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   "metadata": {},
   "source": [
    "This notebook was prepared by [Donne Martin](http://donnemartin.com). 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 quick sort.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Pythonic-Code](#Pythonic-Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Is a naive solution sufficient (ie not in-place)?\n",
    "    * Yes\n",
    "* Are duplicates allowed?\n",
    "    * Yes\n",
    "* Can we assume the input is valid?\n",
    "    * No\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* None -> Exception\n",
    "* Empty input -> []\n",
    "* One element -> [element]\n",
    "* Two or more elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "Wikipedia's animation:\n",
    "![alt text](http://upload.wikimedia.org/wikipedia/commons/6/6a/Sorting_quicksort_anim.gif)\n",
    "\n",
    "* Set pivot to the middle element in the data\n",
    "* For each element:\n",
    "    * If current element is the pivot, continue\n",
    "    * If the element is less than the pivot, add to left array\n",
    "    * Else, add to right array\n",
    "* Recursively apply quicksort to the left array\n",
    "* Recursively apply quicksort to the right array\n",
    "* Merge the left array + pivot + right array\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n log(n)) average, best, O(n^2) worst\n",
    "* Space: O(n)\n",
    "\n",
    "Misc:\n",
    "\n",
    "* More sophisticated implementations are in-place, although they still take up recursion depth space\n",
    "* Most implementations are not stable\n",
    "\n",
    "See [Quicksort on wikipedia](https://en.wikipedia.org/wiki/Quicksort):\n",
    "\n",
    "Typically, quicksort is significantly faster in practice than other Θ(nlogn) algorithms, because its inner loop can be efficiently implemented on most architectures [presumably because it has good cache locality], and in most real-world data, it is possible to make design choices which minimize the probability of requiring quadratic time.\n",
    "\n",
    "See: [Quicksort vs merge sort](http://stackoverflow.com/questions/70402/why-is-quicksort-better-than-mergesort)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "\n",
    "\n",
    "class QuickSort(object):\n",
    "\n",
    "    def sort(self, data):\n",
    "        if data is None:\n",
    "            raise TypeError('data cannot be None')\n",
    "        return self._sort(data)\n",
    "\n",
    "    def _sort(self, data):\n",
    "        if len(data) < 2:\n",
    "            return data\n",
    "        equal = []\n",
    "        left = []\n",
    "        right = []\n",
    "        pivot_index = len(data) // 2\n",
    "        pivot_value = data[pivot_index]\n",
    "        # Build the left and right partitions\n",
    "        for item in data:\n",
    "            if item == pivot_value:\n",
    "                equal.append(item)\n",
    "            elif item < pivot_value:\n",
    "                left.append(item)\n",
    "            else:\n",
    "                right.append(item)\n",
    "        # Recursively apply quick_sort\n",
    "        left_ = self._sort(left)\n",
    "        right_ = self._sort(right)\n",
    "        return left_ + equal + right_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_quick_sort.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_quick_sort.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestQuickSort(object):\n",
    "\n",
    "    def test_quick_sort(self):\n",
    "        quick_sort = QuickSort()\n",
    "\n",
    "        print('None input')\n",
    "        assert_raises(TypeError, quick_sort.sort, None)\n",
    "\n",
    "        print('Empty input')\n",
    "        assert_equal(quick_sort.sort([]), [])\n",
    "\n",
    "        print('One element')\n",
    "        assert_equal(quick_sort.sort([5]), [5])\n",
    "\n",
    "        print('Two or more elements')\n",
    "        data = [5, 1, 7, 2, 6, -3, 5, 7, -1]\n",
    "        assert_equal(quick_sort.sort(data), sorted(data))\n",
    "\n",
    "        print('Success: test_quick_sort\\n')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestQuickSort()\n",
    "    test.test_quick_sort()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None input\n",
      "Empty input\n",
      "One element\n",
      "Two or more elements\n",
      "Success: test_quick_sort\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%run -i test_quick_sort.py"
   ]
  }
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