Algorithmic thinking : a problem-based introduction

410 Pages·2021·4.115 MB·English

by  Daniel Zingaro

LEARN TO
SOLVE EVEN
THE HARDEST A L G O R I T H M I C
COMPUTING
PROBLEMS
T H I N K I N G
A
L
G
Algorithmic Thinking will teach you how to solve • The union-find data structure to answer questions A P R O B L E M - B A S E D I N T R O D U C T I O N
challenging programming problems and design your about connections in a social network or determine O
own algorithms. Daniel Zingaro, a master teacher, who are friends or enemies
draws his examples from world-class programming R
• The heap data structure to determine the amount of
competit ions like USACO and IOI. You’ll learn how
money given away in a promotion I
to classify problems, choose data structures, and
D A N I E L Z I N G A R O
T
identify appropriate algorithms. You’ll also learn how • The hash-table data structure to determine whether
your choice of data structure, whether a hash table, snowflakes are unique or identify compound words H
heap, or tree, can affect runtime and speed up your in a dictionary
M
algorithms; and how to adopt powerful strategies like
NOTE: Each problem in this book is available on a
recursion, dynamic programming, and binary search
programming-judge website. You’ll find the site’s URL
to solve challenging problems. I
and problem ID in the description. What’s better than
C
Line-by-line breakdowns of the code will teach you how a free correctness check?
to use algorithms and data structures like:
ABOUT THE AUTHOR T
• The breadth-first search algorithm to find the optimal
Daniel Zingaro is an award-winning Assistant Professor H
way to play a board game or find the best way to
of Mathematical and Computational Sciences at the
translate a book
I
University of Toronto Mississauga, where he is well known
N
• Dijkstra’s algorithm to determine how many mice can for his uniquely interactive approach to teaching, and
exit a maze or the number of fastest routes between internationally recognized for his expertise in Active
K
two locations Learning.
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G
THE FINEST IN GEEK ENTERTAINMENT™
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www.nostarch.com IN
$49.95 ($65.95 CDN) G
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“I LIE FLAT.”
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This book uses a durable binding that won’t snap shut

A L G O R I T H M I C
T H I N K I N G
A Problem-Based Introduction
by Daniel Zingaro
SanFrancisco
ALGORITHMICTHINKING.Copyright©2021byDanielZingaro.
Allrightsreserved.Nopartofthisworkmaybereproducedortransmittedinanyformorbyanymeans,electronic
ormechanical,includingphotocopying,recording,orbyanyinformationstorageorretrievalsystem,withoutthe
priorwrittenpermissionofthecopyrightownerandthepublisher.
ISBN-13:978-1-7185-0080-8(print)
ISBN-13:978-1-7185-0081-5(ebook)
Publisher:BillPollock
ExecutiveEditor:BarbaraYien
ProductionEditor:KassieAndreadis
DevelopmentalEditor:AlexFreed
InteriorDesign:OctopodStudios
CoverIllustration:RobGale
TechnicalReviewer:LarryYueliZhang
Copyeditor:DavidCouzens
Proofreader:JamesFraleigh
Forinformationonbookdistributorsortranslations,pleasecontactNoStarchPress,Inc.directly:
NoStarchPress,Inc.
2458thStreet,SanFrancisco,CA94103
phone:[phone];[email protected]
www.nostarch.com
LibraryofCongressCataloging-in-PublicationData
Names: Zingaro, Daniel, author.
Title: Algorithmic thinking : a problem-based introduction / by Daniel
Zingaro.
Description: San Francisco : No Starch Press, [2021] | Includes
bibliographical references and index.
Identifiers: LCCN 2020031510 (print) | LCCN 2020031511 (ebook) | ISBN
9781718500808 (paperback) | ISBN 1718500807 (paperback) | ISBN
9781718500815 (ebook)
Subjects: LCSH: Computer algorithms–Problems, exercises, etc. | Computer
programming–Problems, exercises, etc.
Classification: LCC QA76.9.A43 Z56 2020 (print) | LCC QA76.9.A43 (ebook)
| DDC 005.13–dc23
LC record available at https://lccn.loc.gov/2020031510
LC ebook record available at https://lccn.loc.gov/2020031511
NoStarchPressandtheNoStarchPresslogoareregisteredtrademarksofNoStarchPress,Inc.Otherproductand
companynamesmentionedhereinmaybethetrademarksoftheirrespectiveowners.Ratherthanuseatrademark
symbolwitheveryoccurrenceofatrademarkedname,weareusingthenamesonlyinaneditorialfashionandtothe
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personorentitywithrespecttoanylossordamagecausedorallegedtobecauseddirectlyorindirectlybytheinfor-
mationcontainedinit.
ToDoyali
About the Author
Dr. DanielZingaroisanassistantteachingprofessorofcomputerscience
andaward-winningteacherattheUniversityofToronto. Hismainareaof
researchiscomputerscienceeducationresearch,wherehestudieshowstu-
dentslearn(andsometimesdon’tlearn)computersciencematerial.
About the Technical Reviewer
LarryYueliZhangisanAssistantProfessor,TeachingStreamofComputer
ScienceattheUniversityofTorontoMississauga. Histeachingandresearch
interestsincludealgorithms,datastructures,operatingsystems,computer
networks,socialnetworks,andcomputingeducation. Hehasbeeninthe
programcommitteesofACMSIGCSE,ACMITiCSE,andWCCCE.Heholds
aPhDinComputerSciencefromtheUniversityofToronto.
BRIEF CONTENTS
Foreword........................................................................... xv
Acknowledgments ...................................................................xvii
Introduction......................................................................... xix
Chapter1:HashTables.............................................................. 1
Chapter2:TreesandRecursion....................................................... 31
Chapter3:MemoizationandDynamicProgramming.................................... 71
Chapter4:GraphsandBreadth-FirstSearch............................................119
Chapter5:ShortestPathsinWeightedGraphs .........................................165
Chapter6:BinarySearch ............................................................197
Chapter7:HeapsandSegmentTrees .................................................243
Chapter8:Union-Find ...............................................................295
Afterword...........................................................................339
AppendixA:AlgorithmRuntime.......................................................341
AppendixB:BecauseICan'tResist....................................................347
AppendixC:ProblemCredits.........................................................361
Index...............................................................................365

