1. Sorting Techniques –Selection Sort –Bubble Sort

2. Selection Sort Working : “SELECT” an Element and Put in PROPER PLACE Description : 1. From position 0, find the smallest and then exchange it with the element in position 0. 2. From position 1, find the smallest and exchange with position 1. 3. Now from 2 do the same until you have reached the end of the list General Algorithm: for positions i = 0 to max-1 find smallest from position i exchange with position i

3. SelectionSortSelectionSort 678449507533216784495075332167844950753321678449507533216784495075332167844950753321 Starting from position 0 find the smallest and exhange with element in position 0 start at position 1 ….

4. Selection Sort #define MAX 5 int Min(int a[], int pos) { int i,m,index=pos; m=a[pos]; // Get the Current Value for (i=pos+1;i<MAX;i++) //Search from next { if (a[i]<m) {m=a[i];index=i;} return index; } void main() {int A[MAX],i,temp,k; for (i=0;i >A[i]; //INPUT for (i=0;i<MAX;i++) { k=Min(A,i); //FIND if (A[k]<A[i]) //SWAP { temp=A[k]; A[k]=A[i]; A[i]=temp; } cout<<”Sorted elements “ << endl; for (i=0;i<MAX;i++) cout<<A[i]<<endl; }

5. 84556782332 After pass 5 23832567845 Original list 82332567845 After pass 1 87832562345 After pass 2 87845562332 After pass 3 84578562332 After pass 4 EXERCISEEXERCISE

6. Bubble Sort Working: It works by comparing neighbours in the array and exchanging them if necessary to put the smaller of the pair first. On each pass through the array an element 'bubbles' up into place.  General Algorithm: for (i=0;i<max;i++) for (j=0;j<max-1;j++) if (a[j]>a[j+1] ) {save = a[j] a[j] = a[j+1] a[j+1] = save }

7. BubbleSortBubbleSort 5 8 1 2 3 I = 0 j= 4 ( compare j with j-1and swap ) 5 1 8 2 3 5 3 8 2 1 5 3 8 1 2 1 3 8 5 2 Pass-1 1 2 5 3 8 1 2 5 3 8 Pass-2Pass-3

8. Bubble Sort // The Algorithm Sinks the LARGEST TO THE BOTTOM #define MAX 5 void main() { int A[MAX],i,j,temp,sorted=0; for (i=0;i >A[i]; i=0; while ((i<MAX)&&(sorted==0)) {sorted=1; for (j=0;j<MAX-i-1;j++) {if (A[j]>A[j+1]) // Largest sinks {temp=A[j]; A[j]=A[j+1]; A[j+1]=temp; sorted=0; } i++; } cout<<”Sorted Elements"<<endl; for (i=0;i<MAX;i++) cout<<A[i]<<endl; }

9. 23832567845 Original list 84532562378 After pass 1 87845562332 After pass 2 84578562332 After pass 3 84556782332 After pass 4 Sorted!EXERCISE

10. Merge Sort

11. Concept Used What is the concept used Merge and Quick Sort?What is the concept used in Merge and Quick Sort? This two sorting techniques use “DIVIDE and CONQUER “ Technique. “DIVIDE and CONQUER “ Technique. What is Divide and Conquer Technique? The Problem is divide into similar subproblems When to stop Dividing? When the problem is small enough to be handled. When the problem is small enough to be handled. Outline for divide and conquer Sorting ( NEXT )

12. Outline : Divide and conquer Sorting Sortlist( ) {if the list has length greater than 1 then {partition the list into lowlist,highlist; sort(lowlist); sort(highlist); combine(lowlist,highlist); } Where does the Quick and merge sort differ? They differ in the Way the the List is partitioned

13. Merge Sort Working Break the list into two sublists of size as nearly equal as possible and then sort them separately. Then Merge the two sorted list. Hence know as MERGE sort. EG : 8 7 6 5 4 3 2 1 ( MID = L+H/2 = 1+8 /2 = 4 ) 8 7 6 5 ( 1+4/2=2)4 3 2 1 ( 1+4/2=2) 8 7 6 54 3 2 1 Now Sort & Merge: 7 8 5 6 3 4 1 2 5 6 7 81 2 3 4 1 2 3 4 5 6 7 8

14. EXCERSISEEXCERSISE 26333529191222 2633352919122226333529191222 26332935 121922 26333529 12192226333529121922

15. Algorithm - Merge Sort Void merge(int lpos, int rpos, int rend) { int I,lend,numelements,tmppos,tmparray[MAX] lend = rpos-1; tmppos = lpos; numelements = rend - lpos+1; while ((lpos <= lend) && ( rpos <=rend)) if ( a[lpos] <= a[rpos) tmparray[tmppos++] = a[lpos++]; else tmparray[tmppos++] = a[rpos++]; while (lpos <= lend) tmparray[tmppos++] = a[lpos++]; while (rpos <= rend) tmparray[tmppos++] = a[rpos++]; for (I=0;I<numelements;I++,rend--) a[rend]= tmparray[rend]; } Void mergesort( int left, int right ) int center; if ( left < right) { center = (left=right/2); mergesort(left,center); mergesort(center+1,right); merge(left,center+1,right); } Void main( ) {//input MergeSort(0,Max-1) //output } 7856 7856