeKi0E/dvvFRAOts7OjKqUqO+nPEbwyYFVcWkerBeIheLaaWj1JMLR+1ftiS85ln36sUU8tHKaaWj1Jsj1KOzJE2MWBKPLOIJPx6qRdTy0cpppaPSj9Q4IY5Qt+0ubLo8RhgjnBlEUjBYhEAJhGlwM3T09NXpvcH4D9cLh9vw0RMSscAAPTCbagAAG/UFopmmjkBAFCExSJOWxZblsU+e75do0ms1348xtTyUYqp5aPWD1tyPvPse1u0T4nS2HP8tOubLUo5MkfatRmYEYtFlHgwHqIfGVPLRymmlo9aP2zJ+cyz723RPiVKY8/x0ya2RylH5kibGDAlnlnEac+/uD0YD9EPe9heKR+lmFo+Kv0QpcDNUS4jRSlyopaPSowCN3PPEWBWLBaBwEQLgdREUZEMgQrcSH5xUeQkNqVjAOWcfz/y3YduuA0ViM3rF2Gq6O2r7UNmXJVivoo5oa4oxw8+8vz94Tl3OPOd0QkgFm510boN6P37nNHziXmTM0c+/hJ97tbPvDFoGzvfDuYIfXM29nIlRyUf5khZbIbvR6AGriyitgfjIfpesdzXRsW82Y+1+sxbSm3m3FIeU8tHKaaWD/1Qpy0AdvDMIqri10utX3ZVC4HUtFVYwkxrrJTnSPqv8DoFbtT6JlpMLR+lmFo+9EObc5oHPCeLXlgsAoGpFgKpiS/MPijuASAS79+PnHfRC7ehArFFL7wQvX1KKO4BIBLP5y7PucOb6/XKxtZ0M7suZtfPzK5Lbqz0/ZFjavkoxdTyoR/0Ymr5KMXU8lGKqeVDP9RpCxsb2/42PAG2+NvziflfmV0/y42Vvj9yTC0fpZhaPvSDXkwtH6WYWj5KMbV86Ic6bWFjY9vfhifAFn8zfr1sElPLRymmlg/9oBdTy0cpppaPUkwtH/qhTlvY2Nj2t+V6vRoAAAAAAK9R4AYAAAAAsMJiEUMsiy3LYp89/82j3VjOa2eLqeWjFFPLh37Qi6nloxRTy0cpppYP/ZCfN4BMo++DZZtzs4wHz1NfO1tMLR+lmFo+9INeTC0fpZhaPkoxtXzoh/y82djY8rbhCbDNudmED9HXjqnloxRTy4d+0Iup5aMUU8tHKaaWD/2QnzcbG1veRoEbAAAAAMAKzywCAAAAAFZYLGKI6A/RU2CAvlGIqeWjFFPLRymmlo9STC0f+gFAc6Pvg2Wbc7OMh9FTXztbTC0fpZhaPvSDXkwtH6WYWj5KMbV86Ifyf4+wsbEdb8MTYJtzs+AP0feIqeWjFFPLh37Qi6nloxRTy0cpppYP/VD+7xE2NrbjjQI3AAAAAIAVnlkEAAAAAKywWIQMDw/RK8XU8lGKqeVDP+jF1PJRiqnloxRTyydSPwAQNfo+WDa2l80cPESvFFPLRymmlg/9oBdTy0cpppaPUkwtn0j9wMbGprkNT4CN7WUzBw/RK8XU8lGKqeVDP+jF1PJRiqnloxRTyydSP7CxsWluFLgBAAAAAKzwzCIAAAAAYIXFIsJQevjfa4GBKDG1fOgHvZhaPkoxtXyUYmr5eOgHAM6Nvg+Wja3WZkIP//eIqeWjFFPLh37Qi6nloxRTy0cpppaPh35gY2PzvQ1PgI2t1mZCD//3iKnloxRTy4d+0Iup5aMUU8tHKaaWj4d+YGNj871R4AYAAAAAsMIziwAAAACAFRaLmI5SkQAKLdA39AN9oxZTy0cpppZPrzYDmNjo+2DZ2HpvJlQkoCSmlo9STC0f+kEvppaPUkwtH6WYWj692szGxjbvNjwBNrbemwkVCSiJqeWjFFPLh37Qi6nloxRTy0cpppZPrzazsbHNu1HgBgAAAACwwjOLAAAAAIAVFosAAAAAgBUWi8AOpWp0VOWjb+gH+oa+GR9TyycnbwA4ZfRDk2xsqpsJVaPbiqnloxRTy4d+0Iup5aMUU8tHKaaWT07ebGxsbGe24QmwsaluJlSNbiumlo9STC0f+kEvppaPUkwtH6WYWj45ebOxsbGd2aiGCgAAAABY4ZlFAAAAAMAKi0WgAQotjI2p5UM/6MXU8lGKqeWjFBu9bwDobvR9sGxsETej0MLQmFo+9INeTC0fpZhaPkqx0ftmY2Nj670NT4CNLeJmFFoYGlPLh37Qi6nloxRTy0cpNnrfbGxsbL03CtwAAAAAAFZ4ZhEAAAAAsMJiERjIa6EF9ZhaPvSDXkwtH6WYWj5KsRrvBwBXRt8Hy8Y282ZOCy2ox9TyoR/0Ymr5KMXU8lGK1Xg/Gxsbm6dteAJsbDNv5rTQgnpMLR/6QS+mlo9STC0fpViN97OxsbF52ihwAwAAAABY4ZlFAAAAAMAKi0XAMaXCD0oxtXzoB72YWj5KMbV8lGIAMJ3R98GysbGd30yo8INSTC0f+kEvppaPUkwtH6UYGxsb22zb8ATY2NjObyZU+EEpppYP/aAXU8tHKaaWj1KMjY2NbbaNAjcAAAAAgBWeWQQAAAAArLBYBCalVDSCAh30A32jE1PLp7QtAIACo++DZWNjG7OZUNGI2jG1fOgHvZhaPkoxtXxK28LGxsbGdn4bngAbG9uYzYSKRtSOqeVDP+jF1PJRiqnlU9oWNjY2NrbzGwVuAAAAAAArPLMIAAAAAFhhsQjgkFKxihkLdNAP9M3sfQMAGGj0fbBsbGzamwkVq0iNqeVDP+jF1PJRiinmw8bGxsY2ZhueABsbm/ZmQsUqUmNq+dAPejG1fJRiivmwsbGxsY3ZKHADAAAAAFjhmUUAAAAAwAqLRQDNRC/QocRDoRKlmFo+SrHc1wIA4mKxCKClBzP7s+f/9oz13I+Kkf3gMaaWj1Is97UAgKB4ZhFAM89XIB7M7Mvr1a69Yj33o2JkP3iMqeWjFMt9LQAgLhaLAAAAAIAVbkMFAAAAAKywWAQAbFIqukKBmzptBgAgB4tFAMAepaIrI4u4RIkBAJCFZxYBAJuUiq5Q4CZWQSYAgA8sFgEAAAAAK9yGCgAAAABYYbEIAKhOqbCL1wI3AACMxmIRANCCUmEXrwVuAAAYimcWAQDVKRV28VrgBgCA0VgsAgAAAABWuA0VAAAAALDCYhEAIE+twA0AADNgsQgA8ECtwA0AAOHxzCIAQJ5agRsAAGbAYhEAAAAAsMJtqAAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAIAVFosAAAAAgBUWiwAAAACAFRaLAAAAAICV/x/aq44O0FWXNgAAAABJRU5ErkJggg==\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": 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: 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": 48,
