{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "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",
    "* [Clarifying Questions](#Clarifying-Questions)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Pythonic-Code](#Pythonic-Code)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clarifying Questions\n",
    "\n",
    "* Are you looking for a generic naiive selection sort (ie not stable)?\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": null,
   "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": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def selection_sort_recursive(data, start):\n",
    "    if start < len(data) - 1:\n",
    "        swap(data, start, find_min_index(data, start))\n",
    "        selection_sort_recursive(data, start+1)\n",
    "\n",
    "print('Empty input')\n",
    "data = []\n",
    "selection_sort_recursive(data, 0)\n",
    "print(data)\n",
    "print('One element')\n",
    "data = [5]\n",
    "selection_sort_recursive(data, 0)\n",
    "print(data)\n",
    "print('Two or more elements')\n",
    "data = [5, 1, 7, 2, 6, -3, 5, 7, -1]\n",
    "selection_sort_recursive(data, 0)\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}