search-4e.ipynb

   "metadata": {
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   "source": [
    "def action_sequence(node):\n",
    "    \"The sequence of actions to get to this node.\"\n",
    "    actions = []\n",
    "    while node.previous:\n",
    "        actions.append(node.action)\n",
    "        node = node.previous\n",
    "    return actions[::-1]\n",
    "\n",
    "def state_sequence(node):\n",
    "    \"The sequence of states to get to this node.\"\n",
    "    states = [node.state]\n",
    "    while node.previous:\n",
    "        node = node.previous\n",
    "        states.append(node.state)\n",
    "    return states[::-1]"
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "# Two Location Vacuum World"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "button": false,
    "collapsed": false,
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   "outputs": [],
   "source": [
    "dirt  = '*'\n",
    "clean = ' '\n",
    "\n",
    "class TwoLocationVacuumProblem(Problem):\n",
    "    \"\"\"A Vacuum in a world with two locations, and dirt.\n",
    "    Each state is a tuple of (location, dirt_in_W, dirt_in_E).\"\"\"\n",
    "\n",
    "    def actions(self, state): return ('W', 'E', 'Suck')\n",
    "    \n",
    "    def is_goal(self, state): return dirt not in state\n",
    " \n",
    "    def result(self, state, action):\n",
    "        \"The state that results from executing this action in this state.\"        \n",
    "        (loc, dirtW, dirtE) = state\n",
    "        if   action == 'W':                   return ('W', dirtW, dirtE)\n",
    "        elif action == 'E':                   return ('E', dirtW, dirtE)\n",
    "        elif action == 'Suck' and loc == 'W': return (loc, clean, dirtE)\n",
    "        elif action == 'Suck' and loc == 'E': return (loc, dirtW, clean) \n",
    "        else: raise ValueError('unknown action: ' + action)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "button": false,
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    "new_sheet": false,
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Node ('E', ' ', ' '): 3>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem = TwoLocationVacuumProblem(initial=('W', dirt, dirt))\n",
    "result = uniform_cost_search(problem)\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Suck', 'E', 'Suck']"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "action_sequence(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('W', '*', '*'), ('W', ' ', '*'), ('E', ' ', '*'), ('E', ' ', ' ')]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state_sequence(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Suck']"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem = TwoLocationVacuumProblem(initial=('E', clean, dirt))\n",
    "result = uniform_cost_search(problem)\n",
    "action_sequence(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
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   },
   "source": [
    "# Water Pouring Problem\n",
    "\n",
    "Here is another problem domain, to show you how to define one. The idea is that we have a number of water jugs and a water tap and the goal is to measure out a specific amount of water (in, say, ounces or liters). You can completely fill or empty a jug, but because the jugs don't have markings on them, you can't partially fill them with a specific amount. You can, however, pour one jug into another, stopping when the seconfd is full or the first is empty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
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   },
   "outputs": [],
   "source": [
    "class PourProblem(Problem):\n",
    "    \"\"\"Problem about pouring water between jugs to achieve some water level.\n",
    "    Each state is a tuples of levels. In the initialization, provide a tuple of \n",
