interactive-coding-challenges/graphs_trees/graph_path_exists/path_exists_challenge.ipynb

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    "<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>"
   ]
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   "metadata": {},
   "source": [
    "# Challenge Notebook"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Determine whether there is a path between two nodes in a graph.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)\n",
    "* [Solution Notebook](#Solution-Notebook)"
   ]
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   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Is the graph directed?\n",
    "    * Yes\n",
    "* Can we assume we already have Graph and Node classes?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
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   "cell_type": "markdown",
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   "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",
    "* search_path(start=0, end=2) -> True\n",
    "* search_path(start=0, end=0) -> True\n",
    "* search_path(start=4, end=5) -> False"
   ]
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   "cell_type": "markdown",
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   "source": [
    "## Algorithm\n",
    "\n",
    "Refer to the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_path_exists/path_exists_solution.ipynb).  If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "%run ../graph/graph.py\n",
    "%load ../graph/graph.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
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   "source": [
    "def path_exists(start, end):\n",
    "    # TODO: Implement me\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The following unit test is expected to fail until you solve the challenge.**"
   ]
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  {
   "cell_type": "code",
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   "source": [
    "# %load test_path_exists.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestPathExists(object):\n",
    "\n",
    "    def test_path_exists(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",
    "\n",
    "        assert_equal(path_exists(nodes[0], nodes[2]), True)\n",
    "        assert_equal(path_exists(nodes[0], nodes[0]), True)\n",
    "        assert_equal(path_exists(nodes[4], nodes[5]), False)\n",
    "\n",
    "        print('Success: test_path_exists')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestPathExists()\n",
    "    test.test_path_exists()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Notebook\n",
    "\n",
    "Review the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_path_exists/path_exists_solution.ipynb) for a discussion on algorithms and code solutions."
   ]
  }
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