Bubble Sort Algorithm - GeeksforGeeks

Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. 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ImproveArticle SaveArticle LikeArticle DifficultyLevel: EasyLastUpdated: 14Jul,2022BubbleSortisthesimplestsortingalgorithmthatworksbyrepeatedlyswappingtheadjacentelementsiftheyareinthewrongorder.Thisalgorithmisnotsuitableforlargedatasetsasitsaverageandworst-casetimecomplexityisquitehigh.HowBubbleSortWorks?Consideranarrayarr[]={5,1,4,2,8} ClickherefortheCompleteCourse!FirstPass: Bubblesortstartswithveryfirsttwoelements,comparingthemtocheckwhichoneisgreater.(51428)–>(15428),Here,algorithmcomparesthefirsttwoelements,andswapssince5>1. (15428)–> (14528),Swapsince5>4 (14528)–> (14258),Swapsince5>2 (14258)–>(14258),Now,sincetheseelementsarealreadyinorder(8>5),algorithmdoesnotswapthem.SecondPass: Now,duringseconditerationitshouldlooklikethis:(14258)–>(14258) (14258)–>(12458),Swapsince4>2 (12458)–>(12458) (12458)–> (12458) ThirdPass: Now,thearrayisalreadysorted,butouralgorithmdoesnotknowifitiscompleted.Thealgorithmneedsonewholepasswithoutanyswaptoknowitissorted.(12458)–>(12458) (12458)–>(12458) (12458)–>(12458) (12458)–>(12458) Illustration:  RecommendedPracticePunishtheStudentsTryIt!FollowingaretheimplementationsofBubbleSort. C++//C++programforimplementation //ofBubblesort#includeusingnamespacestd;  //AfunctiontoimplementbubblesortvoidbubbleSort(intarr[],intn){    inti,j;    for(i=0;iarr[j+1])                swap(arr[j],arr[j+1]);}  //Functiontoprintanarray voidprintArray(intarr[],intsize){    inti;    for(i=0;i  voidswap(int*xp,int*yp){    inttemp=*xp;    *xp=*yp;    *yp=temp;}  //AfunctiontoimplementbubblesortvoidbubbleSort(intarr[],intn){    inti,j;    for(i=0;iarr[j+1])                swap(&arr[j],&arr[j+1]);}  /*Functiontoprintanarray*/voidprintArray(intarr[],intsize){    inti;    for(i=0;iarr[j+1]){                    //swaparr[j+1]andarr[j]                    inttemp=arr[j];                    arr[j]=arr[j+1];                    arr[j+1]=temp;                }    }      /*Printsthearray*/    voidprintArray(intarr[])    {        intn=arr.length;        for(inti=0;iarr[j+1]:                arr[j],arr[j+1]=arr[j+1],arr[j]    #Drivercodetotestabovearr=[64,34,25,12,22,11,90]  bubbleSort(arr)  print("Sortedarrayis:")foriinrange(len(arr)):    print("%d"%arr[i],end="")C#//C#programforimplementation//ofBubbleSortusingSystem;  classGFG{    staticvoidbubbleSort(int[]arr)    {        intn=arr.Length;        for(inti=0;iarr[j+1]){                    //swaptempandarr[i]                    inttemp=arr[j];                    arr[j]=arr[j+1];                    arr[j+1]=temp;                }    }      /*Printsthearray*/    staticvoidprintArray(int[]arr)    {        intn=arr.Length;        for(inti=0;i$arr[$j+1])            {                $t=$arr[$j];                $arr[$j]=$arr[$j+1];                $arr[$j+1]=$t;            }        }    }}  //Drivercodetotestabove$arr=array(64,34,25,12,22,11,90);  $len=sizeof($arr);bubbleSort($arr);  echo"Sortedarray:\n";  for($i=0;$iJavascriptOutputSortedarray: 12458OptimizedImplementationofBubbleSort: TheabovefunctionalwaysrunsO(n^2)timeevenifthearrayissorted.Itcanbeoptimizedbystoppingthealgorithmiftheinnerloopdidn’tcauseanyswap. Belowistheimplementationfortheaboveapproach: C++//OptimizedimplementationofBubblesort#includeusingnamespacestd;  //AnoptimizedversionofBubbleSortvoidbubbleSort(intarr[],intn){   inti,j;   boolswapped;   for(i=0;iarr[j+1])        {           swap(arr[j],arr[j+1]);           swapped=true;        }     }       //IFnotwoelementswereswapped      //byinnerloop,thenbreak     if(swapped==false)        break;   }}  //Functiontoprintanarray voidprintArray(intarr[],intsize){    inti;    for(i=0;i#include  voidswap(int*xp,int*yp){    inttemp=*xp;    *xp=*yp;    *yp=temp;}  //AnoptimizedversionofBubbleSortvoidbubbleSort(intarr[],intn){   inti,j;   boolswapped;   for(i=0;iarr[j+1])        {           swap(&arr[j],&arr[j+1]);           swapped=true;        }     }       //IFnotwoelementswereswappedbyinnerloop,thenbreak     