{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Find a build order given a list of projects and dependencies.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Is it possible to have a cyclic graph as the input?\n",
    "    * Yes\n",
    "* Can we assume we already have Graph and Node classes?\n",
    "    * Yes\n",
    "* Can we assume this is a connected graph?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* projects: a, b, c, d, e, f, g\n",
    "* dependencies: (d, g), (f, c), (f, b), (f, a), (c, a), (b, a), (a, e), (b, e)\n",
    "* output: d, f, c, b, g, a, e\n",
    "\n",
    "Note: Edge direction is down\n",
    "<pre>\n",
    "    f     d\n",
    "   /|\\    |\n",
    "  c | b   g\n",
    "   \\|/|\n",
    "    a |\n",
    "    |/\n",
    "    e\n",
    "</pre>\n",
    "\n",
    "Test a graph with a cycle, output should be None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "We can determine the build order using a topological sort.\n",
    "\n",
    "* Build the graph with projects (nodes) and dependencies (directed edges)\n",
    "* Add initially non-dependent nodes to processed_nodes\n",
    "    * If none exist, we have a circular dependency, return None\n",
    "* While the length processed_nodes < the length of graph nodes\n",
    "    * Remove outgoing edges from newly added items in processed_nodes\n",
    "    * Add non-dependent nodes to processed_nodes\n",
    "        * If we didn't add any nodes, we have a circular dependency, return None\n",
    "* Return processed_nodes\n",
    "\n",
    "Complexity:\n",
    "* Time: O(V + E)\n",
    "* Space: O(V + E)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import deque\n",
    "\n",
    "\n",
    "class Dependency(object):\n",
    "\n",
    "    def __init__(self, node_key_before, node_key_after):\n",
    "        self.node_key_before = node_key_before\n",
    "        self.node_key_after = node_key_after"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run ../graph/graph.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BuildOrder(object):\n",
    "\n",
    "    def __init__(self, dependencies):\n",
    "        self.dependencies = dependencies\n",
    "        self.graph = Graph()\n",
    "        self._build_graph()\n",
    "\n",
    "    def _build_graph(self):\n",
    "        for dependency in self.dependencies:\n",
    "            self.graph.add_edge(dependency.node_key_before,\n",
    "                                dependency.node_key_after)\n",
    "\n",
    "    def _find_start_nodes(self, processed_nodes):\n",
    "        nodes_to_process = {}\n",
    "        for key, node in self.graph.nodes.items():\n",
    "            if node.incoming_edges == 0 and key not in processed_nodes:\n",
    "                nodes_to_process[key] = node\n",
    "        return nodes_to_process\n",
    "\n",
    "    def _process_nodes(self, nodes_to_process, processed_nodes):\n",
    "        for node in nodes_to_process.values():\n",
    "            # We'll need to iterate on copies since we'll need\n",
    "            # to change the dictionaries during iteration with\n",
    "            # the remove_neighbor call\n",
    "            for adj_node in list(node.adj_nodes.values()):\n",
    "                node.remove_neighbor(adj_node)\n",
    "            processed_nodes[node.key] = node\n",
    "        nodes_to_process = {}\n",
    "\n",
    "    def find_build_order(self):\n",
    "        result = []\n",
    "        nodes_to_process = {}\n",
    "        processed_nodes = {}\n",
    "        while len(result) != len(self.graph.nodes):\n",
    "            nodes_to_process = self._find_start_nodes(processed_nodes)\n",
    "            if not nodes_to_process:\n",
    "                return None\n",
    "            result.extend(nodes_to_process.values())\n",
    "            self._process_nodes(nodes_to_process, processed_nodes)\n",
    "        return result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run ../utils/results.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_build_order.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_build_order.py\n",
    "import unittest\n",
    "\n",
    "\n",
    "class TestBuildOrder(unittest.TestCase):\n",
    "\n",
    "    def __init__(self, *args, **kwargs):\n",
    "        super(TestBuildOrder, self).__init__()\n",
    "        self.dependencies = [\n",
    "            Dependency('d', 'g'),\n",
    "            Dependency('f', 'c'),\n",
    "            Dependency('f', 'b'),\n",
    "            Dependency('f', 'a'),\n",
    "            Dependency('c', 'a'),\n",
    "            Dependency('b', 'a'),\n",
    "            Dependency('a', 'e'),\n",
    "            Dependency('b', 'e'),\n",
    "        ]\n",
    "\n",
    "    def test_build_order(self):\n",
    "        build_order = BuildOrder(self.dependencies)\n",
    "        processed_nodes = build_order.find_build_order()\n",
    "\n",
    "        expected_result0 = ('d', 'f')\n",
    "        expected_result1 = ('c', 'b', 'g')\n",
    "        self.assertTrue(processed_nodes[0].key in expected_result0)\n",
    "        self.assertTrue(processed_nodes[1].key in expected_result0)\n",
    "        self.assertTrue(processed_nodes[2].key in expected_result1)\n",
    "        self.assertTrue(processed_nodes[3].key in expected_result1)\n",
    "        self.assertTrue(processed_nodes[4].key in expected_result1)\n",
    "        self.assertTrue(processed_nodes[5].key is 'a')\n",
    "        self.assertTrue(processed_nodes[6].key is 'e')\n",
    "\n",
    "        print('Success: test_build_order')\n",
    "\n",
    "    def test_build_order_circular(self):\n",
    "        self.dependencies.append(Dependency('e', 'f'))\n",
    "        build_order = BuildOrder(self.dependencies)\n",
    "        processed_nodes = build_order.find_build_order()\n",
    "        self.assertTrue(processed_nodes is None)\n",
    "\n",
    "        print('Success: test_build_order_circular')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestBuildOrder()\n",
    "    test.test_build_order()\n",
    "    test.test_build_order_circular()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_build_order\n",
      "Success: test_build_order_circular\n"
     ]
    }
   ],
   "source": [
    "%run -i test_build_order.py"
   ]
  }
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