Merge Sort is a Divide and Conquer algorithm which sorts given set of elements recursively.

## Pseudocode of merge sort can be written as follows:

```
//A->array, l->left most index, r->right most index
MERGE-SORT(A, l, r)//function named “MERGE-SORT” to sort the array “A”, with the lower bound “l” and upper bound “r” and splits the array later into two parts.
if l < r
mid = (l+(r-l)/2)
MERGE-SORT(A, l, mid)// Function call keeps on splitting the left part of the array till single element is achieved.
MERGE-SORT (A, mid+1, r)// Function call keeps on splitting the right part of the array till single element is achieved..
MERGE(A, l, mid ,r)
end func
MERGE(A, l, mid, r)
nL = mid-l+1 //nL tells the max number of elements in the array L
nR = r-mid //nR tells the max number of elements in the array R
Create arrays L[1..nL+1] and R[1..nR+1]
for i=0 to nL-1
L[i] = A[l+i]
end for
for j=0 to nR-1 // adds elements to the initial array A
R[j] = A[m+l+j]
end for
i=0; j=0; k=l;
while i < nL and j < nR // adds elements to the initial array A
if L[i] <= R[j]
A[k]=L[i]; i=i+1; k=k+1;
else
A[k]=R[j]; j=j+1; k=k+1;
end while
while i < nL // adds elements to the initial array A
A[k]=L[i]; i=i+1; k=k+1;
end while
while j < nR // adds elements to the initial array A
A[k]=R[j]; j=j+1; k=k+1;
end while
end func
```

Merge Sort Explained:

## C program for Merge Sort

```
#include<stdlib.h>
#include<stdio.h>
// Merges two subarrays of arr[ ].
// First subarray is arr[l..m]
// Second subarray is arr[m+1..r]
void merge(int arr[ ], int l, int m, int r)
{
int i, j, k;
int n1 = m - l + 1;
int n2 = r - m;
/* create temp arrays */
int L[n1], R[n2];
/* Copy data to temp arrays L[ ] and R[ ] */
for (i = 0; i < n1; i++)
L[i] = arr[l + i];
for (j = 0; j < n2; j++)
R[j] = arr[m + 1+ j];
/* Merge the temp arrays back into arr[l..r]*/
i = 0; // Initial index of first subarray
j = 0; // Initial index of second subarray
k = l; // Initial index of merged subarray
while (i < n1 && j < n2)
{
if (L[i] <= R[j])
{
arr[k] = L[i];
i++;
}
else
{
arr[k] = R[j];
j++;
}
k++;
}
/* Copy the remaining elements of L[], if there
are any */
while (i < n1)
{
arr[k] = L[i];
i++;
k++;
}
/* Copy the remaining elements of R[], if there
are any */
while (j < n2)
{
arr[k] = R[j];
j++;
k++;
}
}
/* l is for left index and r is right index of the
sub-array of arr to be sorted */
void mergeSort(int arr[], int l, int r)
{
if (l < r)
{
// Same as (l+r)/2, but avoids overflow for
// large l and h
int m = l+(r-l)/2;
// Sort first and second halves
mergeSort(arr, l, m);
mergeSort(arr, m+1, r);
merge(arr, l, m, r);
}
}
/* UTILITY FUNCTIONS */
/* Function to print an array */
void printArray(int A[ ], int size)
{
int i;
for (i=0; i < size; i++)
printf("%d ", A[i]);
printf("\n");
}
/* Driver program to test above functions */
int main()
{
int arr[] = {12, 11, 13, 5, 6, 7};
// or you can take input direct from the user itself using scanf function
int arr_size = sizeof(arr)/sizeof(arr[0]);
printf("Given array is \n");
printArray(arr, arr_size);
mergeSort(arr, 0, arr_size - 1);
printf("\nSorted array is \n");
printArray(arr, arr_size);
return 0;
}
```

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