    "    capacities, e.g. PourProblem(capacities=(8, 16, 32), initial=(2, 4, 3), goals={7}), \n",
    "    which means three jugs of capacity 8, 16, 32, currently filled with 2, 4, 3 units of \n",
    "    water, respectively, and the goal is to get a level of 7 in any one of the jugs.\"\"\"\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.capacities[i]] +\n",
    "                [('Dump', i)    for i in jugs if state[i] != 0] +\n",
    "                [('Pour', i, j) for i in jugs 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, j = action[0], action[1], action[-1]\n",
    "        if act == 'Fill': # Fill i to capacity\n",
    "            result[i] = self.capacities[i]\n",
    "        elif act == 'Dump': # Empty i\n",
    "            result[i] = 0\n",
    "        elif act == 'Pour':\n",
    "            a, b = state[i], state[j]\n",
    "            result[i], result[j] = ((0, a + b) \n",
    "                                    if (a + b <= self.capacities[j]) else\n",
    "                                    (a + b - self.capacities[j], self.capacities[j]))\n",
    "        else:\n",
    "            raise ValueError('unknown action', action)\n",
    "        return tuple(result)\n",
    "\n",
    "    def is_goal(self, state):\n",
    "        \"\"\"True if any of the jugs has a level equal to one of the goal levels.\"\"\"\n",
    "        return any(level in self.goals for level in state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 13)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p7 = PourProblem(initial=(2, 0), capacities=(5, 13), goals={7})\n",
    "p7.result((2, 0),  ('Fill', 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Pour', 0, 1), ('Fill', 0), ('Pour', 0, 1)]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = uniform_cost_search(p7)\n",
    "action_sequence(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# Visualization Output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
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   },
   "outputs": [],
   "source": [
    "def showpath(searcher, problem):\n",
    "    \"Show what happens when searcvher solves problem.\"\n",
    "    problem = Instrumented(problem)\n",
    "    print('\\n{}:'.format(searcher.__name__))\n",
    "    result = searcher(problem)\n",
    "    if result:\n",
    "        actions = action_sequence(result)\n",
    "        state = problem.initial\n",
    "        path_cost = 0\n",
    "        for steps, action in enumerate(actions, 1):\n",
    "            path_cost += problem.step_cost(state, action, 0)\n",
    "            result = problem.result(state, action)\n",
    "            print('  {} =={}==> {}; cost {} after {} steps'\n",
    "                  .format(state, action, result, path_cost, steps,\n",
    "                          '; GOAL!' if problem.is_goal(result) else ''))\n",
    "            state = result\n",
    "    msg = 'GOAL FOUND' if result else 'no solution'\n",
    "    print('{} after {} results and {} goal checks'\n",
    "          .format(msg, problem._counter['result'], problem._counter['is_goal']))\n",
    "        \n",
    "from collections import Counter\n",
    "\n",
    "class Instrumented:\n",
    "    \"Instrument an object to count all the attribute accesses in _counter.\"\n",
    "    def __init__(self, obj):\n",
    "        self._object = obj\n",
    "        self._counter = Counter()\n",
    "    def __getattr__(self, attr):\n",
    "        self._counter[attr] += 1\n",
    "        return getattr(self._object, attr)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "uniform_cost_search:\n",
      "  (2, 0) ==('Pour', 0, 1)==> (0, 2); cost 1 after 1 steps\n",
      "  (0, 2) ==('Fill', 0)==> (5, 2); cost 2 after 2 steps\n",
