search_tables.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Air Cargo Problem Analysis\n",
    "> In this notebook we solve problems 1 through 3 and visually summarize the results. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Import analysis module\n",
    "> We use `search_data()` and `show_path()` functions from analysis module.\n",
    "\n",
    "> The `search_data()` function searches for a solution and the `show_path()` prints\n",
    "solution steps to screen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from analysis import search_data, show_path\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Perform test to solve cargo planning problem with\n",
      "        the given search algorithms.\n",
      "\n",
      "        Paremeters:\n",
      "        ----------\n",
      "        problem_id: int\n",
      "            Cargo planning problem id\n",
      "        \n",
      "        s_choices: list\n",
      "            List of the search algorithm to try.\n",
      "\n",
      "        Returns:\n",
      "        ----------\n",
      "        Returns tuple of two items:\n",
      "            1 = DataFrame that summarizes test result\n",
      "            2 = A list of tuples, where the first item in the \n",
      "                tuple is the search algorithm name and the second\n",
      "                is its corresponding search Node object.\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print(search_data.__doc__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "        Print solution set to screen\n",
      "\n",
      "        Paremeter\n",
      "        ----------\n",
      "        node: Node\n",
      "            Search tree object that has 'solution()' method \n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print(show_path.__doc__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Search Functions Names\n",
    "\n",
    "- 1) Breadth First \n",
    "- 2) Breadth First Tree \n",
    "- 3) Depth First Graph \n",
    "- 4) Depth Limited \n",
    "- 5) Uniform Cost\n",
    "- 6) Recursive Best First w/ h1  \n",
    "- 7) Greedy Best First Graph w/ h1 \n",
    "- 8) Astar w/ h1 \n",
    "- 9) Astar w/ ignore pre-cond. \n",
    "- 10) Astar w/ level-sum "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 1 Solution Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Solving Air Cargo Problem 1 using Breadth First start time 2018-08-27 01:48:47PM...\n",
      "\n",
      "Solving Air Cargo Problem 1 using Breadth First Tree start time 2018-08-27 01:48:47PM...\n",
      "\n",
      "Solving Air Cargo Problem 1 using Depth First Graph start time 2018-08-27 01:48:48PM...\n",
      "\n",
      "Solving Air Cargo Problem 1 using Depth Limited start time 2018-08-27 01:48:48PM...\n",
      "\n",
      "Solving Air Cargo Problem 1 using Uniform Cost start time 2018-08-27 01:48:49PM...\n",
      "\n",
      "Solving Air Cargo Problem 1 using Recursive Best First w/ h1 start time 2018-08-27 01:48:49PM...\n",
      "\n",
      "Solving Air Cargo Problem 1 using Greedy Best First Graph w/ h1 start time 2018-08-27 01:48:51PM...\n",
      "\n",
      "Solving Air Cargo Problem 1 using Astar w/ h1 start time 2018-08-27 01:48:51PM...\n",
      "\n",
      "Solving Air Cargo Problem 1 using Astar w/ ignore pre-cond. start time 2018-08-27 01:48:51PM...\n",
      "\n",
      "Solving Air Cargo Problem 1 using Astar w/ level-sum start time 2018-08-27 01:48:51PM...\n"
     ]
    }
   ],
   "source": [
    "problem1_data, nodes1 = search_data(1,range(1,11))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Function Name</th>\n",
       "      <th>Solution Steps</th>\n",
       "      <th>Expansions</th>\n",
       "      <th>Goal Tests</th>\n",
       "      <th>New_Nodes</th>\n",
       "      <th>Elapsed Seconds</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Breadth First</td>\n",
       "      <td>6</td>\n",
       "      <td>43</td>\n",
       "      <td>56</td>\n",
       "      <td>180</td>\n",
       "      <td>0.044939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Breadth First Tree</td>\n",
       "      <td>6</td>\n",
       "      <td>1458</td>\n",
       "      <td>1459</td>\n",
       "      <td>5960</td>\n",
       "      <td>0.942462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Depth First Graph</td>\n",
       "      <td>12</td>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>48</td>\n",
       "      <td>0.006860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Depth Limited</td>\n",
       "      <td>50</td>\n",
       "      <td>101</td>\n",
       "      <td>271</td>\n",
       "      <td>414</td>\n",
       "      <td>0.113649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Uniform Cost</td>\n",
       "      <td>6</td>\n",
       "      <td>55</td>\n",
       "      <td>57</td>\n",
