diff --git a/search.ipynb b/search.ipynb
index b8edde1e9..019ea8eb4 100644
--- a/search.ipynb
+++ b/search.ipynb
@@ -15,7 +15,6 @@
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {
-    "collapsed": true,
     "scrolled": true
    },
    "outputs": [],
@@ -81,9 +80,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "%psource Problem"
@@ -123,9 +120,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "%psource GraphProblem"
@@ -141,9 +136,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "romania_map = UndirectedGraph(dict(\n",
@@ -188,9 +181,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)"
@@ -221,7 +212,11 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
+<<<<<<< HEAD
+      "{'Rimnicu': (233, 410), 'Timisoara': (94, 410), 'Iasi': (473, 506), 'Neamt': (406, 537), 'Fagaras': (305, 449), 'Giurgiu': (375, 270), 'Urziceni': (456, 350), 'Mehadia': (168, 339), 'Lugoj': (165, 379), 'Sibiu': (207, 457), 'Oradea': (131, 571), 'Zerind': (108, 531), 'Craiova': (253, 288), 'Hirsova': (534, 350), 'Arad': (91, 492), 'Vaslui': (509, 444), 'Drobeta': (165, 299), 'Bucharest': (400, 327), 'Eforie': (562, 293), 'Pitesti': (320, 368)}\n"
+=======
       "{'Oradea': (131, 571), 'Eforie': (562, 293), 'Timisoara': (94, 410), 'Hirsova': (534, 350), 'Bucharest': (400, 327), 'Rimnicu': (233, 410), 'Fagaras': (305, 449), 'Lugoj': (165, 379), 'Giurgiu': (375, 270), 'Mehadia': (168, 339), 'Pitesti': (320, 368), 'Drobeta': (165, 299), 'Craiova': (253, 288), 'Sibiu': (207, 457), 'Iasi': (473, 506), 'Urziceni': (456, 350), 'Vaslui': (509, 444), 'Neamt': (406, 537), 'Zerind': (108, 531), 'Arad': (91, 492)}\n"
+>>>>>>> 8561c52d63fcaef4c0f99d997073aeb93e926e56
      ]
     }
    ],
@@ -240,10 +235,26 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "ImportError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-7-d7e895ad5879>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_line_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'matplotlib'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'inline'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnetworkx\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmatplotlib\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mlines\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/.local/lib/python3.5/site-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36mrun_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2093\u001b[0m                 \u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'local_ns'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_getframe\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstack_depth\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf_locals\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2094\u001b[0m             \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuiltin_trap\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2095\u001b[0;31m                 \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2096\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2097\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<decorator-gen-107>\u001b[0m in \u001b[0;36mmatplotlib\u001b[0;34m(self, line)\u001b[0m\n",
+      "\u001b[0;32m~/.local/lib/python3.5/site-packages/IPython/core/magic.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(f, *a, **k)\u001b[0m\n\u001b[1;32m    185\u001b[0m     \u001b[0;31m# but it's overkill for just that one bit of state.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    186\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mmagic_deco\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 187\u001b[0;31m         \u001b[0mcall\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    188\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    189\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mcallable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/.local/lib/python3.5/site-packages/IPython/core/magics/pylab.py\u001b[0m in \u001b[0;36mmatplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m             \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Available matplotlib backends: %s\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mbackends_list\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     98\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 99\u001b[0;31m             \u001b[0mgui\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbackend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshell\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0menable_matplotlib\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgui\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    100\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_show_matplotlib_backend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgui\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbackend\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    