      "  (5, 2) ==('Pour', 0, 1)==> (0, 7); cost 3 after 3 steps\n",
      "GOAL FOUND after 83 results and 22 goal checks\n"
     ]
    }
   ],
   "source": [
    "showpath(uniform_cost_search, p7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "uniform_cost_search:\n",
      "  (0, 0) ==('Fill', 0)==> (7, 0); cost 1 after 1 steps\n",
      "  (7, 0) ==('Pour', 0, 1)==> (0, 7); cost 2 after 2 steps\n",
      "  (0, 7) ==('Fill', 0)==> (7, 7); cost 3 after 3 steps\n",
      "  (7, 7) ==('Pour', 0, 1)==> (1, 13); cost 4 after 4 steps\n",
      "  (1, 13) ==('Dump', 1)==> (1, 0); cost 5 after 5 steps\n",
      "  (1, 0) ==('Pour', 0, 1)==> (0, 1); cost 6 after 6 steps\n",
      "  (0, 1) ==('Fill', 0)==> (7, 1); cost 7 after 7 steps\n",
      "  (7, 1) ==('Pour', 0, 1)==> (0, 8); cost 8 after 8 steps\n",
      "  (0, 8) ==('Fill', 0)==> (7, 8); cost 9 after 9 steps\n",
      "  (7, 8) ==('Pour', 0, 1)==> (2, 13); cost 10 after 10 steps\n",
      "GOAL FOUND after 110 results and 32 goal checks\n"
     ]
    }
   ],
   "source": [
    "p = PourProblem(initial=(0, 0), capacities=(7, 13), goals={2})\n",
    "showpath(uniform_cost_search, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class GreenPourProblem(PourProblem):    \n",
    "    def step_cost(self, state, action, result=None):\n",
    "        \"The cost is the amount of water used in a fill.\"\n",
    "        if action[0] == 'Fill':\n",
    "            i = action[1]\n",
    "            return self.capacities[i] - state[i]\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "uniform_cost_search:\n",
      "  (0, 0) ==('Fill', 0)==> (7, 0); cost 7 after 1 steps\n",
      "  (7, 0) ==('Pour', 0, 1)==> (0, 7); cost 7 after 2 steps\n",
      "  (0, 7) ==('Fill', 0)==> (7, 7); cost 14 after 3 steps\n",
      "  (7, 7) ==('Pour', 0, 1)==> (1, 13); cost 14 after 4 steps\n",
      "  (1, 13) ==('Dump', 1)==> (1, 0); cost 14 after 5 steps\n",
      "  (1, 0) ==('Pour', 0, 1)==> (0, 1); cost 14 after 6 steps\n",
      "  (0, 1) ==('Fill', 0)==> (7, 1); cost 21 after 7 steps\n",
      "  (7, 1) ==('Pour', 0, 1)==> (0, 8); cost 21 after 8 steps\n",
      "  (0, 8) ==('Fill', 0)==> (7, 8); cost 28 after 9 steps\n",
      "  (7, 8) ==('Pour', 0, 1)==> (2, 13); cost 28 after 10 steps\n",
      "GOAL FOUND after 184 results and 48 goal checks\n"
     ]
    }
   ],
   "source": [
    "p = GreenPourProblem(initial=(0, 0), capacities=(7, 13), goals={2})\n",
    "showpath(uniform_cost_search, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
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   },
   "outputs": [],
   "source": [
    "def compare_searchers(problem, searchers=None):\n",
    "    \"Apply each of the search algorithms to the problem, and show results\"\n",
    "    if searchers is None: \n",
    "        searchers = (breadth_first_search, uniform_cost_search)\n",
    "    for searcher in searchers:\n",
    "        showpath(searcher, problem)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "breadth_first_search:\n",
      "  (0, 0) ==('Fill', 0)==> (7, 0); cost 7 after 1 steps\n",
      "  (7, 0) ==('Pour', 0, 1)==> (0, 7); cost 7 after 2 steps\n",
      "  (0, 7) ==('Fill', 0)==> (7, 7); cost 14 after 3 steps\n",
      "  (7, 7) ==('Pour', 0, 1)==> (1, 13); cost 14 after 4 steps\n",
      "  (1, 13) ==('Dump', 1)==> (1, 0); cost 14 after 5 steps\n",
      "  (1, 0) ==('Pour', 0, 1)==> (0, 1); cost 14 after 6 steps\n",
      "  (0, 1) ==('Fill', 0)==> (7, 1); cost 21 after 7 steps\n",
      "  (7, 1) ==('Pour', 0, 1)==> (0, 8); cost 21 after 8 steps\n",
      "  (0, 8) ==('Fill', 0)==> (7, 8); cost 28 after 9 steps\n",
      "  (7, 8) ==('Pour', 0, 1)==> (2, 13); cost 28 after 10 steps\n",
      "GOAL FOUND after 100 results and 31 goal checks\n",
      "\n",
      "uniform_cost_search:\n",