CONTENTS IN DETAIL
FOREWORD xv
ACKNOWLEDGMENTS xvii
INTRODUCTION xix
Online Resources ............................................................... xx
Who This Book Is For........................................................... xx
The Programming Language .................................................... xx
Why Use C? ........................................................... xxi
Static Keyword......................................................... xxi
Include Files............................................................xxii
Freeing Memory .......................................................xxii
Topics ..........................................................................xxii
Judges..........................................................................xxiii
Anatomy of a Problem Description..............................................xxv
Problem: Food Lines ............................................................xxvi
The Problem............................................................xxvi
Solving the Problem ....................................................xxvii
Notes...........................................................................xxix
1
HASH TABLES 1
Problem 1: Unique Snowflakes ................................................. 1
The Problem............................................................ 2
Simplifying the Problem ................................................ 3
Solving the Core Problem .............................................. 4
Solution 1: Pairwise Comparisons...................................... 7
Solution 2: Doing Less Work........................................... 11
Hash Tables .................................................................... 16
Hash Table Design ..................................................... 16
Why Use Hash Tables? ................................................ 19
Problem 2: Compound Words.................................................. 19
The Problem............................................................ 19
Identifying Compound Words.......................................... 20
Solution ................................................................ 20
Problem 3: Spelling Check: Deleting a Letter ................................... 24
The Problem............................................................ 24
Thinking About Hash Tables............................................ 25
An Ad Hoc Solution.................................................... 27
Summary ....................................................................... 30
Notes........................................................................... 30
2
TREES AND RECURSION 31
Problem 1: Halloween Haul .................................................... 31
The Problem............................................................ 32
Binary Trees............................................................ 33
Solving the Sample Instance............................................ 35
Representing Binary Trees.............................................. 35
Collecting All the Candy ............................................... 39
A Completely Different Solution ........................................ 45
Walking the Minimum Number of Streets............................... 50
Reading the Input ...................................................... 53
Why Use Recursion?............................................................ 59
Problem 2: Descendant Distance ............................................... 59
The Problem............................................................ 59
Reading the Input ...................................................... 62
Number of Descendants from One Node............................... 65
Number of Descendants from All Nodes................................ 67
Sorting Nodes ......................................................... 67
Outputting the Information.............................................. 68
The main Function...................................................... 69
Summary ....................................................................... 70
Notes........................................................................... 70
3
MEMOIZATION AND DYNAMIC PROGRAMMING 71
Problem 1: Burger Fervor....................................................... 72
The Problem............................................................ 72
Forming a Plan......................................................... 72
Characterizing Optimal Solutions ...................................... 74
Solution 1: Recursion................................................... 75
Solution 2: Memoization............................................... 80
Solution 3: Dynamic Programming ..................................... 85
Memoization and Dynamic Programming....................................... 88
Step 1: Structure of Optimal Solutions.................................. 88
Step 2: Recursive Solution.............................................. 89
Step 3: Memoization................................................... 90
Step 4: Dynamic Programming......................................... 90
viii ContentsinDetail