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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>"
   ]
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   "cell_type": "markdown",
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   "source": [
    "## Problem: Implement insertion 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?\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/0/0f/Insertion-sort-example-300px.gif)\n",
    "\n",
    "* For each value index 1 to n - 1\n",
    "    * Compare with all elements to the left of the current value to determine new insertion point\n",
    "        * Hold current value in temp variable\n",
    "        * Shift elements from new insertion point right\n",
    "        * Insert value in temp variable\n",
    "        * Break\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n^2) avarage, worst.  O(1) best if input is already sorted.\n",
    "* Space: O(1), stable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def insertion_sort(data):\n",
    "    if len(data) < 2:\n",
    "        return\n",
    "    for r in xrange(1, len(data)):\n",
    "        for l in xrange(0, r):\n",
    "            if data[l] > data[r]:\n",
    "                temp = data[r]\n",
    "                data[l+1:r+1] = data[l:r]\n",
    "                data[l] = temp\n",
    "                break"
   ]
  },
  {
   "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": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Empty input\n",
      "One element\n",
      "Two or more elements\n",
      "Success: test_insertion_sort\n"
     ]
    }
   ],
   "source": [
    "from nose.tools import assert_equal\n",
    "\n",
    "class Test(object):\n",
    "    def test_insertion_sort(self):\n",
    "        print('Empty input')\n",
    "        data = []\n",
    "        insertion_sort(data)\n",
    "        assert_equal(data, [])\n",
    "\n",
    "        print('One element')\n",
    "        data = [5]\n",
    "        insertion_sort(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",
    "        insertion_sort(data)\n",
    "        assert_equal(data, sorted(data))\n",
    "        \n",
    "        print('Success: test_insertion_sort')\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    test = Test()\n",
    "    test.test_insertion_sort()"
   ]
  }
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