search-4e.ipynb

   "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,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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": {},
   "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": {},
   "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,
    "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,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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,
    "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,
    "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,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# Visualization Output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "button": false,
    "collapsed": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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,
    "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": {},
   "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": {},
   "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,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "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,
    "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": {},
   "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), (1, 2)],\n",
       " (2, 3): [(2, 4), (2, 2), (3, 3), (1, 3)],\n",
       " (2, 4): [(2, 3), (1, 4)],\n",
       " (3, 0): [(3, 1), (4, 0), (2, 0)],\n",
       " (3, 1): [(3, 0), (4, 1), (2, 1)],\n",
       " (3, 2): [(3, 3), (3, 1), (4, 2), (2, 2)],\n",
       " (3, 3): [(4, 3), (2, 3)],\n",
       " (3, 4): [(3, 3), (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)],\n",
       " (4, 3): [(4, 4), (4, 2), (3, 3)],\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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "uniform_cost_search:\n",
      "  (0, 0) ==(0, 1)==> (0, 1); cost 1 after 1 steps\n",
      "  (0, 1) ==(0, 1)==> (0, 2); cost 2 after 2 steps\n",
      "  (0, 2) ==(0, 1)==> (0, 3); cost 3 after 3 steps\n",
      "  (0, 3) ==(1, 0)==> (1, 3); cost 4 after 4 steps\n",
      "  (1, 3) ==(1, 0)==> (2, 3); cost 5 after 5 steps\n",
      "  (2, 3) ==(0, 1)==> (2, 4); cost 6 after 6 steps\n",
      "  (2, 4) ==(1, 0)==> (3, 4); cost 7 after 7 steps\n",
      "  (3, 4) ==(1, 0)==> (4, 4); cost 8 after 8 steps\n",
      "GOAL FOUND after 248 results and 69 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,
    "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": 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,
    "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": {},
   "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,
    "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": {},
   "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,
    "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,
    "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,
    "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,
    "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",
    "    f.add(SF); f.add(SR), f.add(SRP), f.add(SRPB); f.add(SFB)\n",
    "    def cs(n): return (n.path_cost, n.state) # cs: cost and state\n",
    "    assert cs(f.pop()) == (0, 'S')\n",
    "    assert cs(f.pop()) == (80, 'R')\n",
    "    assert cs(f.pop()) == (99, 'F')\n",
    "    assert cs(f.pop()) == (177, 'P')\n",
    "    assert cs(f.pop()) == (278, 'B')\n",
    "    return 'test_frontier ok'\n",
    "\n",
    "test_frontier()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "button": false,
    "collapsed": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "# %matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "p = plt.plot([i**2 for i in range(10)])\n",
    "plt.savefig('destination_path.eps', format='eps', dpi=1200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SE0iMi/Y6ooi0MBV6iHDOsedQKetyClmzp5C/ZuVTWFpFXMcorh6fyLSUBMb0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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f876647a860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OHjzojI6OWvemwuPxaHR0NNNjTDm3262xsbFMjzEtbM2WTCblcrkyPca0sDWbrblsPcYk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\nMAjFDACAQShmAAAMQjEDAGCQ/wdJuZEoaHGMKwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f874e648390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import itertools\n",
    "import random\n",
    "# http://stackoverflow.com/questions/10194482/custom-matplotlib-plot-chess-board-like-table-with-colored-cells\n",
    "\n",
    "from matplotlib.table import Table\n",
    "\n",
    "def main():\n",
    "    grid_table(8, 8)\n",
    "    plt.axis('scaled')\n",
    "    plt.show()\n",
    "\n",
    "def grid_table(nrows, ncols):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.set_axis_off()\n",
    "    colors = ['white', 'lightgrey', 'dimgrey']\n",
    "    tb = Table(ax, bbox=[0,0,2,2])\n",
    "    for i,j in itertools.product(range(ncols), range(nrows)):\n",
    "        tb.add_cell(i, j, 2./ncols, 2./nrows, text='{:0.2f}'.format(0.1234), \n",
    "                    loc='center', facecolor=random.choice(colors), edgecolor='grey') # facecolors=\n",
    "    ax.add_table(tb)\n",
    "    #ax.plot([0, .3], [.2, .2])\n",