数据结构与算法分析C++版答案.docx

数据结构与算法分析C++版答案.docx

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数据结构与算法分析C++版答案

DataStructuresandAlgorithm习题答案

Prefaceii

1DataStructuresandAlgorithms1

2MathematicalPreliminaries5

3AlgorithmAnalysis17

4Lists,Stacks,andQueues23

5BinaryTrees32

6GeneralTrees40

7InternalSorting46

8FileProcessingandExternalSorting54

9Searching58

10Indexing64

11Graphs69

12ListsandArraysRevisited76

13AdvancedTreeStructures82

i

iiContents

14AnalysisTechniques88

15LimitstoComputation94

Preface

ContainedhereinarethesolutionstoallexercisesfromthetextbookAPractical

IntroductiontoDataStructuresandAlgorithmAnalysis,2ndedition.

FormostoftheproblemsrequiringanalgorithmIhavegivenactualcode.In

afewcasesIhavepresentedpseudocode.Pleasebeawarethatthecodepresented

inthismanualhasnotactuallybeencompiledandtested.WhileIbelievethealgorithms

tobeessentiallycorrect,theremaybeerrorsinsyntaxaswellassemantics.

Mostimportantly,thesesolutionsprovideaguidetotheinstructorastotheintended

answer,ratherthanusableprograms.

1

DataStructuresandAlgorithms

Instructor’snote:

Unliketheotherchapters,manyofthequestionsinthischapter

arenotreallysuitableforgradedwork.Thequestionsaremainlyintendedtoget

studentsthinkingaboutdatastructuresissues.

1.1

Thisquestiondoesnothaveaspecificrightanswer,providedthestudent

keepstothespiritofthequestion.Studentsmayhavetroublewiththeconcept

of“operations.”

1.2

Thisexerciseasksthestudenttoexpandontheirconceptofanintegerrepresentation.

AgoodanswerisdescribedbyProject4.5,whereasingly-linked

listissuggested.Themoststraightforwardimplementationstoreseachdigit

initsownlistnode,withdigitsstoredinreverseorder.Additionandmultiplication

areimplementedbywhatamountstograde-schoolarithmetic.For

addition,simplymarchdowninparallelthroughthetwolistsrepresenting

theoperands,ateachdigitappendingtoanewlisttheappropriatepartial

sumandbringingforwardacarrybitasnecessary.Formultiplication,combine

theadditionfunctionwithanewfunctionthatmultipliesasingledigit

byaninteger.Exponentiationcanbedoneeitherbyrepeatedmultiplication

（notreallypractical）orbythetraditionalΘ（logn）-timealgorithmbasedon

thebinaryrepresentationoftheexponent.Discoveringthisfasteralgorithm

willbebeyondthereachofmoststudents,soshouldnotberequired.

1.3

AsampleADTforcharacterstringsmightlookasfollows（withthenormal

interpretationofthefunctionnamesassumed）.

Chap.1DataStructuresandAlgorithms

//Concatenatetwostrings

Stringstrcat（Strings1,Strings2）;

//Returnthelengthofastring

intlength（Strings1）;

//Extractasubstring,startingat‘start’,

//andoflength‘length’

Stringextract（Strings1,intstart,intlength）;

//Getthefirstcharacter

charfirst（Strings1）;

//Comparetwostrings:

thenormalC++strcmpfunction.

Some

//conventionshouldbeindicatedforhowtointerpret

the

//returnvalue.InC++,thisis1

fors1

//and1fors1>s2.

intstrcmp（Strings1,Strings2）

//Copyastring

intstrcpy（Stringsource,Stringdestination）

1.4

TheanswertothisquestionisprovidedbytheADTforlistsgiveninChapter

4.

1.5

One’scomplimentstoresthebinaryrepresentationofpositivenumbers,and

storesthebinaryrepresentationofanegativenumberwiththebitsinverted.

Two’scomplimentisthesame,exceptthatanegativenumberhasitsbits

invertedandthenoneisadded（forreasonsofefficiencyinhardwareimplementation）.

ThisrepresentationisthephysicalimplementationofanADT

definedbythenormalarithmeticoperations,declarations,andothersupport

givenbytheprogramminglanguageforintegers.

1.6

AnADTfortwo-dimensionalarraysmightlookasfollows.

Matrixadd（MatrixM1,MatrixM2）;

Matrixmultiply（MatrixM1,MatrixM2）;

Matrixtranspose（MatrixM1）;

voidsetvalue（MatrixM1,introw,intcol,intval）;

intgetvalue（MatrixM1,introw,intcol）;

Listgetrow（MatrixM1,introw）;

OneimplementationforthesparsematrixisdescribedinSection12.3Anotherimplementation

isahashtablewhosesearchkeyisaconcatenationofthematrixcoordinates.

1.7

Everyproblemcertainlydoesnothaveanalgorithm.AsdiscussedinChapter15,

thereareanumberofreasonswhythismightbethecase.Someproblemsdon’t

haveasufficientlycleardefinition.Someproblems,suchasthehaltingproblem,

arenon-computable.Forsomeproblems,suchasonetypicallystudiedbyartificial

intelligenceresearchers,wesimplydon’tknowasolution.

1.8

Wemustassumethatby“algorithm”wemeansomethingcomposedofstepsare