101\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/.local/lib/python3.5/site-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36menable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   2964\u001b[0m         \"\"\"\n\u001b[1;32m   2965\u001b[0m         \u001b[0;32mfrom\u001b[0m \u001b[0mIPython\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcore\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mpylabtools\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mpt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2966\u001b[0;31m         \u001b[0mgui\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbackend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfind_gui_and_backend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgui\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpylab_gui_select\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2967\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2968\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mgui\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;34m'inline'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/.local/lib/python3.5/site-packages/IPython/core/pylabtools.py\u001b[0m in \u001b[0;36mfind_gui_and_backend\u001b[0;34m(gui, gui_select)\u001b[0m\n\u001b[1;32m    268\u001b[0m     \"\"\"\n\u001b[1;32m    269\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 270\u001b[0;31m     \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    271\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    272\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mgui\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mgui\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;34m'auto'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mImportError\u001b[0m: No module named 'matplotlib'"
+     ]
+    }
+   ],
    "source": [
     "%matplotlib inline\n",
     "import networkx as nx\n",
@@ -266,10 +277,20 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'nx' 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<ipython-input-8-dd8d8e7c0ee0>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# initialise a graph\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mG\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mGraph\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      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;31m# use this while labeling nodes in the map\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mnode_labels\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mNameError\u001b[0m: name 'nx' is not defined"
+     ]
+    }
+   ],
    "source": [
     "# initialise a graph\n",
     "G = nx.Graph()\n",
@@ -1250,6 +1271,219 @@
     "display_visual(user_input = True)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## A* Search Heuristics Comparison\n",
+    "\n",
+    "Different Heuristics have different efficiency in solving a particular problem via A* search which is generally defined by the node of explored nodes as well as the branching factor. With the help of the Classic 8* Puzzle we can effectively visualize the difference in performance of these heuristics. \n",
+    "\n",
+    "### 8-Puzzle Problem\n",
+    "\n",
+    "*8-Puzzle Problem* is another problem that is classified as NP hard for which genetic algorithms provide a better solution than any pre-existing ones.\n",
+    "\n",
+    "The *8-Puzzle Problem* consists of a *3x3 tray* in which 8 tiles numbered 1-8 are placed and the 9<sup>th</sup> tile is uncovered. The aim of the game is that given a initial placement of the tiles, we have to reach the goal state on the constraint that a tile adjacent to be the blank space can be slid into that space.\n",
+    "\n",
+    "*example:*\n",
+    "        Initial State            Goal State\n",
+    "\n",
+    "        | 7 | 2 | 4 |           |   | 1 | 2 |\n",
+    "        | 5 |   | 6 |   ---->   | 3 | 4 | 5 |\n",
+    "        | 8 | 3 | 1 |           | 6 | 7 | 8 |\n",
+    "\n",
+    "We have a total of 8+1(blank) tiles giving us total of 9! initial configurations but of all these configurations only 9!/2 can lead to a solution.The solvability can be checked by calculating the *Permutation Inversion* of each tile and then summing it up.\n",
+    "Inversion is defined as when a tile preceeds another tile with lower number.\n",
+    "Let's calculate the Permutation Inversion of the example shown above -\n",
+    "    \n",
+    "    Tile 7 -> 6 Inversions (for tile 2, 4, 5, 6, 3, 1)\n",
+    "    Tile 2 -> 1 Inversions\n",
+    "    Tile 4 -> 2 Inversions\n",
+    "    Tile 5 -> 2 Inversions\n",
+    "    Tile 6 -> 2 Inversions\n",
+    "    Tile 8 -> 2 Inversions\n",
+    "    Tile 3 -> 1 Inversions\n",
+    "    Tile 1 -> 0 Inversions\n",
