387 lines
9.2 KiB
Plaintext
387 lines
9.2 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8685ea3a",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import timeit\n",
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "markdown",
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"id": "048881d0",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"# Example: Find common words"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2464a282",
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"source": [
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"Problem: given two lists of words, extract all the words that are in common"
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]
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},
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{
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"cell_type": "markdown",
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"id": "71740eab",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"# Implementation with 2x for-loops"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "f175c775",
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"%%timeit\n",
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"\n",
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"scaling_factor = 1 #10, 100\n",
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"\n",
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"words1 = ['apple', 'orange', 'banana', 'melon', 'peach'] * scaling_factor\n",
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"words2 = ['orange', 'kiwi', 'avocado', 'apple', 'banana'] * scaling_factor\n",
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"\n",
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"common_for = []\n",
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"for w in words1:\n",
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" if w in words2:\n",
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" common_for.append(w) # 612 ns, 12.3 us, 928 us "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "affab857",
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"metadata": {
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"slideshow": {
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"slide_type": "subslide"
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}
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},
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"outputs": [],
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"source": [
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"input_size = [1, 10, 100]\n",
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"results_for_loop = [(612/10**9)/(612/10**9), (12.4 /10**6)/(612/10**9), (928/10**6)/(612/10**9)] # in seconds\n",
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"\n",
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"x = np.linspace(0,100,100)\n",
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"fit1 = np.polyfit(input_size,results_for_loop,2)\n",
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"eval1 = np.polyval(fit1, x)\n",
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"\n",
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"plt.plot(x,eval1,c = 'orange')\n",
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"plt.scatter(input_size, results_for_loop, c = 'orange', s = 100, label = '2 for loops')\n",
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"\n",
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"plt.xlabel('input size')\n",
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"plt.ylabel('processing time')\n",
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"plt.yticks(results_for_loop, ['T', str(int((12.4 /10**6)/(513/10**9)))+ 'x T', str(int((928/10**6)/(513/10**9))) + 'x T'])\n",
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"plt.legend()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "2a61bf38",
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"metadata": {
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"slideshow": {
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"slide_type": "skip"
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}
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},
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"outputs": [],
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"source": [
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"print('Data increase 1x, 10x, 100x')\n",
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"print('Time increase 513 ns, 12.4 µs, 928 µs')\n",
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"print('time1, ~ 24x time1, ~ 1800x time1')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "38e47397",
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"metadata": {
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"slideshow": {
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"slide_type": "-"
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}
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},
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"source": [
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"What is the big-O complexity of this implementation? "
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]
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},
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{
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"cell_type": "markdown",
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"id": "4118b38d",
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"metadata": {
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"slideshow": {
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"slide_type": "skip"
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}
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},
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"source": [
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"n * n ~ O(n<sup>2</sup>)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "31cd0e74",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"# Implementation with sorted lists"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "c13a24f4",
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"%%timeit\n",
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"scaling_factor = 100 #10, 100\n",
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"words1 = ['apple', 'orange', 'banana', 'melon', 'peach'] * scaling_factor\n",
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"words2 = ['orange', 'kiwi', 'avocado', 'apple', 'banana'] *scaling_factor\n",
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"words1 = sorted(words1)\n",
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"words2 = sorted(words2)\n",
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"\n",
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"common_sort_list = []\n",
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"idx2 = 0\n",
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"for w in words1:\n",
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" while idx2 < len(words2) and words2[idx2] < w:\n",
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" idx2 += 1\n",
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" if idx2 >= len(words2):\n",
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" break\n",
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" if words2[idx2] == w:\n",
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" common_sort_list.append(w) #1.94 ns, 17.3 us, 204 us"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "f1e8fed2",
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"metadata": {
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"slideshow": {
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"slide_type": "notes"
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}
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},
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"outputs": [],
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"source": [
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"# 1.9 * 10**6\n",
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"# 17.9 * 10**6\n",
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"# 205 * 10**6"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8ce798ab",
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"metadata": {
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"slideshow": {
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"slide_type": "subslide"
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}
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},
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"outputs": [],
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"source": [
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"input_size = [1, 10, 100]\n",
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"results_sorted_lists = [(1.9 * 10**6)/(1.9 * 10**6), (17.9 * 10**6)/(1.9 * 10**6), (205 * 10**6)/(1.9 * 10**6)]\n",
