pareeachelement(exceptthelastone)withitsneighbortotherightIftheyareoutoforder,pareeachelement(exceptthelasttwo)withitsneighbortotherightIftheyareoutoforder,pareeachelement(exceptthelastthree)withitsneighbortotherightContinueasaboveuntilyouhavenounsortedelementsontheleft2Exampleofbubblesort7285427854278542758427548275482574825478275482547824578254782457824578(done)3CodeforbubblesortpublicstaticvoidbubbleSort(int[]a){ intouter,inner; for(outer=-1;outer>0;outer--){//countingdown for(inner=0;inner<outer;inner++){//bubblingup if(a[inner]>a[inner+1]){//ifoutoforder... inttemp=a[inner];//...thenswap a[inner]=a[inner+1]; a[inner+1]=temp; } } } }4Analysisofbubblesortfor(outer=-1;outer>0;outer--){ for(inner=0;inner<outer;inner++){ if(a[inner]>a[inner+1]){ //codeforswapomitted } } }Letn==sizeofthearrayTheouterloopisexecutedn-1times(callitn,that’scloseenough)Eachtimetheouterloopisexecuted,theinnerloopisexecutedInnerloopexecutesn-1timesatfirst,linearlydroppingtojustonceOnaverage,innerloopexecutesaboutn/2timesforeachexecutionoftheouterloopIntheinnerloop,parisonisalwaysdone(constanttime),theswapmightbedone(alsoconstanttime)Resultisn*n/2*k,thatis,O(n2/2+k)=O(n2)5LoopinvariantsYourunaloopinordertochangethingsOddlyenough,whatisusuallymostimportantinunderstandingaloopisfindinganinvariant:thatis,aconditionthatdoesn’tchangeInbubblesort,weputthelargestelementsattheend,andonceweputthemthere,wedon’tmovethemagainThevariableouterstartsatthelastindexinthearrayanddecreasesto0Ourinvariantis:EveryelementtotherightofouterisinthecorrectplaceThatis,forallj>outer,ifi<j,thena[i]<=a[j]binedwithouter==0,weknowthatallelementsofthearrayareinthecorrectplace6SelectionsortGivenanarrayoflengthn,Searchelements0throughn-1andselectthesmallestSwapitwiththeelementinlocation0Searchelements1throughn-1andselectthesmallestSwapitwiththeelementinlocation1Searchelements2throughn-1andselectthesmallestSwapitwiththeelementinlocation2Searchelements3throughn-1andselectthesmallestSwapitwiththeelementin
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