+    "Total Inversions = 16 Inversions, \n",
+    "Is total Inversions are even then the initial configuration is solvable else the configuration is impossible to solve.\n",
+    "\n",
+    "For example we can have a state \"724506831\" where 0 represents the empty tile.\n",
+    "\n",
+    "#### Heuristics:-\n",
+    "1.) Manhattan Distance:- For the 8 Puzzle problem \"Manhattan distance is defined as the distance of a tile from its \n",
+    "                         goal. In the example shown above the manhattan distance for the 'numbered tile 1' is 4\n",
+    "                         (2 unit left and 2 unit up).\n",
+    "\n",
+    "2.) No. of Misplaced Tiles:- This heuristics calculates the number of misplaced tile in the state from the goal \n",
+    "                             state.\n",
+    "\n",
+    "3.) Sqrt of Manhattan Distance:- Uses the sqaure root of the Manhattan distance\n",
+    "\n",
+    "4.) Max Heuristic :- Score on the basis of max of Manhattan Distance and No. of Misplced tiles."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# define heuristics\n",
+    "def linear(state,goal):\n",
+    "    return sum([1 if state[i] != goal[i] else 0 for i in range(8)])\n",
+    "\n",
+    "def manhanttan(state,goal):\n",
+    "    index_goal = {0:[2,2], 1:[0,0], 2:[0,1], 3:[0,2], 4:[1,0], 5:[1,1], 6:[1,2], 7:[2,0], 8:[2,1]}\n",
+    "    index_state = {}\n",
+    "    index = [[0,0], [0,1], [0,2], [1,0], [1,1], [1,2], [2,0], [2,1], [2,2]]\n",
+    "    x=0\n",
+    "    y=0\n",
+    "    for i in range(len(state)):\n",
+    "        index_state[state[i]] = index[i]\n",
+    "    mhd = 0\n",
+    "    for i in range(8):\n",
+    "        for j in range(2):\n",
+    "            mhd = abs(index_goal[i][j] - index_state[i][j]) + mhd\n",
+    "    return mhd\n",
+    "\n",
+    "def sqrt_manhanttan(state,goal):\n",
+    "    index_goal = {0:[2,2], 1:[0,0], 2:[0,1], 3:[0,2], 4:[1,0], 5:[1,1], 6:[1,2], 7:[2,0], 8:[2,1]}\n",
+    "    index_state = {}\n",
+    "    index = [[0,0], [0,1], [0,2], [1,0], [1,1], [1,2], [2,0], [2,1], [2,2]]\n",
+    "    x=0\n",
+    "    y=0\n",
+    "    for i in range(len(state)):\n",
+    "        index_state[state[i]] = index[i]\n",
+    "    mhd = 0\n",
+    "    for i in range(8):\n",
+    "        for j in range(2):\n",
+    "            mhd = (index_goal[i][j] - index_state[i][j])**2 + mhd\n",
+    "    return math.sqrt(mhd)\n",
+    "\n",
+    "def max_heuristic(state,goal):\n",
+    "    score1 = manhanttan(state, goal)\n",
+    "    score2 = linear(state, goal)\n",
+    "    return max(score1, score2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Algorithm for 8 Puzzle problem\n",
+    "\n",
+    "def checkSolvability(state):\n",
+    "    inversion = 0\n",
+    "    for i in range(len(state)):\n",
+    "        for j in range(i,len(state)):\n",
+    "            if (state[i]>state[j] and state[j]!=0):\n",
+    "                inversion += 1\n",
+    "    check = True\n",
+    "    if inversion%2 != 0:\n",
+    "        check = False\n",
+    "    print(check)\n",
+    "    return check\n",
+    "\n",
+    "def getPossibleMoves(state,heuristic,goal,moves):\n",
+    "    move = {0:[1,3], 1:[0,2,4], 2:[1,5], 3:[0,6,4], 4:[1,3,5,7], 5:[2,4,8], 6:[3,7], 7:[6,8], 8:[7,5]} # create a dictionary of moves\n",
+    "    index = state[0].index(0)\n",
+    "    possible_moves = []\n",
+    "    for i in range(len(move[index])):\n",
+    "        conf = list(state[0][:])\n",
+    "        a = conf[index]\n",
+    "        b = conf[move[index][i]]\n",
+    "        conf[move[index][i]] = a\n",
+    "        conf[index] = b\n",
+    "        possible_moves.append(conf)\n",
+    "    scores = []\n",
+    "    for i in possible_moves:\n",
+    "        scores.append(heuristic(i,goal))\n",
+    "    scores = [x+moves for x in scores]\n",
+    "    allowed_state = []\n",
+    "    for i in range(len(possible_moves)):\n",
+    "        node = []\n",
+    "        node.append(possible_moves[i])\n",
+    "        node.append(scores[i])\n",
+    "        node.append(state[0])\n",
+    "        allowed_state.append(node)  \n",
+    "    return allowed_state\n",
+    "\n",
+    "path = []\n",
+    "final = []\n",
+    "def create_path(goal,initial):\n",
+    "    node = goal[0]\n",
+    "    final.append(goal[0])\n",
+    "    if goal[2] == initial:\n",
+    "        return reversed(final)\n",
+    "    else:\n",
+    "        parent = goal[2]\n",
+    "        for i in path:\n",
+    "            if i[0] == parent:\n",
+    "                parent = i\n",
+    "        create_path(parent,initial)\t\n",
+    "\n",
+    "def show_path(initial):\n",
+    "    move = []\n",
+    "    for i in range(0,len(path)):\n",
+    "        move.append(''.join(str(x) for x in path[i][0]))\n",
+    "    print(\"Number of explored nodes by the following heuristic are: \", len(set(move)))\t\n",