       "      <td>224</td>\n",
       "      <td>0.032331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Recursive Best First w/ h1</td>\n",
       "      <td>6</td>\n",
       "      <td>4229</td>\n",
       "      <td>4230</td>\n",
       "      <td>17029</td>\n",
       "      <td>2.451461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Greedy Best First Graph w/ h1</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>28</td>\n",
       "      <td>0.004516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Astar w/ h1</td>\n",
       "      <td>6</td>\n",
       "      <td>55</td>\n",
       "      <td>57</td>\n",
       "      <td>224</td>\n",
       "      <td>0.032781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Astar w/ ignore pre-cond.</td>\n",
       "      <td>6</td>\n",
       "      <td>41</td>\n",
       "      <td>43</td>\n",
       "      <td>170</td>\n",
       "      <td>0.045378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Astar w/ level-sum</td>\n",
       "      <td>6</td>\n",
       "      <td>11</td>\n",
       "      <td>13</td>\n",
       "      <td>50</td>\n",
       "      <td>0.597109</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    Function Name  Solution Steps  Expansions  Goal Tests  \\\n",
       "1                   Breadth First               6          43          56   \n",
       "2              Breadth First Tree               6        1458        1459   \n",
       "3               Depth First Graph              12          12          13   \n",
       "4                   Depth Limited              50         101         271   \n",
       "5                    Uniform Cost               6          55          57   \n",
       "6      Recursive Best First w/ h1               6        4229        4230   \n",
       "7   Greedy Best First Graph w/ h1               6           7           9   \n",
       "8                     Astar w/ h1               6          55          57   \n",
       "9       Astar w/ ignore pre-cond.               6          41          43   \n",
       "10             Astar w/ level-sum               6          11          13   \n",
       "\n",
       "    New_Nodes  Elapsed Seconds  \n",
       "1         180         0.044939  \n",
       "2        5960         0.942462  \n",
       "3          48         0.006860  \n",
       "4         414         0.113649  \n",
       "5         224         0.032331  \n",
       "6       17029         2.451461  \n",
       "7          28         0.004516  \n",
       "8         224         0.032781  \n",
       "9         170         0.045378  \n",
       "10         50         0.597109  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem1_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Search function Greedy Best First Graph w/ h1 plan length: 6 \n",
      "Load(C1, P1, SFO)\n",
      "Load(C2, P2, JFK)\n",
      "Fly(P1, SFO, JFK)\n",
      "Fly(P2, JFK, SFO)\n",
      "Unload(C1, P1, JFK)\n",
      "Unload(C2, P2, SFO)\n"
     ]
    }
   ],
   "source": [
    "show_path(nodes1[6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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94FWhYZzckMRewHOSHgf6kV2An03b70L2b7CGbPLpLyU9SjZEUIr3DEnUUkOW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\nVpQTBjMzMyvKCYOZmZkV9f8B8HXnalJW8IoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27ab70abc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = problem1_data.plot(kind='barh' ,x='Function Name', y='Expansions')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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S+DJgoGVp/sHAHSvYvdfL76U09vd5pWZbwOdtL7eGopXWD32v/dxS3mrAS61GZVrWNrRc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\nXQkYIiIioq4EDBEREVFXAoaIiIio6/8DCVK3FlVahSEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27ab6faa3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = problem1_data.plot(kind='barh' ,x='Function Name', y='Solution Steps')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 2 Solution Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Solving Air Cargo Problem 2 using Breadth First start time 2018-08-27 01:48:52PM...\n",
      "\n",
      "Solving Air Cargo Problem 2 using Depth First Graph start time 2018-08-27 01:49:00PM...\n",
      "\n",
      "Solving Air Cargo Problem 2 using Uniform Cost start time 2018-08-27 01:49:03PM...\n",
      "\n",
      "Solving Air Cargo Problem 2 using Greedy Best First Graph w/ h1 start time 2018-08-27 01:49:14PM...\n",
      "\n",
      "Solving Air Cargo Problem 2 using Astar w/ h1 start time 2018-08-27 01:49:16PM...\n",
      "\n",
      "Solving Air Cargo Problem 2 using Astar w/ ignore pre-cond. start time 2018-08-27 01:49:28PM...\n",
      "\n",
      "Solving Air Cargo Problem 2 using Astar w/ level-sum start time 2018-08-27 01:49:32PM...\n"
     ]
    }
   ],
