CW1-1 Sort.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Algorithms 202: Coursework 1 Task 1: Sorting"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Group-ID: 33"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Group members: Glen Rodgers, Summer Jones, Leanne Lyons "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Objectives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The aim of this coursework is to enhance your algorithmic skills by mastering the divide and conquer and dynamic programming strategies. You are asked to show that you can:\n",
    "\n",
    "- implement divide and conquer solutions for given problems\n",
    "- compare naive and advanced implementations of algorithms solving the same problem\n",
    "\n",
    "This notebook *is* the coursework. It contains cells with function definitions that you will need to complete. You will submit this notebook as your coursework.\n",
    "\n",
    "The comparisons of different algorithms involve textual descriptions and graphical plots. For graphing you will be using [matplotlib](http://matplotlib.org/index.html) to generate plots. [This tutorial](http://matplotlib.org/index.html) will be useful to go through to get you up to speed. For the textual descriptions you may wish to use [LaTeX](http://en.wikipedia.org/wiki/LaTeX) inline like $\\mathcal{O}(n\\log{}n)$. Double click this cell to reveal the required markup - and [see here](http://texblog.org/2014/06/24/big-o-and-related-notations-in-latex/) for useful guidance on producing common symbols used in asymptotic run time analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Preliminaries: helper functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we define a collection of functions that will be useful for the rest of the coursework. You'll need to run this cell to get started."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# so our plots get drawn in the notebook\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "from random import randint\n",
    "from time import clock\n",
    "\n",
    "# a timer - runs the provided function and reports the\n",
    "# run time in ms\n",
    "def time_f(f):\n",
    "    before = clock()\n",
    "    f()\n",
    "    after = clock()\n",
    "    return after - before\n",
    "\n",
    "# remember - lambdas are just one line functions\n",
    "\n",
    "# make us a random list length (between 1 - 2000)\n",
    "# rand_len = lambda max_len=2e3: randint(1, max_len)\n",
    "\n",
    "\n",
    "# choose a random value for a list element (between 0 1e6)\n",
    "rand_int = lambda: randint(0, 1e6)\n",
    "\n",
    "# generate a random list of random length -\n",
    "# here we use a list comprehension, a very tidy\n",
    "# way of transforming lists of data\n",
    "rand_list = lambda max_len=2e3: [rand_int() \n",
    "                                 for i in range(rand_len(max_len=max_len))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task 1: Sorting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this task you are asked to implement `insertion_sort` and `merge_sort`. You need to perform an experimental analysis of their running time. Based on your analysis, you should implement a third sorting algorithm, `hybrid_sort`, which is similar to `merge_sort` but uses `insertion_sort` for the base case. The problem size for which the base case is invoked has to be inferred from the running time analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1a. Implement `insertion_sort`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Complete the below definition for `insertion_sort`. Do not change the name of the function or it's arguments. \n",
    "\n",
    "\n",
    "Hints:\n",
    "\n",
    "- Your sort should be in-place (i.e. it changes the input list for the caller) but you should also return the list so the function can be called as indicated below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def insertion_sort(a):\n",
    "    for i in range(1, len(a)):\n",
    "        curr = a[i]\n",
    "        pos = i\n",
    "        while pos > 0 and a[pos-1] > curr:\n",
    "            a[pos] = a[pos-1]\n",
    "            pos -= 1\n",
    "        a[pos] = curr\n",
    "    return a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use this test to confirm your implementation is correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "x = [2, 4, 1, 3, 5]\n",
    "print(insertion_sort(x) == [1, 2, 3, 4, 5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1b. Implement `merge_sort`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Complete the below definition for `merge_sort`. Do not change the name of the function or it's arguments.\n",
    "\n",
    "Hints:\n",
    "\n",
    "- Your implementation should leave the input list unmodified for the caller\n",
    "- You are free to define other functions in this cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def merge(arr, start, middle, end):\n",
    "    left = arr[start : middle]\n",
    "    right = arr[middle : end]\n",
    "    i, j = 0, 0\n",
    "    #replaced the use of sentinels\n",
    "    for k in range(start, end):\n",
    "        if j >= len(right) or (i < len(left) and left[i] < right[j]):\n",
    "            arr[k] = left[i]\n",
    "            i += 1\n",
    "        else:\n",
    "            arr[k] = right[j]\n",
    "            j += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def merge_divide(arr, start, end):\n",
    "    if start < end-1:\n",
    "        middle = int((start + end) / 2)\n",
    "        merge_divide(arr, start, middle)\n",
    "        merge_divide(arr, middle, end)\n",
    "        merge(arr, start, middle, end)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def merge_sort(a):\n",
    "    sorted_list = list(a)\n",
    "    merge_divide(sorted_list, 0, len(a))\n",
    "    return sorted_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use this test to confirm your implementation is correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "x = [2, 4, 1, 3, 5, 6]\n",
    "print(merge_sort(x) == [1, 2, 3, 4, 5, 6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1c. Analyse the running time performance of `insertion_sort` and `merge_sort`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a graph showing the run time performance of your `insertion_sort` and `merge_sort` for different lengths of random integers. Analyse the performance at the large scale ($n \\approx 10^3$) and small scale ($n \\approx 10$). To remove noisy measurements, you might want to repeat the analysis several times and estimate average performance for different $n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# rand_len = lambda max_len=2e3: randint(1, 50) # n ≈ 10\n",
