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March 31, 2018 01:47
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Big O Notation
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "> # The Big O Notations is realted to how efficient and algorithm is. The measure of it is denoted how Big O." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "> ## Lets create a function and measure its runtime... " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def sum1(n):\n", | |
| " '''\n", | |
| " Take an input of n and return the sum of the numbers from 0 to n\n", | |
| " '''\n", | |
| " final_sum = 0\n", | |
| " for x in range(n+1):\n", | |
| " final_sum += n\n", | |
| " \n", | |
| " return final_sum\n", | |
| "\n", | |
| "def sum2(n):\n", | |
| " '''\n", | |
| " Take an input of n and return the sum of the numbers from 0 to n\n", | |
| " '''\n", | |
| " final_sum = 0\n", | |
| " return (n*(n+1)/2)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "3.1 µs ± 22.4 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%timeit sum1(100)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": { | |
| "scrolled": true | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "112 ns ± 0.84 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%timeit sum2(100)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "> *** The functions above showed that the second sum is more efficient, BUT.. to measure with time consuming is not a good approach since the running processing depends on serveral things like hardware capabilities and so on. So the <font color='red'>Big O</font> notation defines a way to measure the efficiency of an algorithm independently of the hardware which the code in running over.***" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "> ### <font color='blue'>Big O</font> Notation describes how quiclky runtime will grow relative to the input as the input get arbitrarily large." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "> ### Commom Big-O Functions" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "|Big-O|Name|\n", | |
| "|---|---|\n", | |
| "|1|Constant|\n", | |
| "|log(n)|Logaritmic|\n", | |
| "|n|Linear|\n", | |
| "|nlog(n)|Log Linear|\n", | |
| "|n^2|Quadratic|\n", | |
| "|n^3|Cubic |\n", | |
| "|2^n|Exponencial|" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "> ## Lets check how each Big-O notation behaves in terms of efficiency\n", | |
| "> Check the graph below." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 21, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "Text(0.5,0,'n')" | |
| ] | |
| }, | |
| "execution_count": 21, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 864x720 with 1 Axes>" | |
| ] | |
| }, | |
| "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('bmh')\n", | |
| "\n", | |
| "n = np.linspace(1,10,1000)\n", | |
| "labels = ['Constant', 'Logarithmic', 'Linear', 'Log Linear', 'Quadratic', \n", | |
| " '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", | |
| "#Plot setup\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('Relative Runtime')\n", | |
| "plt.xlabel('n')" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "> ### We can see clearly that Logaritmic and Linear functions have very efficient runtime when compared to those like Quadratic, Cubic,.. and the worste... Exponential Big-O's" | |
| ] | |
| } | |
| ], | |
| "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": 2 | |
| } |
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