数据结构课件

AnIntroductiontoSortingChapterContentsOrganizingJavaMethodsthatSortanArraySelectionSortIterativeSelectionSortRecursiveSelectionSortTheEfficiencyofSelectionSortInsertionSortIterativeInsertionSortRecursiveInsertionSortTheEfficiencyofInsertionSortInsertionSortofaChainofLinkedNodesChapterContentsShellSortTheJavaCodeTheEfficiencyofShellSortComparingtheAlgorithmsOrganizingJavaMethods

thatSortanArrayConsideraclassofstaticsortmethodsThusabletocompareelementsinaninheritancehierarchy

OrganizingJavaMethods

thatSortanArrayFig.11-1TheclassGadgetisderivedfromtheclassWidget,whichimplementstheinterfaceComparableSelectionSortTask:rearrangebooksonshelfbyheightShortestbookontheleftApproach:Lookatbooks,selectshortestbookSwapwithfirstbookLookatremainingbooks,selectshortestSwapwithsecondbookRepeat…SelectionSortFig.11-2Beforeandafterexchangingshortestbookandthefirstbook.SelectionSortFig.11-3Aselectionsortofanarrayofintegersintoascendingorder.IterativeSelectionSortViewiterativealgorithmforselectionsortViewclassforsortinganarrayusingselectionsortSearchforindexofsmallestelementSwapvaluesinarrayelementsPutssmallestattopofcurrentsubarrayRecursiveSelectionSortViewrecursivealgorithmforselectionsortJavaimplementationofrecursiveselectionsortConsidergivingparametersforthearray,abeginningandendingindexforflexibilityTheEfficiencyofSelectionSortIterativemethodforloopexecutesn–1timesForeachofn–1calls,innerloopexecutes

n–2times(n–1)+(n–2)+…+1=n(n–1)/2=O(n2)RecursiveselectionsortperformssameoperationsAlsoO(n2)InsertionSortIffirsttwobooksareoutoforderRemovesecondbookSlidefirstbooktorightInsertremovedbookintofirstslotThenlookatthirdbook,ifitisoutoforderRemovethatbookSlide2ndbooktorightInsertremovedbookinto2ndslotRecheckfirsttwobooksagainEtc.InsertionSortFig.11-4Theplacementofthethirdbookduringaninsertionsort.InsertionSortFig.11-5AninsertionsortofbooksIterativeInsertionSortViewiterativealgorithmforinsertionsortNotethealgorithmfortheinsertoftheitemintothearrayFig.11-6AninsertionsortinsertsthenextunsortedelementintoitsproperlocationwithinthesortedportionofanarrayIterativeInsertionSortFig.11-7AninsertionsortofanarrayofintegersintoascendingorderRecursiveInsertionSortViewalgorithmforrecursiveinsertionsortJavaimplementationofrecursiveinsertionsortCanuseaniterativeinsertInOrder(seealgorithm)CanusearecursiveversionRecursiveInsertionSortFig.11-8Insertingthefirstunsortedelementintothesortedportionofthearray.(a)Theelementis≥lastsortedelement;(b)theelementis<thanlastsortedelementEfficiencyofInsertionSortBesttimeefficiencyisO(n)WorsttimeefficiencyisO(n2)IfarrayisclosertosortedorderLessworktheinsertionsortdoesMoreefficientthesortisInsertionsortisacceptableforsmallarraysizesInsertionSortofChainofLinkedNodesFig.11-9Achainofintegerssortedintoascendingorder.InsertionSortofChainofLinkedNodesFig.11-10Duringthetraversalofachaintolocatetheinsertionpoint,saveareferencetothenodebeforethecurrentone.InsertionSortofChainofLinkedNodesConsideraddingasortmethodtoclassLinkedChainListwhichusesADTlistMustimplementComparableViewcodeforsortingandinsertingInsertionSortofChainofLinkedNodesFig.11-11Breakingachainofnodesintotwopiecesasthefirststepinaninsertionsort:

(a)theoriginalchain;(b)thetwopiecesEfficiencyofinsertionsortofachainisO(n2)ShellSortAvariationoftheinsertionsortButfasterthanO(n2)DonebysortingsubarraysofequallyspacedindicesInsteadofmovingtoanadjacentlocationanelementmovesseverallocationsawayResultsinanalmostsortedarrayThisarraysortedefficientlywithordinaryinsertionsortShellSortFig.11-12Anarrayandthesubarraysformedbygroupingelementswhoseindicesare6apart.ShellSortFig.11-13ThesubarraysofFig.11-12aftertheyaresorted,andthearraythatcontainsthem.ShellSortFig.11-14ThesubarraysofthearrayinFig.11-13formedbygroupingelementswhoseindicesare3apartShellSortFig.11-15ThesubarraysofFig.11-14aftertheyaresorted,andthearraythatcontainsthem.Viewsourcecodefor

incrementalInsertionSortand

shellSortEfficiencyofShellSortEfficiencyisO(n2)forworstcaseIfnisapowerof2Average-casebehaviorisO(n1.5)Anytimethevariablespace(seesourcecode)iseven,add1ThisalsoresultsinO(n1.5)ComparingtheAlgorithms Best Average Worst

