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   "source": [
    "<small><i>This notebook was prepared by [Donne Martin](http://donnemartin.com). Source and license info is on [GitHub](https://bit.ly/code-notes).</i></small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Implement selection sort.\n",
    "\n",
    "* [Constraints and Assumptions](#Constraints-and-Assumptions)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints and Assumptions\n",
    "\n",
    "*Problem statements are often intentionally ambiguous.  Identifying constraints and stating assumptions can help to ensure you code the intended solution.*\n",
    "\n",
    "* Are you looking for a naiive solution (ie not stable, not based on a heap)?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* Empty input\n",
    "* One 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/9/94/Selection-Sort-Animation.gif)\n",
    "\n",
    "We can do this recursively or iteratively.  Iteratively will be more efficient as it doesn't require the extra space overhead with the recursive calls.\n",
    "\n",
    "* For each element\n",
    "    * Check every element to the right to find the min\n",
    "    * If min < current element, swap\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n^2) average, worst, best\n",
    "* Space: O(1) iterative, O(n) recursive (unless tail-call elimination is available, then O(1)), generally not stable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def find_min_index(data, start):\n",
    "    min_index = start\n",
    "    for i in xrange(start + 1, len(data)):\n",
    "        if data[i] < data[min_index]:\n",
    "            min_index = i\n",
    "    return min_index\n",
    "\n",
    "def swap(data, i, j):\n",
    "    if (i != j):\n",
    "        data[i], data[j] = data[j], data[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "def selection_sort_recursive(data, start=0):\n",
    "    if start < len(data) - 1:\n",
    "        swap(data, start, find_min_index(data, start))\n",
    "        selection_sort_recursive(data, start+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def selection_sort_iterative(data):\n",
    "    if len(data) == 0 or len(data) == 1:\n",
    "        return\n",
    "    for i in xrange(0, len(data) - 1):\n",
    "        swap(data, i, find_min_index(data, i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test\n",
    "\n",
    "*It is important to identify and run through general and edge cases from the [Test Cases](#Test-Cases) section by hand.  You generally will not be asked to write a unit test like what is shown below.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Empty input\n",
      "One element\n",
      "Two or more elements\n",
      "Success: test_selection_sort\n",
      "\n",
      "Empty input\n",
      "One element\n",
      "Two or more elements\n",
      "Success: test_selection_sort\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from nose.tools import assert_equal\n",
    "\n",
    "class Test(object):\n",
    "    def test_selection_sort(self, func):\n",
    "        print('Empty input')\n",
    "        data = []\n",
    "        func(data)\n",
    "        assert_equal(data, [])\n",
    "\n",
    "        print('One element')\n",
    "        data = [5]\n",
    "        func(data)\n",
    "        assert_equal(data, [5])\n",
    "\n",
    "        print('Two or more elements')\n",
    "        data = [5, 1, 7, 2, 6, -3, 5, 7, -1]\n",
    "        func(data)\n",
    "        assert_equal(data, sorted(data))\n",
    "        \n",
    "        print('Success: test_selection_sort\\n')\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    test = Test()\n",
    "    test.test_selection_sort(selection_sort_recursive)\n",
    "    test.test_selection_sort(selection_sort_iterative)"
   ]
  }
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