      "  (0, 0) ==('Fill', 0)==> (7, 0); cost 7 after 1 steps\n",
      "  (7, 0) ==('Pour', 0, 1)==> (0, 7); cost 7 after 2 steps\n",
      "  (0, 7) ==('Fill', 0)==> (7, 7); cost 14 after 3 steps\n",
      "  (7, 7) ==('Pour', 0, 1)==> (1, 13); cost 14 after 4 steps\n",
      "  (1, 13) ==('Dump', 1)==> (1, 0); cost 14 after 5 steps\n",
      "  (1, 0) ==('Pour', 0, 1)==> (0, 1); cost 14 after 6 steps\n",
      "  (0, 1) ==('Fill', 0)==> (7, 1); cost 21 after 7 steps\n",
      "  (7, 1) ==('Pour', 0, 1)==> (0, 8); cost 21 after 8 steps\n",
      "  (0, 8) ==('Fill', 0)==> (7, 8); cost 28 after 9 steps\n",
      "  (7, 8) ==('Pour', 0, 1)==> (2, 13); cost 28 after 10 steps\n",
      "GOAL FOUND after 184 results and 48 goal checks\n"
     ]
    }
   ],
   "source": [
    "compare_searchers(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Random Grid\n",
    "\n",
    "An environment where you can move in any of 4 directions, unless there is an obstacle there.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(0, 0): [(0, 1), (1, 0)],\n",
       " (0, 1): [(0, 2), (0, 0), (1, 1)],\n",
       " (0, 2): [(0, 3), (0, 1), (1, 2)],\n",
       " (0, 3): [(0, 4), (0, 2), (1, 3)],\n",
       " (0, 4): [(0, 3), (1, 4)],\n",
       " (1, 0): [(1, 1), (2, 0), (0, 0)],\n",
       " (1, 1): [(1, 2), (1, 0), (2, 1), (0, 1)],\n",
       " (1, 2): [(1, 3), (1, 1), (2, 2), (0, 2)],\n",
       " (1, 3): [(1, 4), (1, 2), (2, 3), (0, 3)],\n",
       " (1, 4): [(1, 3), (2, 4), (0, 4)],\n",
       " (2, 0): [(2, 1), (3, 0), (1, 0)],\n",
       " (2, 1): [(2, 2), (2, 0), (3, 1), (1, 1)],\n",
       " (2, 2): [(2, 3), (2, 1), (3, 2), (1, 2)],\n",
       " (2, 3): [(2, 4), (2, 2), (1, 3)],\n",
       " (2, 4): [(2, 3), (1, 4)],\n",
       " (3, 0): [(3, 1), (4, 0), (2, 0)],\n",
       " (3, 1): [(3, 2), (3, 0), (4, 1), (2, 1)],\n",
       " (3, 2): [(3, 1), (4, 2), (2, 2)],\n",
       " (3, 3): [(3, 2), (4, 3), (2, 3)],\n",
       " (3, 4): [(4, 4), (2, 4)],\n",
       " (4, 0): [(4, 1), (3, 0)],\n",
       " (4, 1): [(4, 2), (4, 0), (3, 1)],\n",
       " (4, 2): [(4, 3), (4, 1), (3, 2)],\n",
       " (4, 3): [(4, 4), (4, 2)],\n",
       " (4, 4): [(4, 3)]}"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "N, S, E, W = DIRECTIONS = [(0, 1), (0, -1), (1, 0), (-1, 0)]\n",
    "\n",
    "def Grid(width, height, obstacles=0.1):\n",
    "    \"\"\"A 2-D grid, width x height, with obstacles that are either a collection of points,\n",
    "    or a fraction between 0 and 1 indicating the density of obstacles, chosen at random.\"\"\"\n",
    "    grid = {(x, y) for x in range(width) for y in range(height)}\n",
    "    if isinstance(obstacles, (float, int)):\n",
    "        obstacles = random.sample(grid, int(width * height * obstacles))\n",
    "    def neighbors(x, y):\n",
    "        for (dx, dy) in DIRECTIONS:\n",
    "            (nx, ny) = (x + dx, y + dy)\n",
    "            if (nx, ny) not in obstacles and 0 <= nx < width and 0 <= ny < height:\n",
    "                yield (nx, ny)\n",
    "    return {(x, y): list(neighbors(x, y))\n",
    "            for x in range(width) for y in range(height)}\n",
    "\n",
    "Grid(5, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class GridProblem(Problem):\n",
    "    \"Create with a call like GridProblem(grid=Grid(10, 10), initial=(0, 0), goal=(9, 9))\"\n",
    "    def actions(self, state): return DIRECTIONS\n",
    "    def result(self, state, action):\n",
    "        #print('ask for result of', state, action)\n",
    "        (x, y) = state\n",
    "        (dx, dy) = action\n",
    "        r = (x + dx, y + dy)\n",
    "        return r if r in self.grid[state] else state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "uniform_cost_search:\n",
      "no solution after 132 results and 33 goal checks\n"
     ]
    }
   ],
   "source": [
