SORTING Sorting is the process of rearranging a

SORTING Sorting is the process of rearranging a set of objects in a specific order. • Internal sorting (sorting of arrays) • External sorting (sorting of sequential files) Simple Sorting methods: • insertion Sort • selection Sort • exchange Sort

Insertion sort The items are divided into a sorted sequence a[0]. . . a[i-1] and a source sequence a[i]. . . a[n-1]. FOR i : = 1 TO n-1 DO x : = a[i]; insert x at the appropriate place in a[0]. . . a[i] END

Insertion sort А = 18, 20, 5, 13, 15

Insertion sort for (i=1; i<n; i++) { j=i; temp=a[i]; while(j>0 && temp<a[j-1]) { a[j]=a[j-1]; j--; } a[j]=temp; } //i determines sequence a[0]. . . a[i] //moving // insert

Insertion sort O(n 2)

Binary insertion sort void binsort(int a[], int n) {int item; for (int i=1; i<n; i++) { item=a[i]; int l=0; int r=i-1; while (l<=r) { int m=(l+r)/2; if (item<a[m]) r=m-1; else l=m+1; } for (int j=i-1; j>=l; j--) a[j+1]=a[j]; a[l]=item; }} O(n 2)

Insertion Sort by Diminishing Increment 1, 4, 13, 40, 121, . . . hk-1 = 3 hk+1, ht-1 = 1, t = log 3(n) - 1. 1, 3, 7, 15, 31, . . . hk-1 = 2 hk+1, ht-1 = 1, t = log 2(n) - 1.

Selection sort 1. Select the item with the smallest key. 2. Exchange it with the first item a[0]. 3. Then repeat these operations with the remaining n-1 items, then with n-2 items, until only one item - the largest - is left. FOR i : = 0 TO n-1 DO assign the index of the least item of a[i]. . . a[n-1] to k; exchange a[i] with a[k] END

Selection sort Example: Array: 18, 20, 5, 13, 15. O(n 2)

Exchange sort (Bubblesort) compares two consecutive items in the list, and swaps them if they are out of order. for (i=1; i<n; i++) for(j=n-1; j>=i; j--) if (a[j]<a[j-1]) {temp=a[j]; a[j]=a[j-1]; a[j-1]=temp; }

Bubblesort

int ilast; i=n-1; while (i>0) { ilast=0; for(j=0; j<i; j++) if (a[j]>a[j+1]) {temp=a[j]; a[j]=a[j+1]; a[j+1]=temp; ilast=j; } i=ilast; }

Pass 0 Pass 1 ilast=2 ilast=3

Pass 2 ilast=0 O(n 2)

Shaker sort O(n 2)