   "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": 49,
   "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": 50,
   "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": 51,
   "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": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['suck', {5: ['forward', 'suck'], 7: []}]"
      ]
     },
     "execution_count": 52,
     "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": 53,
   "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": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{s: and_or_search(ErraticVacuum(s, {7,8})) \n",
    " for s in range(1, 9)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparing Algorithms on EightPuzzle Problems of Different Lengths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import lru_cache\n",
    "\n",
    "def build_table(table, depth, state, problem):\n",
    "    if depth > 0 and state not in table:\n",
    "        problem.initial = state\n",
    "        table[state] = len(astar_search(problem))\n",
    "        for a in problem.actions(state):\n",
    "            build_table(table, depth - 1, problem.result(state, a), problem)\n",
    "    return table\n",
    "\n",
    "def invert_table(table):\n",
    "    result = defaultdict(list)\n",
    "    for key, val in table.items():\n",
    "        result[val].append(key)\n",
    "    return result\n",
    "\n",
    "goal = (0, 1, 2, 3, 4, 5, 6, 7, 8)\n",
    "table8 = invert_table(build_table({}, 25, goal, EightPuzzle(goal)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6724"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def report8(table8, M, Ds=range(2, 25, 2), searchers=(breadth_first_search, astar_misplaced_tiles, astar_search)):\n",
    "    \"Make a table of average nodes generated and effective branching factor\"\n",
    "    for d in Ds:\n",
    "        line = [d]\n",
    "        N = min(M, len(table8[d]))\n",
    "        states = random.sample(table8[d], N)\n",
    "        for searcher in searchers:\n",
    "            nodes = 0\n",
    "            for s in states:\n",
    "                problem = CountCalls(EightPuzzle(s))\n",
    "                searcher(problem)\n",
    "                nodes += problem._counts['result']\n",
    "            nodes = int(round(nodes/N))\n",
    "            line.append(nodes)\n",
    "        line.extend([ebf(d, n) for n in line[1:]])\n",
    "        print('{:2} & {:6} & {:5} & {:5} && {:.2f} & {:.2f} & {:.2f}'\n",
    "              .format(*line))\n",
    "\n",
    "        \n",
    "def ebf(d, N, possible_bs=[b/100 for b in range(100, 300)]):\n",
    "    \"Effective Branching Factor\"\n",
    "    return min(possible_bs, key=lambda b: abs(N - sum(b**i for i in range(1, d+1))))\n",
    "\n",
    "def edepth_reduction(d, N, b=2.67):\n",
    "    \n",