    "gp = GridProblem(grid=Grid(5, 5, 0.3), initial=(0, 0), goals={(4, 4)})\n",
    "showpath(uniform_cost_search, gp)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# Finding a hard PourProblem\n",
    "\n",
    "What solvable two-jug PourProblem requires the most steps? We can define the hardness as the number of steps, and then iterate over all PourProblems with capacities up to size M, keeping the hardest one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def hardness(problem):\n",
    "    L = breadth_first_search(problem)\n",
    "    #print('hardness', problem.initial, problem.capacities, problem.goals, L)\n",
    "    return len(action_sequence(L)) if (L is not None) else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hardness(p7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Pour', 0, 1), ('Fill', 0), ('Pour', 0, 1)]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "action_sequence(breadth_first_search(p7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0, 0), (7, 9), {8})"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = 9 # Maximum capacity to consider\n",
    "\n",
    "phard = max((PourProblem(initial=(a, b), capacities=(A, B), goals={goal})\n",
    "             for A in range(C+1) for B in range(C+1)\n",
    "             for a in range(A) for b in range(B)\n",
    "             for goal in range(max(A, B))),\n",
    "            key=hardness)\n",
    "\n",
    "phard.initial, phard.capacities, phard.goals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "breadth_first_search:\n",
      "  (0, 0) ==('Fill', 1)==> (0, 9); cost 1 after 1 steps\n",
      "  (0, 9) ==('Pour', 1, 0)==> (7, 2); cost 2 after 2 steps\n",
      "  (7, 2) ==('Dump', 0)==> (0, 2); cost 3 after 3 steps\n",
      "  (0, 2) ==('Pour', 1, 0)==> (2, 0); cost 4 after 4 steps\n",
      "  (2, 0) ==('Fill', 1)==> (2, 9); cost 5 after 5 steps\n",
      "  (2, 9) ==('Pour', 1, 0)==> (7, 4); cost 6 after 6 steps\n",
      "  (7, 4) ==('Dump', 0)==> (0, 4); cost 7 after 7 steps\n",
      "  (0, 4) ==('Pour', 1, 0)==> (4, 0); cost 8 after 8 steps\n",
      "  (4, 0) ==('Fill', 1)==> (4, 9); cost 9 after 9 steps\n",
      "  (4, 9) ==('Pour', 1, 0)==> (7, 6); cost 10 after 10 steps\n",
      "  (7, 6) ==('Dump', 0)==> (0, 6); cost 11 after 11 steps\n",
      "  (0, 6) ==('Pour', 1, 0)==> (6, 0); cost 12 after 12 steps\n",
      "  (6, 0) ==('Fill', 1)==> (6, 9); cost 13 after 13 steps\n",
      "  (6, 9) ==('Pour', 1, 0)==> (7, 8); cost 14 after 14 steps\n",
      "GOAL FOUND after 150 results and 44 goal checks\n"
     ]
    }
   ],
   "source": [
    "showpath(breadth_first_search, PourProblem(initial=(0, 0), capacities=(7, 9), goals={8}))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "uniform_cost_search:\n",
      "  (0, 0) ==('Fill', 1)==> (0, 9); cost 1 after 1 steps\n",
      "  (0, 9) ==('Pour', 1, 0)==> (7, 2); cost 2 after 2 steps\n",
      "  (7, 2) ==('Dump', 0)==> (0, 2); cost 3 after 3 steps\n",
      "  (0, 2) ==('Pour', 1, 0)==> (2, 0); cost 4 after 4 steps\n",
      "  (2, 0) ==('Fill', 1)==> (2, 9); cost 5 after 5 steps\n",
      "  (2, 9) ==('Pour', 1, 0)==> (7, 4); cost 6 after 6 steps\n",
      "  (7, 4) ==('Dump', 0)==> (0, 4); cost 7 after 7 steps\n",
      "  (0, 4) ==('Pour', 1, 0)==> (4, 0); cost 8 after 8 steps\n",
      "  (4, 0) ==('Fill', 1)==> (4, 9); cost 9 after 9 steps\n",
      "  (4, 9) ==('Pour', 1, 0)==> (7, 6); cost 10 after 10 steps\n",
      "  (7, 6) ==('Dump', 0)==> (0, 6); cost 11 after 11 steps\n",
      "  (0, 6) ==('Pour', 1, 0)==> (6, 0); cost 12 after 12 steps\n",
      "  (6, 0) ==('Fill', 1)==> (6, 9); cost 13 after 13 steps\n",
      "  (6, 9) ==('Pour', 1, 0)==> (7, 8); cost 14 after 14 steps\n",
      "GOAL FOUND after 159 results and 45 goal checks\n"
     ]
    }
   ],
   "source": [
