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.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
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