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OUTLINE

IntroductionAlgorithm for merge sortExampleQuick SortAlgorithm For Quick SortExample

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What Is Meant By Merge Sort ? Merge sort is northing but the given

array is divided into two parts. i) LEFT Part ii) RIGHT Part Both the left part and the right part

should be in sorted recursively. Latter the sorted left part and the

sorted right part are finally merged in to a single sorted array.

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The process of merging of two sorted vectors into a single sorted vector is called as “simple merging”.

The only condition in merge sort is that the both vectors should be sorted either in Ascending order (or) Descending order.

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Algorithm For MERGE Sort Merge sort (a, low, high){ if (low < high) { mid = (low+high)/2; merge sort(a,low,mid); merge sort(a,mid+1,high); simple

merge(a,low,mid,high); }}

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simple merge(a,low,mid,high){ while(i<=mid && j<=high) { if(a[i] < a[j]) { c[k] = a[i]; i = i+1; k = k+1; } else { c[k] = a[j]; j = j+1; k = k+1;

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} }while (i <= mid) c[k++] = a[i++]; while (j <= high) c[k++] = a[j++]; for (i= low;i<= high; i++) a[i] = c[i];

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Example for Merge sort

7,5,9,2,3,1,4,6,10,8

7,5,9,2,3 1,4,6,10,8

7,5,9 1,4,6 10,82,3

7,5

7

9 2 3 1,4 6 10 8

5 1 4

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5,7 9 2 3 1,4 6 10 8

5,7,9 1,4,6 10,82,3

1,2,3,4,5,6,7,8,9,10

2,3,7,5,9 1,4,6,10,8

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What is Quick sort ?- Quick sort is a very popular sorting method .Quack

sort is also known as partition exchange sorting. - The name comes from the fact that quick sort

can sort a list of data elements significantly faster than any of the common sorting algorithms.

- This algorithm is based on the fact that it is faster and easier to sort two small arrays in to one large one.

- The basic strategy of quick sort is to divide and

conquer.

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Algorithm for Quick sort

Quick-sort (a ,low ,high) { if (low<high) { mid = partition (a ,low ,high); quicksort (a ,low ,mid-1); quicksort ( a, mid+1 ,high); } } partition (a ,low, high) { while (I <= j) { do i++; while (key >= a[i] );

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do j--; while (key <= a[j]); if (I < j) temp = a[i]; a[i] = a[j]; a[j] = temp; } temp = a[low]; a[low] = a[j]; a[j] = temp; return j; }

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Example for Quick sort:

33 77 88 55 22 11 99 55 44

The box element is the pivot element, Blue elements are less or equal to pivot & brown elements are larger than pivot.

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33 77 88 55 22 11 99 55 44

33 77 88 44 22 11 99 55 55

The elements 4<5 therefore it is interchanged (swapped).

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33 77 88 44 22 11 99 55 55

The elements 4<7 & 2<8 therefore it is interchanged (swapped).

After swapping the array elements are as follows:

33 44 22 77 88 11 99 55 55

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33 44 22 77 88 11 99 55 55

The elements 1<7 & 5<8 therefore it is interchanged (swapped). After swapping the array elements are as follows:

33 44 22 11 55 77 99 88 55

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33 44 22 11 55 77 99 88 55

The elements pivot 5<7 therefore it is interchanged (swapped). After swapping the array elements are as follows:

33 44 22 11 55 55 99 88 77

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The pivot has taken its place & the greater elements are on the right side & lesser elements are on the left side. The elements are shown below,

33 44 22 11 55 55 99 88 77

Repeat the steps until all the elements get sorted. The elements after sorting will be:

11 22 33 44 55 55 77 88 99

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