一入深似海系列课程-二期四节集合框架算法运用

「一入Java深似讲师信•劝退师，ApacheCloud••「一入Java深似讲师信•劝退师，ApacheCloud••••主要议•实•二分搜索算•Java二分搜索算法主要议•实•二分搜索算•Java二分搜索算法实•课程总•基本介Analgorithmthatputselementsofalistinacertainorder.Themostfrequentlyusedordersarenumericalorderandlexicographicalorder.基本介Analgorithmthatputselementsofalistinacertainorder.Themostfrequentlyusedordersarenumericalorderandlexicographicalorder.Efficientsortingisimportantforoptimizingtheefficiencyofotheralgorithms(suchassearchandmergealgorithms)whichrequireinputdatatobeinsortedlists.Sortingisalsooftenusefulforcanonicalizingdataandforproducinghuman-readableoutput.Moreformally,theoutputofanysortingalgorithmmustsatisfytwo•Theoutputisinnondecreasingorder(eachelementisnosmallerthanthepreviouselementaccordingtothedesiredtotalorder);•Theoutputisapermutation(areordering,yetretainingalloftheoriginalelements)ofthe•分••••稳定性：当相同的健存在时，经过排序后，其值也保持相对的顺序（不发生变化••分••••稳定性：当相同的健存在时，经过排序后，其值也保持相对的顺序（不发生变化••分••分••计算复杂度计算复杂度•Theamountofresourcesrequiredforrunningit.Thecomputationalcomplexityofaproblemistheminimumofthecomplexitiesofallpossiblealgorithmsforthisproblem(includingtheunknownalgorithms).Astheamountofneededresourcesvarieswiththeinput,thecomplexityisgenerallyexpressedasafunctionn→f(n),wherenisthesizeoftheinput,andf(n)iseithertheworst-casecomplexity,thatisthemaximumoftheamountofresourcesthatareneededforallinputsofsizen,ortheaverage-casecomplexity,thatisaverageoftheamountofresourcesoverallinputofsizen.计算复杂度计算复杂度•Whenthenatureoftheresourcesisnotexplicitlygiven,thisisusuallythetimeneededforrunningthealgorithm,andonetalksoftimecomplexity.However,thisdependsonthecomputerthatisused,andthetimeisgenerallyexpressedasthenumberofneededelementaryoperations,whicharesupposedtotakeaconstanttimeonagivencomputer,andtochangebyaconstantfactorwhenonechangesofcomputer.Otherwise,theresourcethatisconsideredisoftenthesizeofthememorythatisneeded,andonetalksofspacecomplexity.时间复杂度（时间复杂度（Time•Theamountoftimeittakestorunanalgorithm.Timecomplexityiscommonlyestimatedbycountingthenumberofelementaryoperationsperformedbythealgorithm,supposingthateachelementaryoperationtakesafixedamountoftimetoperform.Thus,theamountoftimetakenandthenumberofelementaryoperationsperformedbythealgorithmaretakentodifferbyatmostaconstantfactor.时间复杂度（时间复杂度（Time•Sinceanalgorithm'srunningtimemayvaryamongdifferentinputsofthesamesize,onecommonlyconsiderstheworst-casetimecomplexity,whichisthemaximumamountoftimerequiredforinputsofagivensize.Lesscommon,andusuallyspecifiedexplicitly,istheaverage-casecomplexity,whichistheaverageofthetimetakenoninputsofagivensize(thismakessensebecausethereareonlyafinitenumberofpossibleinputsofagivensize).Inbothcases,thetimecomplexityisgenerallyexpressedasafunctionofthesizeoftheinput.Sincethisfunctionisgenerallydifficulttocomputeexactly,andtherunningtimeforsmallinputsisusuallynotconsequential,onecommonlyfocusesonthebehaviorofthecomplexitywhentheinputsizeincreases—thatis,theasymptoticbehaviorofthe时间复杂度（Time•表达式：BigO•常量时间：T(n)O(1)（数组随机访问•线性时间：T(n)=O(n)（在未排序数组中找寻最值•时间复杂度（Time•表达式：BigO•常量时间：T(n)O(1)（数组随机访问•线性时间：T(n)=O(n)（在未排序数组中找寻最值•对数时间：T(n)=O(logn)（二进制搜索•指数时间：T(n)=O(n^c)（冒泡排序、插入排序•BigO••无限渐进•无限小渐进BigO••无限渐进•无限小渐进•稳定性稳定性•Stablesortalgorithmssortrepeatedelementsinthesameorderthattheyappearintheinput.Whensortingsomekindsofdata,onlypartofthedataisexaminedwhendeterminingthesortorder.Forexample,inthecardsortingexampletotheright,thecardsarebeingsortedbytheirrank,andtheirsuitisbeingignored.Thisallowsthepossibilityofmultipledifferentcorrectlysortedversionsoftheoriginallist.Stablesortingalgorithmschooseoneofthese,accordingtothefollowingrule:iftwoitemscompareasequal,likethetwo5cards,thentheirrelativeorderwillbepreserved,sothatifonecamebeforetheotherintheinput,itwillalsocomebeforetheotherintheoutput.稳定性••稳定性••稳定性••稳定性••比较排•Acomparisonsortisatypeofsortingalgorithmthatonlyreadsthelistelementsthroughasingleabstractcomparison比较排•Acomparisonsortisatypeofsortingalgorithmthatonlyreadsthelistelementsthroughasingleabstractcomparisonoperation(oftena"lessthanorequalto"operatororathree-waycomparison)thatdetermineswhichoftwoelementsshouldoccurfirstinthefinalsortedlist.Theonlyrequirementisthattheoperatorobeytwoofthepropertiesofatotalifa≤bandb≤cthena≤cforallaandb,eithera≤borb≤a(totalnessor比较排•冒泡排序（BubbleSort）：最佳O(n)、平均O(n^2)、最坏•插入排序（InsertionSort）：最佳O(n)、平均O(n^2)、最坏•快速排序（QuickSort）：最佳O(nlogn)、平均比较排•冒泡排序（BubbleSort）：最佳O(n)、平均O(n^2)、最坏•插入排序（InsertionSort）：最佳O(n)、平均O(n^2)、最坏•快速排序（QuickSort）：最佳O(nlogn)、平均O(nlogn)、最坏•合并排序（MergeSort）：最佳O(nlogn)、平均O(nlogn)、最坏•Tim排序（TimSort）：最佳O(n)、平均O(nlogn)、最坏•冒泡排序（Bubble•时间复杂度：最佳O(n)、平均O(n^2)冒泡排序（Bubble•时间复杂度：最佳O(n)、平均O(n^2)、最坏••插入排序（Insertion•时间复杂度：最佳O(n)、平均O(n^2)插入排序（Insertion•时间复杂度：最佳O(n)、平均O(n^2)、最坏••快速排序（Quick•时间复杂度：最佳O(nlogn)、平均O(nlogn)、最坏••获取pivot（轴•分区快速排序（Quick•时间复杂度：最佳O(nlogn)、平均O(nlogn)、最坏••获取pivot（轴•分区•递归•快速排序（Quick快速排序（Quick••合并排序（Merge•时间复杂度：最佳O(nlogn)、平均O(nlogn)、最坏••分块合并排序（Merge•时间复杂度：最佳O(nlogn)、平均O(nlogn)、最坏••分块•递归合并•合并排序（Merge合并排序（Merge••Tim排序•时间复杂度：最佳O(n)、平均O(nlogn)、最坏Tim排序•时间复杂度：最佳O(n)、平均O(nlogn)、最坏••实实集合框实内建实•冒泡排序•插入排序（7时•快速排序•合并排序Sort）：java.util.Arrays#mergeSort集合框实内建实•冒泡排序•插入排序（7时•快速排序•合并排序Sort）：java.util.Arrays#mergeSort之后需要激活•Tim排序•二分搜索（Binary二分搜索（Binary•Alsoknownashalf-intervalsearch,logarithmicsearch,orbinarychop,isasearchalgorithmthatfindsthepositionofatargetvaluewithinasortedarray.Binarysearchcomparesthetargetvaluetothemiddleelementofthearray.Iftheyarenotequal,thehalfinwhichthetargetcannotlieiseliminatedandthesearchcontinuesontheremaininghalf,againtakingthemiddleelementtocomparetothetarget