{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<small><i>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).</i></small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Implement breadth-first search on a graph.\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 the graph directed?\n",
    "    * Yes\n",
    "* Can we assume we already have Graph and Node classes?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "Input:\n",
    "* `add_edge(source, destination, weight)`\n",
    "\n",
    "```\n",
    "graph.add_edge(0, 1, 5)\n",
    "graph.add_edge(0, 4, 3)\n",
    "graph.add_edge(0, 5, 2)\n",
    "graph.add_edge(1, 3, 5)\n",
    "graph.add_edge(1, 4, 4)\n",
    "graph.add_edge(2, 1, 6)\n",
    "graph.add_edge(3, 2, 7)\n",
    "graph.add_edge(3, 4, 8)\n",
    "```\n",
    "\n",
    "Result:\n",
    "* Order of nodes visited: [0, 1, 4, 5, 3, 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "We generally use breadth-first search to determine the shortest path.\n",
    "\n",
    "* Add the current node to the queue and mark it as visited\n",
    "* While the queue is not empty\n",
    "    * Dequeue a node and visit it\n",
    "    * Iterate through each adjacent node\n",
    "        * If the node has not been visited, add it to the queue and mark it as visited\n",
    "\n",
    "Complexity:\n",
    "* Time: O(V + E), where V = number of vertices and E = number of edges\n",
    "* Space: O(V + E)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run ../graph/graph.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from collections import deque\n",
    "\n",
    "\n",
    "def bfs(root, visit_func):\n",
    "    if root is None:\n",
    "        return\n",
    "    queue = deque()\n",
    "    queue.append(root)\n",
    "    root.visit_state = State.visited\n",
    "    while queue:\n",
    "        node = queue.popleft()\n",
    "        visit_func(node)\n",
    "        for adjacent_node in node.adjacent:\n",
    "            if adjacent_node.visit_state == State.unvisited:\n",
    "                queue.append(adjacent_node)\n",
    "                adjacent_node.visit_state = State.visited"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run ../utils/results.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_bfs.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_bfs.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestBfs(object):\n",
    "\n",
    "    def __init__(self):\n",
    "        self.results = Results()\n",
    "\n",
    "    def test_bfs(self):\n",
    "        nodes = []\n",
    "        graph = Graph()\n",
    "        for id in range(0, 6):\n",
    "            nodes.append(graph.add_node(id))\n",
    "        graph.add_edge(0, 1, 5)\n",
    "        graph.add_edge(0, 4, 3)\n",
    "        graph.add_edge(0, 5, 2)\n",
    "        graph.add_edge(1, 3, 5)\n",
    "        graph.add_edge(1, 4, 4)\n",
    "        graph.add_edge(2, 1, 6)\n",
    "        graph.add_edge(3, 2, 7)\n",
    "        graph.add_edge(3, 4, 8)\n",
    "        bfs(nodes[0], self.results.add_result)\n",
    "        assert_equal(str(self.results), \"[0, 1, 4, 5, 3, 2]\")\n",
    "\n",
    "        print('Success: test_bfs')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestBfs()\n",
    "    test.test_bfs()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_bfs\n"
     ]
    }
   ],
   "source": [
    "%run -i test_bfs.py"
   ]
  }
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