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"fit2 = np.polyfit(input_size, results_sorted_lists, 2)\n",
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"eval2 = np.polyval(fit2, x)\n",
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"plt.plot(x,eval1,c = 'orange')\n",
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"plt.plot(x,eval2,c = 'pink')\n",
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"plt.scatter(input_size, results_for_loop, c = 'orange', s = 100, label = '2 for loops')\n",
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"plt.scatter(input_size, results_sorted_lists, c = 'pink', s = 100, label = 'sorted lists')\n",
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"plt.xlabel('input size')\n",
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"plt.ylabel('processing time')\n",
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"plt.yticks(results_for_loop + results_sorted_lists[1:], ['T', str(int((12.4 /10**6)/(513/10**9)))+ 'x T', str(int((928/10**6)/(513/10**9))) + 'x T',\n",
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" str(int((17.9 * 10**6)/(1.9 * 10**6)))+ 'x T', str(int((205 * 10**6)/(1.9 * 10**6))) + 'x T',])\n",
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"plt.legend()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1da4c22f",
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"metadata": {
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"slideshow": {
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"slide_type": "-"
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}
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},
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"source": [
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"What is the big-O complexity of this implementation? "
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]
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},
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{
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"cell_type": "markdown",
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"id": "4b068a1b",
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"metadata": {
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"slideshow": {
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"slide_type": "-"
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}
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},
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"source": [
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"2 * sorting + traversing two lists = 2*n log<sub>2</sub> + 2*n ~ O(n * log<sub>n</sub>)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "13c96239",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"# Implementation with sets"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "61edb9f3",
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"%%timeit\n",
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"\n",
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"scaling_factor = 1\n",
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"\n",
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"words1 = ['apple', 'orange', 'banana', 'melon', 'peach'] * scaling_factor\n",
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"words2 = ['orange', 'kiwi', 'avocado', 'apple', 'banana'] *scaling_factor\n",
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"\n",
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"words2 = set(words2)\n",
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"\n",
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"common_sets = []\n",
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"for w in words1:\n",
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" if w in words2:\n",
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" common_sets.append(w) # 630 ns, 3.13 us, 28.6 us"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "c90d8e68",
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"metadata": {
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"slideshow": {
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"slide_type": "notes"
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}
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},
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"outputs": [],
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"source": [
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"# 630 * 10**9\n",
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"# 3.13 * 10**6\n",
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"# 28.6 * 10**6"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "236c132d",
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"metadata": {
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"scrolled": true,
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"slideshow": {
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"slide_type": "subslide"
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}
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},
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"outputs": [],
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"source": [
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"results_sets = [(630 * 10**9)/(630 * 10**9), (3.13 * 10**6)/(630 * 10**9), (28.6 * 10**6)/(630 * 10**9)]\n",
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"fit3 = np.polyfit(input_size, results_sets, 2)\n",
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"eval3 = np.polyval(fit3, x)\n",
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"plt.plot(x,eval1,c = 'orange')\n",
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"plt.plot(x,eval2,c = 'pink')\n",
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"plt.plot(x, eval3, c = 'blue')\n",
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"plt.scatter(input_size, results_for_loop, c = 'orange', s = 100, label = '2 for loops')\n",
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"plt.scatter(input_size, results_sorted_lists, c = 'pink', s = 100, label = 'sorted lists')\n",
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"plt.scatter(input_size, results_sets, c = 'blue', s = 100, label = 'sets')\n",
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"plt.xlabel('input size')\n",
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"plt.ylabel('processing time')\n",
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"plt.yticks(results_for_loop + results_sorted_lists[1:], ['T', str(int((12.4 /10**6)/(513/10**9)))+ 'x T', str(int((928/10**6)/(513/10**9))) + 'x T', str(int((17.9 * 10**6)/(1.9 * 10**6)))+ 'x T', str(int((205 * 10**6)/(1.9 * 10**6))) + 'x T'])\n",
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"plt.legend()\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "c9780532",
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"metadata": {
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"slideshow": {
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"slide_type": "-"
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}
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},
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"source": [
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"What is the big-O complexity of this implementation? "
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]
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},
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{
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"cell_type": "markdown",
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"id": "297bcd7d",
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"metadata": {
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"slideshow": {
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"slide_type": "-"
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}
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},
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"source": [
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"transforming one list to set + 1 for loop = 2 * n ~ O(n)\n",
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"\n",
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"It’s the exact same code as for lists, but now looking up an element in sets \u000b",
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"(if w in words2) takes constant time!\n",
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"How could you have known that set lookup is fast? Learning about data structures!"
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]
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}
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],
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"metadata": {
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"celltoolbar": "Slideshow",
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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