原创力文档- 1、本文档共25页，可阅读全部内容。
- 2、原创力文档（book118）网站文档一经付费（服务费），不意味着购买了该文档的版权，仅供个人/单位学习、研究之用，不得用于商业用途，未经授权，严禁复制、发行、汇编、翻译或者网络传播等，侵权必究。
- 3、本站所有内容均由合作方或网友上传，本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺！文档内容仅供研究参考，付费前请自行鉴别。如您付费，意味着您自己接受本站规则且自行承担风险，本站不退款、不进行额外附加服务；查看《如何避免下载的几个坑》。如果您已付费下载过本站文档，您可以点击 这里二次下载。
- 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等，请点击“版权申诉”（推荐），也可以打举报电话：400-050-0827(电话支持时间：9:00-18:30)。
1SimpleReviewRecurrencesSubstitutionmethodRecursion-treemethodMastermethod
DesignandAnalysisofAlgorithms
Heapsort(Ch6)
3DesignandAnalysisofAlgorithmsHeapsandHeapsortTopics:HeapsHeapsortPriorityqueue
4RecapandoverviewThestorysofar…--InsertionsortrunningtimeofΘ(n2);sortsinplace--MergesortrunningtimeofΘ(nlgn);needsauxiliarystorageΘ(n).Next…--HeapsortrunningtimeofΘ(nlgn);sortinplace.--QuicksortrunningtimeofΘ(nlgn)onaverage;mostpractical(andhencewidely-used)sortingalgorithm.--Sortinginlineartime.
5HeapsDatastructureindexedbyintegers1,2,…,n.EachelementsupportstheoperationPARENT,LEFT,RIGHT.EasilyimplementedusinganarraywithPARENT(i)=,LEFT(i)=2i,andRIGHT(i)=2i+1.maxheapA[PARENT(i)]≥A[i]minheapA[PARENT(i)]≤A[i]TherootoftheheapisA[1].Theheightofanodeisthelongestdownwardpathfromthenodetoaleaf.Theheightoftheheapistheheightoftheroot.
6HeapsViewedasabinarytree,itiscompletelyfilledonalllevelsexceptpossiblythelast.161410879324112345678910PARENT(i)=,LEFT(i)=2i,andRIGHT(i)=2i+1.
7HeapsOperationssupportedbyaheap:MAX-HEAPIFYensuresthataheapismaxheap.O(logn)Tosortanarray,wecanfirstconvertitintoamaxheap,repeatedlyextracttheroot(thelargestelementbydefinition)andMAX-HEAPIFYtherest.Θ(nlogn)Exercise.TheheightofheapwithnelementsisBUILD-MAX-HEAPproducesamaxheapfromanunorderedarray.Θ(n)
8MAX-HEAPIFY(a)TheinitialwithA[2]atnodei=2violatingthemax-heapproperty(b)ByexchangeA[2]withA[4],whichDestroysthemax-heappropertyfornode4.RecursivecallMAX-HEAPIFY(A,4)hasi=4…(c)MAX-HEAPFIFY(A,9)yieldsnofurtherchangetothedatastructure.
9MAX-HEAPIFYheap-size[A]keepstrackofthesizeoftheheapstoredinthearrayA.Runningtime:O(h),wherehistheheightofelementA[i].
10BUI
文档评论（0）