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Grokking Algorithms.pdf

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    Cover
    contents
    preface
    acknowledgments
    about this book
    Chapter 1 Introduction to Algorithms
    Introduction
    What you’ll learn about performance
    What you’ll learn about solving problems
    Binary search
    A better way to search
    Running time
    Big O notation
    Algorithm running times grow at different rates
    Visualizing different Big O run times
    Big O establishes a worst-case run time
    Some common Big O run times
    The traveling salesperson
    Recap
    Chapter 2 Selection Sort
    How memory works
    Arrays and linked lists
    Linked lists
    Arrays
    Terminology
    Inserting into the middle of a list
    Deletions
    Selection sort
    Recap
    Chapter 3 Recursion
    Recursion
    Base case and recursive case
    The stack
    The call stack
    The call stack with recursion
    Recap
    Chapter 4 Quicksort
    Divide & conquer
    Quicksort
    Big O notation revisited
    Merge sort vs. quicksort
    Average case vs. worst case
    Recap
    Chapter 5 Hash Tables
    Hash functions
    Use cases
    Using hash tables for lookups
    Preventing duplicate entries
    Using hash tables as a cache
    Recap
    Collisions
    Performance
    Load factor
    A good hash function
    Recap
    Chapter 6 Breadth-First Search
    Introduction to graphs
    What is a graph?
    Breadth-first search
    Finding the shortest path
    Queues
    Implementing the graph
    Implementing the algorithm
    Running time
    Recap
    Chapter 7 Dijkstra’s Algorithm
    Working with Dijkstra’s algorithm
    Terminology
    Trading for a piano
    Negative-weight edges
    Implementation
    Recap
    Chapter 8 Greedy Algorithms
    The classroom scheduling problem
    The knapsack problem
    The set-covering problem
    Approximation algorithms
    NP-complete problems
    Traveling salesperson, step by step
    How do you tell if a problem is NP-complete?
    Recap
    Chapter 9 Dynamic Programming
    The knapsack problem
    The simple solution
    Dynamic programming
    Knapsack problem FAQ
    What happens if you add an item?
    What happens if you change the order of the rows?
    Can you fill in the grid column-wise insteadof row-wise?
    What happens if you add a smaller item?
    Can you steal fractions of an item?
    Optimizing your travel itinerary
    Handling items that depend on each other
    Is it possible that the solution will requiremore than two sub-knapsacks?
    Is it possible that the best solution doesn’tfill the knapsack completely?
    Longest common substring
    Making the grid
    Filling in the grid
    The solution
    Longest common subsequence
    Longest common subsequence—solution
    Recap
    Chapter 10 K-nearestneighbors
    Classifying oranges vs. grapefruit
    Building a recommendations system
    Feature extraction
    Regression
    Picking good features
    Introduction to machine learning
    OCR
    Building a spam filter
    Predicting the stock market
    Recap
    Chapter 11 Where to Go Next
    Trees
    Inverted indexes
    The Fourier transform
    Parallel algorithms
    MapReduce
    Why are distributed algorithms usefule?
    The map function
    The reduce function
    Bloom filters and HyperLogLog
    Bloom filters
    HyperLogLog
    The SHA algorithms
    Comparing files
    Checking passwords
    Locality-sensitive hashing
    Diffie-Hellman key exchange
    Linear programming
    Epilogue
    Answers to Exercises
    CHAPTER 1
    CHAPTER 2
    CHAPTER 3
    CHAPTER 4
    CHAPTER 5
    CHAPTER 6
    CHAPTER 7
    CHAPTER 8
    CHAPTER 9
    CHPATER 10
    grokking algorithms
    grokking algorithms An illustrated guide for programmers and other curious people Aditya Y. Bhargava M A N N I N G Shelter ISland
    For online information and ordering of this and other Manning books, please visit www.manning.com. The publisher offers discounts on this book when ordered in quantity. For more information, please contact Special Sales Department Manning Publications Co. 20 Baldwin Road, PO Box 761 Shelter Island, NY 11964 Email: orders@manning.com ©2016 by Manning Publications Co. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by means electronic, mechanical, photocopying, or otherwise, without prior written permission of the publisher. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in the book, and Manning Publications was aware of a trademark claim, the designations have been printed in initial caps or all caps. ∞ Recognizing the importance of preserving what has been written, it is Manning’s policy to have the books we publish printed on acid-free paper, and we exert our best efforts to that end. Recognizing also our responsibility to conserve the resources of our planet, Manning books are printed on paper that is at least 15 percent recycled and processed without the use of elemental chlorine. Manning Publications Co. 20 Baldwin Road Shelter Island, NY 11964 Development editor: Jennifer Stout Technical development editor: Damien White Project manager: Tiffany Taylor Copyeditor: Tiffany Taylor Technical proofreader: Jean-François Morin Typesetter: Leslie Haimes Cover and interior design: Leslie Haimes Illustrations by the author ISBN: 9781617292231 Printed in the United States of America 1 2 3 4 5 6 7 8 9 10 – EBM – 21 20 19 18 17 16
    For my parents, Sangeeta and Yogesh
    vii contents preface acknowledgments about this book 1 Introduction to algorithms Introduction What you’ll learn about performance What you’ll learn about solving problems Binary search A better way to search Running time Big O notation Algorithm running times grow at different rates Visualizing different Big O run times Big O establishes a worst-case run time Some common Big O run times The traveling salesperson Recap 2 Selection sort How memory works Arrays and linked lists Linked lists Arrays Terminology Inserting into the middle of a list Deletions xiii xiv xv 1 1 2 2 3 5 10 10 11 13 15 15 17 19 21 22 24 25 26 27 29 30
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