+    "    print(initial)\n",
+    "    for i in reversed(final):\n",
+    "        print(i)\n",
+    "    return\n",
+    "\n",
+    "def solve(initial,goal,heuristic):\n",
+    "    root = [initial,heuristic(initial,goal),'']\n",
+    "    nodes = [] # nodes is a priority Queue based on the state score \n",
+    "    nodes.append(root)\n",
+    "    moves = 0\n",
+    "    while len(nodes) != 0:\n",
+    "        node = nodes[0]\n",
+    "        del nodes[0]\n",
+    "        path.append(node)\n",
+    "        if node[0] == goal:\n",
+    "            soln = create_path(path[-1],initial )\n",
+    "            show_path(initial)\n",
+    "            return  \n",
+    "        moves +=1\n",
+    "        opened_nodes = getPossibleMoves(node,heuristic,goal,moves)\n",
+    "        nodes = sorted(opened_nodes+nodes, key=itemgetter(1))\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Heuristics is max_heuristic\n",
+      "True\n",
+      "Number of explored nodes by the following heuristic are:  126\n",
+      "[2, 4, 3, 1, 5, 6, 7, 8, 0]\n",
+      "[2, 4, 3, 1, 5, 0, 7, 8, 6]\n",
+      "[2, 4, 3, 1, 0, 5, 7, 8, 6]\n",
+      "[2, 0, 3, 1, 4, 5, 7, 8, 6]\n",
+      "[0, 2, 3, 1, 4, 5, 7, 8, 6]\n",
+      "[1, 2, 3, 0, 4, 5, 7, 8, 6]\n",
+      "[1, 2, 3, 4, 0, 5, 7, 8, 6]\n",
+      "[1, 2, 3, 4, 5, 0, 7, 8, 6]\n",
+      "[1, 2, 3, 4, 5, 6, 7, 8, 0]\n"
+     ]
+    }
+   ],
+   "source": [
+    "goal_state = [1,2,3,4,5,6,7,8,0] # define the goal state\n",
+    "initial_state = [2,4,3,1,5,6,7,8,0] # define the initial state\n",
+    "print(\"Heuristics is max_heuristic\")\n",
+    "checkSolvability(initial_state)\n",
+    "solve(initial_state,goal_state,max_heuristic) # to check the different heuristics change the function name in solve"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1360,9 +1594,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "%psource genetic_algorithm"
@@ -1401,9 +1633,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "%psource reproduce"
@@ -1421,9 +1651,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "%psource mutate"
@@ -1441,9 +1669,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "%psource init_population"
@@ -1484,10 +1710,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 12,
+   "metadata": {},
    "outputs": [],
    "source": [
     "edges = {\n",
@@ -1509,14 +1733,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[['R', 'G', 'G', 'R'], ['R', 'G', 'R', 'R'], ['G', 'R', 'G', 'R'], ['R', 'G', 'R', 'G'], ['G', 'R', 'R', 'G'], ['G', 'R', 'G', 'R'], ['G', 'R', 'R', 'R'], ['R', 'G', 'G', 'G']]\n"
+      "[['R', 'G', 'G', 'R'], ['G', 'R', 'G', 'G'], ['G', 'G', 'G', 'G'], ['R', 'G', 'G', 'G'], ['R', 'G', 'G', 'R'], ['G', 'R', 'G', 'R'], ['G', 'G', 'G', 'R'], ['G', 'R', 'G', 'R']]\n"
      ]
     }
    ],
@@ -1536,10 +1760,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 14,
+   "metadata": {},
    "outputs": [],
    "source": [
     "def fitness(c):\n",
@@ -1555,14 +1777,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "['R', 'G', 'R', 'G']\n"
+      "['G', 'R', 'G', 'R']\n"
      ]
     }
    ],
@@ -1580,7 +1802,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -1625,14 +1847,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[0, 2, 7, 1, 7, 3, 2, 4], [2, 7, 5, 4, 4, 5, 2, 0], [7, 1, 6, 0, 1, 3, 0, 2], [0, 3, 6, 1, 3, 0, 5, 4], [0, 4, 6, 4, 7, 4, 1, 6]]\n"
+      "[[6, 7, 3, 6, 3, 0, 1, 4], [7, 1, 4, 1, 5, 2, 0, 0], [1, 4, 7, 0, 0, 2, 5, 2], [2, 0, 3, 7, 5, 7, 0, 0], [6, 3, 1, 7, 5, 6, 3, 0]]\n"
      ]
     }
    ],
@@ -1656,10 +1878,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 7,
+   "metadata": {},
    "outputs": [],
    "source": [
     "def fitness(q):\n",
@@ -1688,20 +1908,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[5, 0, 6, 3, 7, 4, 1, 3]\n",
-      "26\n"
+      "[3, 5, 7, 2, 0, 6, 4, 1]\n",
+      "28\n"
      ]
     }
    ],
    "source": [
-    "solution = genetic_algorithm(population, fitness, f_thres=25, gene_pool=range(8))\n",
+    "solution = genetic_algorithm(population, fitness, f_thres=28, gene_pool=range(8))\n",
     "print(solution)\n",
     "print(fitness(solution))"
    ]
@@ -1719,6 +1939,13 @@
    "source": [
     "With that this tutorial on the genetic algorithm comes to an end. Hope you found this guide helpful!"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -1737,7 +1964,11 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
+<<<<<<< HEAD
+   "version": "3.5.4rc1"
+=======
    "version": "3.5.2"
+>>>>>>> 8561c52d63fcaef4c0f99d997073aeb93e926e56
   },
   "widgets": {
    "state": {
diff --git a/search.py b/search.py
index 19481ea31..ea58d18f1 100644
--- a/search.py
+++ b/search.py
@@ -15,6 +15,7 @@
 import random
 import sys
 import bisect
+from operator import itemgetter
 
 infinity = float('inf')