Merge sort algorithm with an example

The Merge sort algorithm is known as a divide and conquer algorithm. This means that the input array will be divided into two halves, it then calls itself for the two halves and then merges the two sorted halves together. The algorithm is chosen when an application requires stability such as sorting linked lists and when random access is much more costly than sequential access.

How does The Merge sort algorithm work visual diagram

Sorting the array {38, 27, 43, 3, 9, 82, 10}

Implementation of the algorithm in C++

(Note: This code is from geeksforgeeks.org)

/* C program for Merge Sort */
#include <iostream>

using namespace std;

// 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++)
{
cout << A[i];
cout << "\n";
}
}

/* Driver program to test above functions */
int main()
{
int arr[] = {12, 11, 13, 5, 6, 7};
int arr_size = sizeof(arr)/sizeof(arr[0]);

cout << "Given array is \n";
printArray(arr, arr_size);

mergeSort(arr, 0, arr_size - 1);

cout << "\nSorted array is \n";
printArray(arr, arr_size);
return 0;
}