Case Case CaseSelectionsort O(n2) O(n2) O(n2)Insertionsort O(n) O(n2) O(n2)Shellsort O(n) O(n1.5) O(n1.5)Fig.11-16Thetimeefficienciesofthreesortingalgorithms,expressedinBigOhnotation.FasterSortingMethods2024年5月3日ChapterContentsMergeSortMergingArraysRecursiveMergeSortTheEfficiencyofMergeSortIterativeMergeSortMergeSortintheJavaClassLibraryChapterContentsQuickSortTheEfficiencyofQuickSortCreatingthePartitionJavaCodeforQuickSortQuickSortintheJavaClassLibraryRadixSortPseudocodeforRadixSortComparingtheAlgorithmsMergeSortDivideanarrayintohalvesSortthetwohalvesMergethemintoonesortedarrayReferredtoasadivideandconqueralgorithmThisisoftenpartofarecursivealgorithmHoweverrecursionisnotarequirementMergeSortFig.12-1Mergingtwosortedarraysintoonesortedarray.MergeSortFig.12-2Themajorstepsinamergesort.MergeSortViewalgorithmsmergeSortmergewhichisusedbymergeSortTracestepsofthealgorithminFigure12-3onnextslideMergeSortFig.12-3Theeffectoftherecursivecallsandthemergesduringamergesort.MergeSortEfficiencyMergesortisO(nlogn)inallcasesIt'sneedforatemporaryarrayisadisadvantageMergesortintheJavaClassLibraryTheclassArrayshassortroutinesthatusesthemergesortforarraysofobjectsMergeSortEfficiencyFig.12-4Aworst-casemergeoftwosortedarraysQuickSortDividesthearrayintotwopiecesNotnecessarilyhalvesofthearrayAnelementofthearrayisselectedasthepivotElementsarerearrangedsothat:ThepivotisinitsfinalpositioninsortedarrayElementsinpositionsbeforepivotarelessthanthepivotElementsafterthepivotaregreaterthanthepivotQuickSortViewQuickSortalgorithmFig.12-5Apartitionofanarrayduringaquicksort.QuickSortQuicksortisO(nlogn)intheaveragecaseO(n2)intheworstcaseWorstcasecanbeavoidedbycarefulchoiceofthepivotQuickSortFig.12-6Apartitionstrategyforquicksort…continued→QuickSortFig.12-6(ctd.)Apartitionstrategyforquicksort.QuickSortFig.12-7Median-of-threepivotselection:

(a)theoriginalarray;(b)thearraywithitsfirst,middle,andlastelementssortedQuickSortFig.12-8(a)Thearraywithitsfirst,middle,andlastelementssorted;(b)thearrayafterpositioningthepivotandjustbeforepartitioning.QuickSortQuicksortrearrangestheelementsinanarrayduringpartitioningprocessAftereachstepintheprocessOneelement(thepivot)isplacedinitscorrectsortedpositionTheelementsineachofthetwosubarraysRemainintheirrespectivesubarraysViewJavacodeforQuickSortNotesortmethodsinjava.utilforArraysclassRadixSortDoesnotcompareobjectsTreatsarrayelementsasiftheywerestringsofthesamelengthGroupselementsbyaspecifieddigitorcharacterofthestringElementsplacedinto"buckets"whichmatchthedigit(character)Originatedwithcardsorterswhencomputersused80columnpunchedcardsRadixSortFig.12-9(a)Originalarrayandbucketsafterfirstdistribution;(b)reorderedarrayandbucketsafterseconddistribution…continued→

RadixSortFig.12-9(c)reorderedarrayandbucketsafterthirddistribution;(d)sortedarrayRadixSortViewalgorithmforRadixSortNoteRadixsortisO(n)CanonlybeusedforcertainkindsofdataComparingtheAlgorithmsFig.12-10ThetimeefficiencyofvariousalgorithmsinBigOhnotationComparingtheAlgorithmsFig.12-11Acomparisonofgrowth-ratefunctionsasnincreases.AHeapImplementationChapterContentsReprise:TheADTHeapUsinganArraytoRepresentaHeapAddinganEntryRemovingtheRootCreatingaHeapHeapsortReprise:TheADTHeapAcompletebinarytreeNodescontainComparableobjectsInamaxheapObjectineachnode≥objectsindescendantsNotecontrastofusesoftheword"heap"TheADTheapTheheapoftheoperatingsystemfromwhichmemoryisallocatedwhennewexecutesReprise:TheADTHeapInterfaceusedforimplementationofmaxheapUsinganArraytoRepresentaHeapFig.28-1(a)Acompletebinarytreewithitsnodesnumberedinlevelorder;(b)itsrepresentationasanarray.UsinganArraytoRepresentaHeapWhenabinarytreeiscompleteCanuselevel-ordertraversaltostoredatainconsecutivelocationsofanarrayEnableseasylocationofthedatainanode'sparentorchildrenParentofanodeatiisfoundati/2

(unlessiis1)Childrenofnodeatifoundatindices

2iand2i+1ClicktoviewJavaimplementationofclassMaxHeapClassMaxHeapFig.28-2Thestepsinadding85tothemaxheapofFigure28-1aClassMaxHeapBeginatnextavailablepositionforaleafFollowpathfromthisleaftowardrootuntilfindcorrectpositionfornewentryAsthisisdoneMoveentriesfromparenttochildMakesroomfornewentryAddinganEntryFig.28-3ArevisionofstepsshowninFig.28-2toavoidswaps.….continued→AddinganEntryFig.28-3(ctd.)ArevisionofstepsshowninFig.28-2toavoidswaps.AddinganEntryFig.28-4AnarrayrepresentationofthestepsinFig.28-3…continued→AddinganEntryFig.28-4(ctd.)AnarrayrepresentationofthestepsinFig.28-3.