Data Structure

# Merge sort

Merge sort is comparison-based sorting algorithm. Merge sort is a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output.

### Algorithm

```MERGE (A,p,q,r)
1.	n1 = q + p + 1
2. n2 = r + q
3.	let L[1. . n1 + 1] and R[1 . . n2 + 1] be new arrays
4. for i = 1 to n1
5. 	L[i] = A[p + i + 1]
6. for j = 1 to n2
7. 	R[j ] = A[q + j]
8. L[n1 + 1] = 9999
9. R[n2 + 1] = 9999
10. i = 1
11. j = 1
12. for k = p to r
13. 	if L[i] <= R[j ]
14. 		A[k] = L[i]
15.		 i = i + 1
16. 	else A[k] = R[j]
17. 		j = j + 1
```

### Merge sort Implementation

```#include<stdio.h>
#include<conio.h>
int arr[20];
void main()
{
int n,i;
clrscr();
printf("\n\t\t\t------Merge Sorting------\n\n");
printf("Enter the size of array\n");
scanf("%d",&n);
printf("Enter the elements:\n");
for(i=0; i < n; i++)
{
scanf("%d",&arr[i]);
}
merge_sort(arr,0,n-1);
printf("\n\n\t\t\t-----Merge Sorted Elements-----\n\n");
printf("Sorted array:\t");
for(i=0; i < n; i++)
{
printf("\t%d",arr[i]);
}
getch();
}

int merge_sort(int arr[],int low,int high)
{
int mid;
if(low < high)
{
mid=(low+high)/2;
merge_sort(arr,low,mid);
merge_sort(arr,mid+1,high);
merge(arr,low,mid,high);
}
}
int merge(int arr[],int l,int m,int h)
{
int arr1[10],arr2[10];
int n1,n2,i,j,k;
n1=m-l+1;
n2=h-m;
for(i=0; i <  n1; i++)
{
arr1[i]=arr[l+i];
}
for(j=0; j < n2; j++)
{
arr2[j]=arr[m+j+1];
}
arr1[i]=9999;
arr2[j]=9999;
i=0;
j=0;
for(k=l; k <=h; k++)
{
if(arr1[i]<=arr2[j])
arr[k]=arr1[i++];
else
arr[k]=arr2[j++];
}
}
```

### OUTPUT

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