{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Analyzing the running time of algorithms\n", "\n", "We'll use sorting algorithms to demonstrate the need to carefully consider algorithm running time.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1, 2, 3, 5, 53]" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def bubble_sort(array) :\n", " for passes in range(len(array)-1, 0, -1):\n", " for i in range(passes):\n", " if array[i]>array[i+1]:\n", " array[i],array[i+1] = array[i+1],array[i]\n", " return array\n", "bubble_sort([53,2,1,3,5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the built in ```%timeit``` magic function in jupyter to compare the execution time of Python code." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 loop, best of 1: 589 µs per loop\n" ] } ], "source": [ "import random\n", "array = list(range(2000))\n", "random.shuffle(array)\n", "%timeit -n 1 -r 1 array.sort()\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 loop, best of 3: 176 ms per loop\n" ] } ], "source": [ "array = list(range(2000))\n", "random.shuffle(array)\n", "%timeit bubble_sort(array)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly Python's sort method is faster than bubble sort. But how does timing vary with the size of the array?" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5,0,'problem size')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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f5KmnnuLJJ5/kD3/4A2+//TZut5uGhgYuuOAC/vGPf3Dvvffi9Xo/ZrUrqboltztaXaDX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\nmXDUcNKMCfzmvAP41glT064Ysu3KdrT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zjEzg9XqpqKhQrTFotH9qCIYjbDzexLN1jZzolEl022Q7d0ytwlaS3+PzssV/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\n+h7WDJSVYFs6D9vyaFE5J0FDX77Itv4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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import timeit\n", "import random\n", "import time\n", "def bubble_sort_test(size) :\n", " times = []\n", " num_tests = 3\n", " for i in range(num_tests) : \n", " array = list(range(size))\n", " random.shuffle(array)\n", " t0=time.time()\n", " bubble_sort(array)\n", " times.append(time.time() - t0)\n", " return sum(times)/num_tests\n", "\n", "def python_sort_test(size) :\n", " times = []\n", " num_tests = 1000\n", " for i in range(num_tests) :\n", " array = list(range(size))\n", " random.shuffle(array)\n", " t0=time.time()\n", " array.sort()\n", " times.append(time.time() - t0)\n", " return sum(times)/num_tests\n", "\n", "problem_sizes = [25,50,100,200,500,750,1000,1250,1500,2000]\n", "bubble_sort_running_times = []\n", "python_sort_running_times = []\n", "for size in problem_sizes :\n", " bubble_sort_running_times.append(bubble_sort_test(size))\n", " python_sort_running_times.append(python_sort_test(size))\n", "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "plt.style.use('bmh')\n", "\n", "plt.figure()\n", "plt.plot(problem_sizes, bubble_sort_running_times,\n", " label = 'bubble_sort')\n", "plt.plot(problem_sizes, python_sort_running_times,\n", " label = 'python_sort')\n", "\n", "plt.legend(loc=0)\n", "plt.ylabel('Running time')\n", "plt.xlabel('problem size')\n", "\n", "plt.figure()\n", "plt.loglog(problem_sizes, bubble_sort_running_times,\n", " label = 'bubble_sort', basex=2,basey=2)\n", "plt.loglog(problem_sizes, python_sort_running_times,\n", " label = 'python_sort', basex=2,basey=2)\n", "\n", "plt.legend(loc=0)\n", "plt.ylabel('Running time')\n", "plt.xlabel('problem size')\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the next couple of lectures we will discuss a framework for analyzing the running time of algorithms, called **big O**. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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6Nf71J6IB01nuxUoK9YN2P8poD1ZR9KmiogJXr14VzbGKQkSmikkKEQ2ISqlC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\n6BoICDIRMsd0IcoOEEIIeRo02ttEmgkNGr5fj4f/1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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import log\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "plt.style.use('fivethirtyeight')\n", "\n", "n = np.linspace(1,10,1000)\n", "labels = ['Constant','Logarithmic','Linear','Log Linear','Quadratic','Cubic','Exponential']\n", "big_o = [np.ones(n.shape),np.log(n),n,n*np.log(n),n**2,n**3,2**n]\n", "\n", "plt.figure(figsize=(12,10))\n", "plt.ylim(0,50)\n", "\n", "for i in range(len(big_o)):\n", " plt.plot(n,big_o[i],label = labels[i])\n", "\n", "plt.legend(loc=0)\n", "plt.ylabel('Running time')\n", "plt.xlabel('n')\n", "plt.savefig('running_time.pdf')" ] } ], "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 1 }