    "showpath(uniform_cost_search, phard)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "class GridProblem(Problem):\n",
    "    \"\"\"A Grid.\"\"\"\n",
    "\n",
    "    def actions(self, state): return ['N', 'S', 'E', 'W']        \n",
    " \n",
    "    def result(self, state, action):\n",
    "        \"\"\"The state that results from executing this action in this state.\"\"\"  \n",
    "        (W, H) = self.size\n",
    "        if action == 'N' and state > W:           return state - W\n",
    "        if action == 'S' and state + W < W * W:   return state + W\n",
    "        if action == 'E' and (state + 1) % W !=0: return state + 1\n",
    "        if action == 'W' and state % W != 0:      return state - 1\n",
    "        return state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "breadth_first_search:\n",
      "  0 ==S==> 10; cost 1 after 1 steps\n",
      "  10 ==S==> 20; cost 2 after 2 steps\n",
      "  20 ==S==> 30; cost 3 after 3 steps\n",
      "  30 ==S==> 40; cost 4 after 4 steps\n",
      "  40 ==E==> 41; cost 5 after 5 steps\n",
      "  41 ==E==> 42; cost 6 after 6 steps\n",
      "  42 ==E==> 43; cost 7 after 7 steps\n",
      "  43 ==E==> 44; cost 8 after 8 steps\n",
      "GOAL FOUND after 135 results and 49 goal checks\n",
      "\n",
      "uniform_cost_search:\n",
      "  0 ==S==> 10; cost 1 after 1 steps\n",
      "  10 ==S==> 20; cost 2 after 2 steps\n",
      "  20 ==E==> 21; cost 3 after 3 steps\n",
      "  21 ==E==> 22; cost 4 after 4 steps\n",
      "  22 ==E==> 23; cost 5 after 5 steps\n",
      "  23 ==S==> 33; cost 6 after 6 steps\n",
      "  33 ==S==> 43; cost 7 after 7 steps\n",
      "  43 ==E==> 44; cost 8 after 8 steps\n",
      "GOAL FOUND after 1036 results and 266 goal checks\n"
     ]
    }
   ],
   "source": [
    "compare_searchers(GridProblem(initial=0, goals={44}, size=(10, 10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'test_frontier ok'"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def test_frontier():\n",
    "    \n",
    "    #### Breadth-first search with FIFO Q\n",
    "    f = FrontierQ(Node(1), LIFO=False)\n",
    "    assert 1 in f and len(f) == 1\n",
    "    f.add(Node(2))\n",
    "    f.add(Node(3))\n",
    "    assert 1 in f and 2 in f and 3 in f and len(f) == 3\n",
    "    assert f.pop().state == 1\n",
    "    assert 1 not in f and 2 in f and 3 in f and len(f) == 2\n",
    "    assert f\n",
    "    assert f.pop().state == 2\n",
    "    assert f.pop().state == 3\n",
    "    assert not f\n",
    "    \n",
    "    #### Depth-first search with LIFO Q\n",
    "    f = FrontierQ(Node('a'), LIFO=True)\n",
    "    for s in 'bcdef': f.add(Node(s))\n",
    "    assert len(f) == 6 and 'a' in f and 'c' in f and 'f' in f\n",
    "    for s in 'fedcba': assert f.pop().state == s\n",
    "    assert not f\n",
    "\n",
    "    #### Best-first search with Priority Q\n",
    "    f = FrontierPQ(Node(''), lambda node: len(node.state))\n",
    "    assert '' in f and len(f) == 1 and f\n",
    "    for s in ['book', 'boo', 'bookie', 'bookies', 'cook', 'look', 'b']:\n",
    "        assert s not in f\n",
    "        f.add(Node(s))\n",
    "        assert s in f\n",
    "    assert f.pop().state == ''\n",
    "    assert f.pop().state == 'b'\n",
    "    assert f.pop().state == 'boo'\n",
    "    assert {f.pop().state for _ in '123'} == {'book', 'cook', 'look'}\n",
    "    assert f.pop().state == 'bookie'\n",
    "    \n",
    "    #### Romania: Two paths to Bucharest; cheapest one found first\n",
    "    S    = Node('S')\n",
    "    SF   = Node('F', S, 'S->F', 99)\n",
    "    SFB  = Node('B', SF, 'F->B', 211)\n",
    "    SR   = Node('R', S, 'S->R', 80)\n",
    "    SRP  = Node('P', SR, 'R->P', 97)\n",
    "    SRPB = Node('B', SRP, 'P->B', 101)\n",
    "    f = FrontierPQ(S)\n",