topo_sort.ipynb

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   "source": [
    "from collections import defaultdict\n",
    "from itertools import chain"
   ]
  },
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    "class Graph:\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.adjacency = defaultdict(list)\n",
    "    \n",
    "    def add_edge(self, a, b):\n",
    "        self.adjacency[a].append(b)\n",
    "    \n",
    "    def __repr__(self):\n",
    "        return \"Graph: \" + repr(dict(self.adjacency))        \n",
    "    \n",
    "    def topo_sort(self):\n",
    "        \n",
    "        def helper(v, visited, stack):\n",
    "            if visited[v]:\n",
    "                return\n",
    "            visited[v] = True\n",
    "            for i in self.adjacency[v]:\n",
    "                helper(i, visited, stack)\n",
    "            stack.insert(0, v)\n",
    "        \n",
    "        stack = []\n",
    "        \n",
    "        visited = list(\n",
    "            chain(*\n",
    "                  [val for val in self.adjacency.values()] + \n",
    "                  [[key for key in self.adjacency.keys()]]\n",
    "                 )\n",
    "        )\n",
    "         \n",
    "        visited = {k: False for k in visited}\n",
    "        \n",
    "        for k, v in visited.items():\n",
    "            if not v:\n",
    "                helper(k, visited, stack)\n",
    "                \n",
    "        return stack"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Topologically sort the graph below:\n",
    "\n",
    "![graph](https://www.geeksforgeeks.org/wp-content/uploads/graph.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "g = Graph()\n",
    "g.add_edge(5, 2)\n",
    "g.add_edge(5, 0)\n",
    "g.add_edge(4, 0)\n",
    "g.add_edge(4, 1)\n",
    "g.add_edge(2, 3)\n",
    "g.add_edge(3, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Graph: {5: [2, 0], 4: [0, 1], 2: [3], 3: [1]}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 5, 0, 2, 3, 1]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.topo_sort()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: The above is just one of the possible topological sorts\n",
    "Here are all the possibilities for this graph:\n",
    "\n",
    "    4 5 0 2 3 1 \n",
    "    4 5 2 0 3 1 \n",
    "    4 5 2 3 0 1 \n",
    "    4 5 2 3 1 0 \n",
    "    5 2 3 4 0 1 \n",
    "    5 2 3 4 1 0 \n",
    "    5 2 4 0 3 1 \n",
    "    5 2 4 3 0 1 \n",
    "    5 2 4 3 1 0 \n",
    "    5 4 0 2 3 1 \n",
    "    5 4 2 0 3 1 \n",
    "    5 4 2 3 0 1 \n",
    "    5 4 2 3 1 0 "
   ]
  }
 ],
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