diff --git a/search.ipynb b/search.ipynb
index 019ea8eb4..d537bd6c0 100644
--- a/search.ipynb
+++ b/search.ipynb
@@ -80,7 +80,9 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "%psource Problem"
@@ -120,7 +122,9 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "%psource GraphProblem"
@@ -136,7 +140,9 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "romania_map = UndirectedGraph(dict(\n",
@@ -181,7 +187,9 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)"
@@ -212,11 +220,7 @@
      "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
      ]
     }
    ],
@@ -235,26 +239,10 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "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'"
-     ]
-    }
-   ],
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
    "source": [
     "%matplotlib inline\n",
     "import networkx as nx\n",
@@ -277,20 +265,10 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "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"
-     ]
-    }
-   ],
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
    "source": [
     "# initialise a graph\n",
     "G = nx.Graph()\n",
@@ -429,7 +407,9 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "metadata": {},
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [
     {
      "data": {
@@ -1275,51 +1255,32 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## A* Search Heuristics Comparison\n",
+    "## A* Heuristics\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",
+    "Different heuristics provide different efficiency in solving A* problems which are generally defined by the number of explored nodes as well as the branching factor. With the classic 8 puzzle we can show the efficiency of different heuristics through the number of explored nodes.\n",
     "\n",
-    "### 8-Puzzle Problem\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",
+    "The *8 Puzzle Problem* consists of a 3x3 tray in which the goal is to get the initial configuration to the goal state by shifting the numbered tiles into the blank space.\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",
+    "example:- \n",
     "\n",
-    "*example:*\n",
-    "        Initial State            Goal State\n",
+    "              Initial State                        Goal State\n",
+    "              | 7 | 2 | 4 |                       | 0 | 1 | 2 |\n",
+    "              | 5 | 0 | 6 |                       | 3 | 4 | 5 |\n",
+    "              | 8 | 3 | 1 |                       | 6 | 7 | 8 |\n",
+    "              \n",
+    "We have a total of 9 blank tiles giving us a total of 9! initial configuration but not all of these are solvable, the solvability of a configuration can be checked by calculating the Inversion Permutation. If the total Inversion Permutation is even then the initial configuration is solvable else the initial configuration is not solvable which means that only 9!/2 initial states lead to a solution.\n",
     "\n",
-    "        | 7 | 2 | 4 |           |   | 1 | 2 |\n",
-    "        | 5 |   | 6 |   ---->   | 3 | 4 | 5 |\n",
-    "        | 8 | 3 | 1 |           | 6 | 7 | 8 |\n",
+    "#### Heuristics :-\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",
+    "1.) Manhattan Distance:- For the 8 puzzle problem Manhattan distance is defined as the distance of a tile from its goal state( for the tile numbered '1' in the initial configuration Manhattan distance is 4 \"2 for left and 2 for upward displacement\").\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",
+    "2.) No. of Misplaced Tiles:- The heuristic calculates the number of misplaced tiles between the current state and goal state.\n",
     "\n",
-    "2.) No. of Misplaced Tiles:- This heuristics calculates the number of misplaced tile in the state from the goal \n",
-    "                             state.\n",
+    "3.) Sqrt of Manhattan Distance:- It calculates the square root of Manhattan distance.\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."
+    "4.) Max Heuristic:- It assign the score as max of Manhattan Distance and No. of misplaced tiles. "
    ]
   },
   {
@@ -1328,128 +1289,43 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "# define heuristics\n",
+    "# heuristics for 8 Puzzle Problem\n",
+    "\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",
+    "\tindex_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",
+    "\tindex_state = {}\n",
+    "\tindex = [[0,0], [0,1], [0,2], [1,0], [1,1], [1,2], [2,0], [2,1], [2,2]]\n",
+    "\tx=0\n",
+    "\ty=0\n",
+    "\tfor i in range(len(state)):\n",
+    "\t\tindex_state[state[i]] = index[i]\n",
+    "\tmhd = 0\n",
+    "\tfor i in range(8):\n",
+    "\t\tfor j in range(2):\n",
+    "\t\t\tmhd = abs(index_goal[i][j] - index_state[i][j]) + mhd\n",
+    "\treturn 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",
+    "\tindex_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",
+    "\tindex_state = {}\n",
+    "\tindex = [[0,0], [0,1], [0,2], [1,0], [1,1], [1,2], [2,0], [2,1], [2,2]]\n",
+    "\tx=0\n",
+    "\ty=0\n",
+    "\tfor i in range(len(state)):\n",
+    "\t\tindex_state[state[i]] = index[i]\n",
+    "\tmhd = 0\n",
+    "\tfor i in range(8):\n",
+    "\t\tfor j in range(2):\n",
+    "\t\t\tmhd = (index_goal[i][j] - index_state[i][j])**2 + mhd\n",
+    "\treturn 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"
+    "\tscore1 = manhanttan(state, goal)\n",
+    "\tscore2 = linear(state, goal)\n",
+    "\treturn max(score1, score2)\t\t\n"
    ]
   },
   {
@@ -1461,7 +1337,6 @@
      "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",
@@ -1472,16 +1347,48 @@
       "[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",
+      "Number of explored nodes by the following heuristic are:  129\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",
+      "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",
+      "Number of explored nodes by the following heuristic are:  139\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"
+    "# Solving the puzzle \n",
+    "puzzle = EightPuzzle()\n",
+    "puzzle.checkSolvability([2,4,3,1,5,6,7,8,0]) # checks whether the initialized configuration is solvable or not\n",
+    "puzzle.solve([2,4,3,1,5,6,7,8,0],[1,2,3,4,5,6,7,8,0],max_heuristic) # Max_heuristic\n",
+    "puzzle.solve([2,4,3,1,5,6,7,8,0],[1,2,3,4,5,6,7,8,0],linear) # Linear\n",
+    "puzzle.solve([2,4,3,1,5,6,7,8,0],[1,2,3,4,5,6,7,8,0],manhanttan) # Manhattan\n",
+    "puzzle.solve([2,4,3,1,5,6,7,8,0],[1,2,3,4,5,6,7,8,0],sqrt_manhanttan) # Sqrt_manhattan"
    ]
   },
   {
@@ -1594,7 +1501,9 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "%psource genetic_algorithm"
@@ -1633,7 +1542,9 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "%psource reproduce"
@@ -1651,7 +1562,9 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "%psource mutate"
@@ -1669,7 +1582,9 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "%psource init_population"
@@ -1710,8 +1625,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "edges = {\n",
@@ -1733,14 +1650,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[['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"
+      "[['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"
      ]
     }
    ],
@@ -1760,8 +1677,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "def fitness(c):\n",
@@ -1777,14 +1696,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "['G', 'R', 'G', 'R']\n"
+      "['R', 'G', 'R', 'G']\n"
      ]
     }
    ],
@@ -1802,7 +1721,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -1847,14 +1766,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[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"
+      "[[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"
      ]
     }
    ],
@@ -1878,8 +1797,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "def fitness(q):\n",
@@ -1908,20 +1829,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[3, 5, 7, 2, 0, 6, 4, 1]\n",
-      "28\n"
+      "[5, 0, 6, 3, 7, 4, 1, 3]\n",
+      "26\n"
      ]
     }
    ],
    "source": [
-    "solution = genetic_algorithm(population, fitness, f_thres=28, gene_pool=range(8))\n",
+    "solution = genetic_algorithm(population, fitness, f_thres=25, gene_pool=range(8))\n",
     "print(solution)\n",
     "print(fitness(solution))"
    ]
@@ -1939,13 +1860,6 @@
    "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": {
@@ -1964,11 +1878,7 @@
    "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 ea58d18f1..46bef1557 100644
--- a/search.py
+++ b/search.py
@@ -17,6 +17,7 @@
 import bisect
 from operator import itemgetter
 
