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   "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": [
    "# Challenge Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Implement a min heap with extract_min and insert methods.\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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Can we assume the inputs are ints?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* Extract min of an empty tree\n",
    "* Extract min general case\n",
    "* Insert into an empty tree\n",
    "* Insert general case (left and right insert)\n",
    "\n",
    "<pre>\n",
    "          _5_\n",
    "        /     \\\n",
    "       20     15\n",
    "      / \\    /  \\\n",
    "     22  40 25\n",
    "     \n",
    "extract_min(): 5\n",
    "\n",
    "          _15_\n",
    "        /      \\\n",
    "       20      25\n",
    "      / \\     /  \\\n",
    "     22  40 \n",
    "\n",
    "insert(2):\n",
    "\n",
    "          _2_\n",
    "        /     \\\n",
    "       20      5\n",
    "      / \\     / \\\n",
    "     22  40  25  15\n",
    "</pre>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "Refer to the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/min_heap/min_heap_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": false
   },
   "outputs": [],
   "source": [
    "class MinHeap(object):\n",
    "\n",
    "    def __init__(self):\n",
    "        # TODO: Implement me\n",
    "        pass\n",
    "\n",
    "    def extract_min(self):\n",
    "        # TODO: Implement me\n",
    "        pass    \n",
    "\n",
    "    def peek_min(self):\n",
    "        # TODO: Implement me\n",
    "        pass\n",
    "\n",
    "    def insert(self, data):\n",
    "        # TODO: Implement me\n",
    "        pass\n",
    "\n",
    "    def _bubble_up(self, index):\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.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# %load test_min_heap.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestMinHeap(object):\n",
    "\n",
    "    def test_min_heap(self):\n",
    "        heap = MinHeap()\n",
    "        assert_equal(heap.peek_min(), None)\n",
    "        assert_equal(heap.extract_min(), None)\n",
    "        heap.insert(20)\n",
    "        assert_equal(heap.peek_min(), 20)\n",
    "        heap.insert(5)\n",
    "        assert_equal(heap.peek_min(), 5)\n",
    "        heap.insert(15)\n",
    "        heap.insert(22)\n",
    "        heap.insert(40)\n",
    "        heap.insert(5)\n",
    "        assert_equal(heap.peek_min(), 5)\n",
    "        heap.insert(3)\n",
    "        assert_equal(heap.peek_min(), 3)\n",
    "        assert_equal(heap.extract_min(), 3)\n",
    "        assert_equal(heap.peek_min(), 5)\n",
    "        print('Success: test_min_heap')\n",
    "\n",
    "        \n",
    "def main():\n",
    "    test = TestMinHeap()\n",
    "    test.test_min_heap()\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/min_heap/min_heap_solution.ipynb) for a discussion on algorithms and code solutions."
   ]
  }
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