    "rand_len = lambda max_len=2e3: randint(1, 5000) # n ≈ 10^3\n",
    "random_lists = [rand_list() for i in range(100)] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#insertion sort data\n",
    "num_insertion = []\n",
    "time_insertion = []\n",
    "for r_list in random_lists:\n",
    "    time_insertion.append(time_f(lambda: insertion_sort(r_list)))\n",
    "    num_insertion.append(len(r_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#merge sort data\n",
    "num_merge = []\n",
    "time_merge = []\n",
    "for r_list in random_lists:\n",
    "    time_merge.append(time_f(lambda: merge_sort(r_list)))\n",
    "    num_merge.append(len(r_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 2.0)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nwhARkZj8f6dRenmV2UIhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7834b12048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(num_merge, time_merge, c='blue')\n",
    "plt.scatter(num_insertion, time_insertion, c='red')\n",
    "plt.xlabel('n')\n",
    "plt.ylabel('time (/s)')\n",
    "plt.legend(['merge-sort', 'insertion-sort'])\n",
    "plt.xlim(0)\n",
    "plt.ylim(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Now discuss your findings in a few lines in the below cell:**"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "At values of n≈10 (We choose 50), insertion sort and merge sort have similar runtimes, although insertion sort is slightly faster up until around n = 70, where it starts to slowly curve upwards whilst merge sort stays relatively linear. At higher values of n≈1000 (we choose 5000) the difference in runtime was quite stark as the insertion sort curved upwards quite dramatically while the merge sort only curved upwards gradually. We expected this as this reflects their worst case runtimes of O(n^2) and O(nlogn) respectively.  \n",
    "\n",
    "Due to insertion sorts better performance for numbers less than 70, it is reasonable to suspect that using insertion sort for the base case of merge sort would create a more efficent algorithm than both, as shown below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1d. Implement `hybrid_sort()`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement `hybrid_sort()`, a `merge_sort()` variant which uses `insertion_sort()` for the base case. The problem size for which the base case is invoked has to be inferred from your above running time analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def hybrid_conquer(arr, start, end):\n",
    "    threshold = 700\n",
    "    if end - start - 1 >= threshold:\n",
    "        middle = int((start + end) / 2)\n",
    "        hybrid_conquer(arr, start, middle)\n",
    "        hybrid_conquer(arr, middle, end)\n",
    "        merge(arr, start, middle, end)\n",
    "    else:\n",
    "        insertion_sort(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def hybrid_sort(a):\n",
    "    sorted_list = list(a)\n",
    "    hybrid_conquer(sorted_list, 0, len(a))\n",
    "    return sorted_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use this test to confirm your implementation is correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "x = [2, 4, 1, 3]\n",
    "print(hybrid_sort(x) == [1, 2, 3, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1e. Analyse all three sorting implementations together"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a graph showing the running time performance of your `insertion_sort()`, `merge_sort()` and `hybrid_sort()` for different lengths of random integers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#hybrid sort data\n",
    "num_hybrid = []\n",
    "time_hybrid = []\n",
    "for r_list in random_lists:\n",
    "    time_hybrid.append(time_f(lambda: hybrid_sort(r_list)))\n",
    "    num_hybrid.append(len(r_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 2.0)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\njfNaNXMRlgYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f78320a6080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(num_insertion, time_insertion, c='red')\n",
    "plt.scatter(num_hybrid, time_hybrid, c='green')\n",
    "plt.xlabel('n')\n",
    "plt.ylabel('time (/s)')\n",
    "plt.legend(['insertion-sort', 'hybrid-sort'])\n",
    "plt.xlim(0)\n",
    "plt.ylim(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0.039999999999999994)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZkAAAEPCAYAAACQmrmQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7832165e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(num_merge, time_merge, c='blue')\n",
    "plt.scatter(num_hybrid, time_hybrid, c='green')\n",
    "plt.xlabel('n')\n",
    "plt.ylabel('time (/s)')\n",
    "plt.legend(['merge-sort', 'hybrid-sort'])\n",
    "plt.xlim(0)\n",
    "plt.ylim(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Now discuss your findings in a few lines in the below cell:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our implementation of hybrid sort performs extremely well in comparision to the merge sort and especially towards the insertion sort.  At list length less than or equal to 70, insertion sort and our hybrid sort perform similarly as they both use insertion sort due to our threshold size and are both slightly faster than merge sort at almost all of these list sizes as well.  At greater sizes, the merge sort again had a faster runtime than insertion sort but our hybrid sort sort maintained almost linear running time even up to 5000 along side merge sort.  \n",
    "\n",
    "Due to our hybrid's implementation, it has a faster running time than merge sort and insertion sort at all values up to list lengths of 5000.  This allows us to hypothesis that a worst case upper bound of our hybrid sort is O(nlogn) and it could be less.  \n",
    "\n",
    "We at first decided to choose 70 as our threshold for the base case of our hybrid sort but then realised that higher numbers resulted in a smaller runtime.  We deduced that this was due to solving more subproblems of mergesort with insertion sort meant that less divisions were needed in the merge sort.  We then settled for list lengths of 700 being the best option for our base case as it meant we still had a faster runtime ast smaller values of n and drastically smaller values for large values of n."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}