   "source": [
    "problem2_data, nodes2 = search_data(2,[1,3,5,7,8,9,10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Function Name</th>\n",
       "      <th>Solution Steps</th>\n",
       "      <th>Expansions</th>\n",
       "      <th>Goal Tests</th>\n",
       "      <th>New_Nodes</th>\n",
       "      <th>Elapsed Seconds</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Breadth First</td>\n",
       "      <td>9</td>\n",
       "      <td>3343</td>\n",
       "      <td>4609</td>\n",
       "      <td>30509</td>\n",
       "      <td>7.650436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Depth First Graph</td>\n",
       "      <td>575</td>\n",
       "      <td>582</td>\n",
       "      <td>583</td>\n",
       "      <td>5211</td>\n",
       "      <td>2.802844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Uniform Cost</td>\n",
       "      <td>9</td>\n",
       "      <td>4853</td>\n",
       "      <td>4855</td>\n",
       "      <td>44041</td>\n",
       "      <td>11.203868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Greedy Best First Graph w/ h1</td>\n",
       "      <td>21</td>\n",
       "      <td>998</td>\n",
       "      <td>1000</td>\n",
       "      <td>8982</td>\n",
       "      <td>2.235381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Astar w/ h1</td>\n",
       "      <td>9</td>\n",
       "      <td>4853</td>\n",
       "      <td>4855</td>\n",
       "      <td>44041</td>\n",
       "      <td>11.566661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Astar w/ ignore pre-cond.</td>\n",
       "      <td>9</td>\n",
       "      <td>1450</td>\n",
       "      <td>1452</td>\n",
       "      <td>13303</td>\n",
       "      <td>4.486422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Astar w/ level-sum</td>\n",
       "      <td>9</td>\n",
       "      <td>86</td>\n",
       "      <td>88</td>\n",
       "      <td>841</td>\n",
       "      <td>54.272250</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Function Name  Solution Steps  Expansions  Goal Tests  \\\n",
       "1                  Breadth First               9        3343        4609   \n",
       "2              Depth First Graph             575         582         583   \n",
       "3                   Uniform Cost               9        4853        4855   \n",
       "4  Greedy Best First Graph w/ h1              21         998        1000   \n",
       "5                    Astar w/ h1               9        4853        4855   \n",
       "6      Astar w/ ignore pre-cond.               9        1450        1452   \n",
       "7             Astar w/ level-sum               9          86          88   \n",
       "\n",
       "   New_Nodes  Elapsed Seconds  \n",
       "1      30509         7.650436  \n",
       "2       5211         2.802844  \n",
       "3      44041        11.203868  \n",
       "4       8982         2.235381  \n",
       "5      44041        11.566661  \n",
       "6      13303         4.486422  \n",
       "7        841        54.272250  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem2_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Search function Astar w/ ignore pre-cond. plan length: 9 \n",
      "Load(C3, P3, ATL)\n",
      "Fly(P3, ATL, SFO)\n",
      "Unload(C3, P3, SFO)\n",
      "Load(C2, P2, JFK)\n",
      "Fly(P2, JFK, SFO)\n",
      "Unload(C2, P2, SFO)\n",
      "Load(C1, P1, SFO)\n",
      "Fly(P1, SFO, JFK)\n",
      "Unload(C1, P1, JFK)\n"
     ]
    }
   ],
   "source": [
    "#astar with ignore pre conditins\n",
    "show_path(nodes2[5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mYAPwsbR+ArAgTQb8OHCJpCXA0rRNsyJiubIx/GmpaAbQKyLWpnP/myJifTO7mUyWZDwF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27ab93c3438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = problem2_data.plot(kind='barh' ,x='Function Name', y='Expansions')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XnQhMauDwPkzPmyju7/NBwbaAKyJimzUYVUQtryvb2wF4r8qsTeXaiMqZgYlkCVteHxZs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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27ab7858048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = problem2_data.plot(kind='barh' ,x='Function Name', y='Solution Steps')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 3 Solution Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Solving Air Cargo Problem 3 using Breadth First start time 2018-08-27 01:50:27PM...\n",
      "\n",
      "Solving Air Cargo Problem 3 using Depth First Graph start time 2018-08-27 01:51:08PM...\n",
      "\n",
      "Solving Air Cargo Problem 3 using Uniform Cost start time 2018-08-27 01:51:12PM...\n",
      "\n",
      "Solving Air Cargo Problem 3 using Greedy Best First Graph w/ h1 start time 2018-08-27 01:52:04PM...\n",
      "\n",
      "Solving Air Cargo Problem 3 using Astar w/ h1 start time 2018-08-27 01:52:20PM...\n",