if(swapped==false)        break;   }}  /*Functiontoprintanarray*/voidprintArray(intarr[],intsize){    inti;    for(i=0;iarr[j+1])                 {                    //swaparr[j]andarr[j+1]                    temp=arr[j];                    arr[j]=arr[j+1];                    arr[j+1]=temp;                    swapped=true;                }            }              //IFnotwoelementswere             //swappedbyinnerloop,thenbreak            if(swapped==false)                break;        }    }      //Functiontoprintanarray     staticvoidprintArray(intarr[],intsize)    {        inti;        for(i=0;iarr[j+1]:                arr[j],arr[j+1]=arr[j+1],arr[j]                swapped=True          #IFnotwoelementswereswapped        #byinnerloop,thenbreak        ifswapped==False:            break           #Drivercodetotestabovearr=[64,34,25,12,22,11,90]   bubbleSort(arr)   print("Sortedarray:")foriinrange(len(arr)):    print("%d"%arr[i],end="")  #ThiscodeiscontributedbyShreyanshiArunC#//OptimizedC#implementation//ofBubblesortusingSystem;  classGFG{     //AnoptimizedversionofBubbleSort    staticvoidbubbleSort(int[]arr,intn)    {        inti,j,temp;        boolswapped;        for(i=0;iarr[j+1])                 {                    //swaparr[j]andarr[j+1]                    temp=arr[j];                    arr[j]=arr[j+1];                    arr[j+1]=temp;                    swapped=true;                }            }              //IFnotwoelementswere             //swappedbyinnerloop,thenbreak            if(swapped==false)                break;        }    }      //Functiontoprintanarray     staticvoidprintArray(int[]arr,intsize)    {        inti;        for(i=0;i$arr[$j+1])            {                $t=$arr[$j];                $arr[$j]=$arr[$j+1];                $arr[$j+1]=$t;                $swapped=True;            }        }          //IFnotwoelementswereswapped        //byinnerloop,thenbreak        if($swapped==False)            break;    }}          //Drivercodetotestabove$arr=array(64,34,25,12,22,11,90); $len=sizeof($arr);bubbleSort($arr);  echo"Sortedarray:\n";  for($i=0;$iJavascriptOutputSortedarray: 12345789TimeComplexity:O(N2)AuxiliarySpace:O(1)WorstCaseAnalysisforBubbleSort:Theworst-caseconditionforbubblesortoccurswhenelementsofthearrayarearrangedindecreasingorder.Intheworstcase,thetotalnumberofiterationsorpassesrequiredtosortagivenarrayis(n-1).where‘n’isanumberofelementspresentinthearray. Atpass1: Numberofcomparisons=(n-1)           Numberofswaps=(n-1) Atpass2: Numberofcomparisons=(n-2)           Numberofswaps=(n-2) Atpass3: Numberofcomparisons=(n-3)          Numberofswaps=(n-3)               .               .               . Atpassn-1: Numberofcomparisons=1            Numberofswaps=1Now,calculatingtotalnumberofcomparisonrequiredtosortthearray=(n-1)+(n-2)+ (n-3)+...2+1=(n-1)*(n-1+1)/2 {byusingsumofNnaturalNumberformula}=n(n-1)/2   FortheWorstcase:Totalnumberofswaps=TotalnumberofcomparisonTotalnumberofcomparison(Worstcase)=n(n-1)/2Totalnumberofswaps(Worstcase)=n(n-1)/2WorstandAverageCaseTimeComplexity:O(N2).Theworstcaseoccurswhenanarrayisreversesorted.BestCaseTimeComplexity:O(N).Thebestcaseoccurswhenanarrayisalreadysorted.AuxiliarySpace:O(1)RecursiveImplementationOfBubbleSort:Theideaistoplacethelargestelementattheirpositionandkeepdoingthesameforeveryotherelements.Approach:Placethelargestelementattheirposition,thisoperationmakessurethatfirstlargestelementwillbeplacedattheendofarray.Recursivelycallforrestn–1elementswithsameoperationandplacingthenextgreaterelementattheirposition.Baseconditionforthisrecursioncallwouldbe,whennumberofelementsinthearraybecomes0or1then,simplyreturn(astheyarealreadysorted).Belowistheimplementationoftheaboveapproach:C++//C++codeforrecursivebubblesortalgorithm#includeusingnamespacestd;voidbubblesort(intarr[],intn){    if(n==0||n==1)    {        return;    }    for(inti=0;iarr[i+1])        {            swap(arr[i],arr[i+1]);        }    }    bubblesort(arr,n-1);}intmain(){    intarr[5]={2,5,1,6,9};    bubblesort(arr,5);    for(inti=0;i<5;i++)    {        cout<