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   "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: Implement a priority queue backed by an array.\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",
    "* Do we expect the methods to be insert, extract_min, and decrease_key?\n",
    "    * Yes\n",
    "* Can we assume there aren't any duplicate keys?\n",
    "    * Yes\n",
    "* Do we need to validate inputs?\n",
    "    * No\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "### insert\n",
    "\n",
    "* `insert` general case -> inserted node\n",
    "\n",
    "### extract_min\n",
    "\n",
    "* `extract_min` from an empty list -> None\n",
    "* `extract_min` general case -> min node\n",
    "\n",
    "### decrease_key\n",
    "\n",
    "* `decrease_key` an invalid key -> None\n",
    "* `decrease_key` general case -> updated node"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "### insert\n",
    "\n",
    "* Append to the internal array.\n",
    "\n",
    "Complexity:\n",
    "* Time: O(1)\n",
    "* Space: O(1)\n",
    "\n",
    "### extract_min\n",
    "\n",
    "* Loop through each item in the internal array\n",
    "    * Update the min value as needed\n",
    "* Remove the min element from the array and return it\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n)\n",
    "* Space: O(1)\n",
    "\n",
    "### decrease_key\n",
    "\n",
    "* Loop through each item in the internal array to find the matching input\n",
    "    * Update the matching element's key\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n)\n",
    "* Space: O(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting priority_queue.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile priority_queue.py\n",
    "import sys\n",
    "\n",
    "\n",
    "class PriorityQueueNode(object):\n",
    "\n",
    "    def __init__(self, obj, key):\n",
    "        self.obj = obj\n",
    "        self.key = key\n",
    "\n",
    "    def __repr__(self):\n",
    "        return str(self.obj) + ': ' + str(self.key)\n",
    "\n",
    "\n",
    "class PriorityQueue(object):\n",
    "\n",
    "    def __init__(self):\n",
    "        self.array = []\n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self.array)\n",
    "\n",
    "    def insert(self, node):\n",
    "        self.array.append(node)\n",
    "        return self.array[-1]\n",
    "\n",
    "    def extract_min(self):\n",
    "        if not self.array:\n",
    "            return None\n",
    "        minimum = sys.maxsize\n",
    "        for index, node in enumerate(self.array):\n",
    "            if node.key < minimum:\n",
    "                minimum = node.key\n",
    "                minimum_index = index\n",
    "        return self.array.pop(minimum_index)\n",
    "\n",
    "    def decrease_key(self, obj, new_key):\n",
    "        for node in self.array:\n",
    "            if node.obj is obj:\n",
    "                node.key = new_key\n",
    "                return node\n",
    "        return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run priority_queue.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_priority_queue.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_priority_queue.py\n",
    "import unittest\n",
    "\n",
    "\n",
    "class TestPriorityQueue(unittest.TestCase):\n",
    "\n",
    "    def test_priority_queue(self):\n",
    "        priority_queue = PriorityQueue()\n",
    "        self.assertEqual(priority_queue.extract_min(), None)\n",
    "        priority_queue.insert(PriorityQueueNode('a', 20))\n",
    "        priority_queue.insert(PriorityQueueNode('b', 5))\n",
    "        priority_queue.insert(PriorityQueueNode('c', 15))\n",
    "        priority_queue.insert(PriorityQueueNode('d', 22))\n",
    "        priority_queue.insert(PriorityQueueNode('e', 40))\n",
    "        priority_queue.insert(PriorityQueueNode('f', 3))\n",
    "        priority_queue.decrease_key('f', 2)\n",
    "        priority_queue.decrease_key('a', 19)\n",
    "        mins = []\n",
    "        while priority_queue.array:\n",
    "            mins.append(priority_queue.extract_min().key)\n",
    "        self.assertEqual(mins, [2, 5, 15, 19, 22, 40])\n",
    "        print('Success: test_min_heap')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestPriorityQueue()\n",
    "    test.test_priority_queue()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_min_heap\n"
     ]
    }
   ],
   "source": [
    "%run -i test_priority_queue.py"
   ]
  }
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