      "\n",
      "Solving Air Cargo Problem 3 using Astar w/ ignore pre-cond. start time 2018-08-27 01:53:10PM...\n",
      "\n",
      "Solving Air Cargo Problem 3 using Astar w/ level-sum start time 2018-08-27 01:53:27PM...\n"
     ]
    }
   ],
   "source": [
    "problem3_data, nodes3 = search_data(3,[1,3,5,7,8,9,10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Function Name</th>\n",
       "      <th>Solution Steps</th>\n",
       "      <th>Expansions</th>\n",
       "      <th>Goal Tests</th>\n",
       "      <th>New_Nodes</th>\n",
       "      <th>Elapsed Seconds</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Breadth First</td>\n",
       "      <td>12</td>\n",
       "      <td>14663</td>\n",
       "      <td>18098</td>\n",
       "      <td>129631</td>\n",
       "      <td>40.950965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Depth First Graph</td>\n",
       "      <td>596</td>\n",
       "      <td>627</td>\n",
       "      <td>628</td>\n",
       "      <td>5176</td>\n",
       "      <td>3.437929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Uniform Cost</td>\n",
       "      <td>12</td>\n",
       "      <td>18223</td>\n",
       "      <td>18225</td>\n",
       "      <td>159618</td>\n",
       "      <td>52.598583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Greedy Best First Graph w/ h1</td>\n",
       "      <td>22</td>\n",
       "      <td>5578</td>\n",
       "      <td>5580</td>\n",
       "      <td>49150</td>\n",
       "      <td>15.707169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Astar w/ h1</td>\n",
       "      <td>12</td>\n",
       "      <td>18223</td>\n",
       "      <td>18225</td>\n",
       "      <td>159618</td>\n",
       "      <td>50.415847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Astar w/ ignore pre-cond.</td>\n",
       "      <td>12</td>\n",
       "      <td>5040</td>\n",
       "      <td>5042</td>\n",
       "      <td>44944</td>\n",
       "      <td>16.469685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Astar w/ level-sum</td>\n",
       "      <td>12</td>\n",
       "      <td>325</td>\n",
       "      <td>327</td>\n",
       "      <td>3002</td>\n",
       "      <td>243.639970</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Function Name  Solution Steps  Expansions  Goal Tests  \\\n",
       "1                  Breadth First              12       14663       18098   \n",
       "2              Depth First Graph             596         627         628   \n",
       "3                   Uniform Cost              12       18223       18225   \n",
       "4  Greedy Best First Graph w/ h1              22        5578        5580   \n",
       "5                    Astar w/ h1              12       18223       18225   \n",
       "6      Astar w/ ignore pre-cond.              12        5040        5042   \n",
       "7             Astar w/ level-sum              12         325         327   \n",
       "\n",
       "   New_Nodes  Elapsed Seconds  \n",
       "1     129631        40.950965  \n",
       "2       5176         3.437929  \n",
       "3     159618        52.598583  \n",
       "4      49150        15.707169  \n",
       "5     159618        50.415847  \n",
       "6      44944        16.469685  \n",
       "7       3002       243.639970  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem3_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Search function Astar w/ ignore pre-cond. plan length: 12 \n",
      "Load(C2, P2, JFK)\n",
      "Fly(P2, JFK, ORD)\n",
      "Load(C4, P2, ORD)\n",
      "Fly(P2, ORD, SFO)\n",
      "Unload(C4, P2, SFO)\n",
      "Load(C1, P1, SFO)\n",
      "Fly(P1, SFO, ATL)\n",
      "Load(C3, P1, ATL)\n",
      "Fly(P1, ATL, JFK)\n",
      "Unload(C3, P1, JFK)\n",
      "Unload(C2, P2, SFO)\n",
      "Unload(C1, P1, JFK)\n"
     ]
    }
   ],
   "source": [
    "#astar with ignore pre conditins\n",
    "show_path(nodes3[5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PfCbNHw/MTwP6LgAulbQYWJKWyRURy5T1z09LRTOAPSNiTbqWvzEi1uWsZjJZYvE08DLZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27ab91aada0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = problem3_data.plot(kind='barh' ,x='Function Name', y='Expansions')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JRhL6pLssVutOdhdCMzMz+4Soaw7DvWT3//8xMLqg/L2Cp0yamZnZJ0BdcxhW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\nZmZmuZwwmJmZWS4nDGZmZpbr/wOSAvI8qUt0EgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27ab74e7c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = problem3_data.plot(kind='barh' ,x='Function Name', y='Solution Steps')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:aind]",
   "language": "python",
   "name": "conda-env-aind-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}