    "    \n",
    "\n",
    "from statistics import mean \n",
    "\n",
    "def random_state():\n",
    "    x = list(range(9))\n",
    "    random.shuffle(x)\n",
    "    return tuple(x)\n",
    "\n",
    "meanbf = mean(len(e3.actions(random_state())) for _ in range(10000))\n",
    "meanbf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 1,\n",
       " 1: 2,\n",
       " 2: 4,\n",
       " 3: 8,\n",
       " 4: 16,\n",
       " 5: 20,\n",
       " 6: 36,\n",
       " 7: 60,\n",
       " 8: 87,\n",
       " 9: 123,\n",
       " 10: 175,\n",
       " 11: 280,\n",
       " 12: 397,\n",
       " 13: 656,\n",
       " 14: 898,\n",
       " 15: 1452,\n",
       " 16: 1670,\n",
       " 17: 2677,\n",
       " 18: 2699,\n",
       " 19: 4015,\n",
       " 20: 3472,\n",
       " 21: 4672,\n",
       " 22: 3311,\n",
       " 23: 3898,\n",
       " 24: 1945,\n",
       " 25: 1796,\n",
       " 26: 621,\n",
       " 27: 368,\n",
       " 28: 63,\n",
       " 29: 19,\n",
       " 30: 0}"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{n: len(v) for (n, v) in table30.items()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 24min 7s, sys: 11.6 s, total: 24min 19s\n",
      "Wall time: 24min 44s\n"
     ]
    }
   ],
   "source": [
    "%time table30 = invert_table(build_table({}, 30, goal, EightPuzzle(goal)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 2 &      5 &     6 &     6 && 1.79 & 2.00 & 2.00\n",
      " 4 &     33 &    12 &    12 && 2.06 & 1.49 & 1.49\n",
      " 6 &    128 &    24 &    19 && 2.01 & 1.42 & 1.34\n",
      " 8 &    368 &    48 &    31 && 1.91 & 1.40 & 1.30\n",
      "10 &   1033 &   116 &    48 && 1.85 & 1.43 & 1.27\n",
      "12 &   2672 &   279 &    84 && 1.80 & 1.45 & 1.28\n",
      "14 &   6783 &   678 &   174 && 1.77 & 1.47 & 1.31\n",
      "16 &  17270 &  1683 &   364 && 1.74 & 1.48 & 1.32\n",
      "18 &  41558 &  4102 &   751 && 1.72 & 1.49 & 1.34\n",
      "20 &  91493 &  9905 &  1318 && 1.69 & 1.50 & 1.34\n",
      "22 & 175921 & 22955 &  2548 && 1.66 & 1.50 & 1.34\n",
      "24 & 290082 & 53039 &  5733 && 1.62 & 1.50 & 1.36\n",
      "CPU times: user 6min, sys: 3.63 s, total: 6min 4s\n",
      "Wall time: 6min 13s\n"
     ]
    }
   ],
   "source": [
    "%time report8(table30, 20, range(26, 31, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "26 & 395355 & 110372 & 10080 && 1.58 & 1.50 & 1.35\n",
      "28 & 463234 & 202565 & 22055 && 1.53 & 1.49 & 1.36\n"
     ]
    },
    {
     "ename": "ZeroDivisionError",
     "evalue": "division by zero",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mZeroDivisionError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<timed eval>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m<ipython-input-69-674fb01939fb>\u001b[0m in \u001b[0;36mreport8\u001b[0;34m(table8, M, Ds, searchers)\u001b[0m\n\u001b[1;32m     11\u001b[0m                 \u001b[0msearcher\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproblem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m                 \u001b[0mnodes\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_counts\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'result'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 