+
 infinity = float('inf')
 
 # ______________________________________________________________________________
@@ -400,6 +401,95 @@ def astar_search(problem, h=None):
     h = memoize(h or problem.h, 'h')
     return best_first_graph_search(problem, lambda n: n.path_cost + h(n))
 
+# ______________________________________________________________________________
+# A* heuristics 
+
+class EightPuzzle():
+
+    def __init__(self):
+        self.path = []
+        self.final = []
+    
+    def checkSolvability(self, state):
+        inversion = 0
+        for i in range(len(state)):
+               for j in range(i,len(state)):
+                    if (state[i]>state[j] and state[j]!=0):
+                                    inversion += 1
+        check = True
+        if inversion%2 != 0:
+                check = False
+        print(check)
+
+    def getPossibleMoves(self,state,heuristic,goal,moves):
+        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
+        index = state[0].index(0)
+        possible_moves = []
+        for i in range(len(move[index])):
+                conf = list(state[0][:])
+                a = conf[index]
+                b = conf[move[index][i]]
+                conf[move[index][i]] = a
+                conf[index] = b
+                possible_moves.append(conf)
+        scores = []
+        for i in possible_moves:
+                scores.append(heuristic(i,goal))
+        scores = [x+moves for x in scores]
+        allowed_state = []
+        for i in range(len(possible_moves)):
+                node = []
+                node.append(possible_moves[i])
+                node.append(scores[i])
+                node.append(state[0])
+                allowed_state.append(node)  
+        return allowed_state
+
+
+    def create_path(self,goal,initial):
+        node = goal[0]
+        self.final.append(goal[0])
+        if goal[2] == initial:
+                return reversed(self.final)
+        else:
+                parent = goal[2]
+                for i in self.path:
+                        if i[0] == parent:
+                                parent = i
+                self.create_path(parent,initial)
+
+    def show_path(self,initial):
+        move = []
+        for i in range(0,len(self.path)):
+                move.append(''.join(str(x) for x in self.path[i][0]))
+
+        print("Number of explored nodes by the following heuristic are: ", len(set(move)))	
+        print(initial)
+        for i in reversed(self.final):
+            print(i)
+
+        del self.path[:]
+        del self.final[:]
+        return
+
+    def solve(self,initial,goal,heuristic):
+        root = [initial,heuristic(initial,goal),'']
+        nodes = [] # nodes is a priority Queue based on the state score 
+        nodes.append(root)
+        moves = 0
+        while len(nodes) != 0:
+                node = nodes[0]
+                del nodes[0]
+                self.path.append(node)
+                if node[0] == goal:
+                        soln = self.create_path(self.path[-1],initial )
+                        self.show_path(initial)
+                        return  
+                moves +=1
+                opened_nodes = self.getPossibleMoves(node,heuristic,goal,moves)
+                nodes = sorted(opened_nodes+nodes, key=itemgetter(1))
+
+
 # ______________________________________________________________________________
 # Other search algorithms
 

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