13\u001b[0;31m             \u001b[0mnodes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mround\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnodes\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     14\u001b[0m             \u001b[0mline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnodes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m         \u001b[0mline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mextend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mebf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mline\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mZeroDivisionError\u001b[0m: division by zero"
     ]
    }
   ],
   "source": [
    "%time report8(table30, 20, range(26, 31, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 116 116 ['A']\n",
      "140 0 140 ['A', 'S']\n",
      "0 83 83 ['A']\n",
      "118 0 118 ['A', 'T']\n",
      "0 45 45 ['A']\n",
      "75 0 75 ['A', 'Z']\n",
      "0 176 176 ['B']\n",
      "101 92 193 ['B', 'P']\n",
      "211 0 211 ['B', 'F']\n",
      "0 77 77 ['B']\n",
      "90 0 90 ['B', 'G']\n",
      "0 100 100 ['B']\n",
      "101 0 101 ['B', 'P']\n",
      "0 80 80 ['B']\n",
      "85 0 85 ['B', 'U']\n",
      "0 87 87 ['C']\n",
      "120 0 120 ['C', 'D']\n",
      "0 109 109 ['C']\n",
      "138 0 138 ['C', 'P']\n",
      "0 128 128 ['C']\n",
      "146 0 146 ['C', 'R']\n",
      "0 47 47 ['D']\n",
      "75 0 75 ['D', 'M']\n",
      "0 62 62 ['E']\n",
      "86 0 86 ['E', 'H']\n",
      "0 98 98 ['F']\n",
      "99 0 99 ['F', 'S']\n",
      "0 77 77 ['H']\n",
      "98 0 98 ['H', 'U']\n",
      "0 85 85 ['I']\n",
      "87 0 87 ['I', 'N']\n",
      "0 78 78 ['I']\n",
      "92 0 92 ['I', 'V']\n",
      "0 36 36 ['L']\n",
      "70 0 70 ['L', 'M']\n",
      "0 86 86 ['L']\n",
      "111 0 111 ['L', 'T']\n",
      "0 136 136 ['O']\n",
      "151 0 151 ['O', 'S']\n",
      "0 48 48 ['O']\n",
      "71 0 71 ['O', 'Z']\n",
      "0 93 93 ['P']\n",
      "97 0 97 ['P', 'R']\n",
      "0 65 65 ['R']\n",
      "80 0 80 ['R', 'S']\n",
      "0 127 127 ['U']\n",
      "142 0 142 ['U', 'V']\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(1.2698088530709188, 1.2059558858330393)"
      ]
     },
     "execution_count": 315,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from itertools import combinations\n",
    "from statistics import median, mean\n",
    "\n",
    "# Detour index for Romania\n",
    "\n",
    "L = romania.locations\n",
    "def ratio(a, b): return astar_search(RouteProblem(a, b, map=romania)).path_cost / sld(L[a], L[b])\n",
    "nums = [ratio(a, b) for a,b in combinations(L, 2) if b in r1.actions(a)]\n",
    "mean(nums), median(nums) # 1.7, 1.6 # 1.26, 1.2 for adjacent cities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function __main__.straight_line_distance(A, B)>"
      ]
     },
     "execution_count": 300,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sld"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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