Data Modelling & AI Data Structure & Algorithm

Iterative Merge Sort

31 July 2024

2

Following is a typical recursive implementation of Merge Sort

C++

// Recursive C++ program for merge sort 
#include<bits/stdc++.h>
using namespace std;
 
// Function to merge the two haves
// arr[l..m] and arr[m+1..r] of array arr[] 
void merge(int arr[], int l, int m, int r);
 
// 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 & h
        int m = l + (r - l) / 2;
        mergeSort(arr, l, m);
        mergeSort(arr, m + 1, r);
        merge(arr, l, m, r);
    }
}
 
// Function to merge the two haves arr[l..m]
// and arr[m+1..r] of array arr[] 
void merge(int arr[], int l, int m, int r)
{
    int 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(int i = 0; i < n1; i++)
        L[i] = arr[l + i];
    for(int j = 0; j < n2; j++)
        R[j] = arr[m + 1+ j];
 
    // Merge the temp arrays
    // back into arr[l..r]
    int i = 0;
    int j = 0;
    k = l;
     
    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++;
    }
}
 
// Function to print an array 
void printArray(int A[], int size)
{
    for(int i = 0; i < size; i++)
        printf("%d ", A[i]);
         
    cout << "\n";
}
 
// Driver code
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;
}
 
// This code is contributed by Mayank Tyagi

C

/* Recursive C program for merge sort */
#include<stdlib.h>
#include<stdio.h>
 
/* Function to merge the two haves
 arr[l..m] and arr[m+1..r] of array arr[] */
void merge(int arr[], int l, int m, int r);
 
/* 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 & h
      int m = l+(r-l)/2; 
      mergeSort(arr, l, m);
      mergeSort(arr, m+1, r);
      merge(arr, l, m, r);
   }
}
 
/* Function to merge the two haves arr[l..m]
 and arr[m+1..r] of array arr[] */
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;
    j = 0;
    k = l;
    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++;
    }
}
 
/* 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};
    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;
}

Java

// Recursive Java Program for merge sort
 
import java.util.Arrays;
public class GFG
{
    public static void mergeSort(int[] array)
    {
        if(array == null)
        {
            return;
        }
 
        if(array.length > 1)
        {
            int mid = array.length / 2;
 
            // Split left part
            int[] left = new int[mid];
            for(int i = 0; i < mid; i++)
            {
                left[i] = array[i];
            }
             
            // Split right part
            int[] right = new int[array.length - mid];
            for(int i = mid; i < array.length; i++)
            {
                right[i - mid] = array[i];
            }
            mergeSort(left);
            mergeSort(right);
 
            int i = 0;
            int j = 0;
            int k = 0;
 
            // Merge left and right arrays
            while(i < left.length && j < right.length)
            {
                if(left[i] < right[j])
                {
                    array[k] = left[i];
                    i++;
                }
                else
                {
                    array[k] = right[j];
                    j++;
                }
                k++;
            }
            // Collect remaining elements
            while(i < left.length)
            {
                array[k] = left[i];
                i++;
                k++;
            }
            while(j < right.length)
            {
                array[k] = right[j];
                j++;
                k++;
            }
        }
    }
 
    // Driver program to test above functions.
    public static void main(String[] args)
    {
        int arr[] = {12, 11, 13, 5, 6, 7};
        int i=0;
        System.out.println("Given array is");
 
        for(i=0; i<arr.length; i++)
            System.out.print(arr[i]+" ");
 
        mergeSort(arr);
 
        System.out.println("\n");
        System.out.println("Sorted array is");
 
        for(i=0; i<arr.length; i++)
            System.out.print(arr[i]+" ");
    }
}
 
// Code Contributed by Mohit Gupta_OMG

Python3

# Recursive Python Program for merge sort
 
def merge(left, right):
    if not len(left) or not len(right):
        return left or right
 
    result = []
    i, j = 0, 0
    while (len(result) < len(left) + len(right)):
        if left[i] < right[j]:
            result.append(left[i])
            i+= 1
        else:
            result.append(right[j])
            j+= 1
        if i == len(left) or j == len(right):
            result.extend(left[i:] or right[j:])
            break
 
    return result
 
def mergesort(list):
    if len(list) < 2:
        return list
 
    middle = int(len(list)/2)
    left = mergesort(list[:middle])
    right = mergesort(list[middle:])
 
    return merge(left, right)
     
seq = [12, 11, 13, 5, 6, 7]
print("Given array is")
print(seq); 
print("\n")
print("Sorted array is")
print(mergesort(seq))
 
# Code Contributed by Mohit Gupta_OMG 

C#

/* Iterative C# program for merge
sort */
using System;
 
class GFG {
  
    /* l is for left index and r
    is right index of the sub-array 
    of arr to be sorted */
    static void mergeSort(int[] arr,
                           int l, int r)
    {
        if (l < r)
        {
            
            // Same as (l+r)/2 but avoids 
            // overflow for large l & h
            int m = l + (r - l) / 2; 
            mergeSort(arr, l, m);
            mergeSort(arr, m+1, r);
            merge(arr, l, m, r);
       }
    }
 
    /* Function to merge the two haves
    arr[l..m] and arr[m+1..r] of array 
    arr[] */
    static 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 = new int[n1];
        int []R = new int[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;
        j = 0;
        k = l;
        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++;
        }
    }
     
    /* Function to print an array */
    static void printArray(int []A, int size)
    {
        int i;
        for (i=0; i < size; i++)
            Console.Write(A[i]+" ");
        Console.Write("\n");
    }
     
    /* Driver program to test above functions */
    public static void Main()
    {
        int []arr = {12, 11, 13, 5, 6, 7};
        int arr_size = arr.Length;
     
        Console.Write("Given array is \n");
        printArray(arr, arr_size);
     
        mergeSort(arr, 0, arr_size - 1);
     
        Console.Write("\nSorted array is \n");
        printArray(arr, arr_size);
    }
}
 
// This code is contributed by Smitha

Javascript

<script>
 
// Recursive javascript Program for merge sort
 
    function mergeSort(array) {
        if (array == null) {
            return;
        }
 
        if (array.length > 1) {
            var mid = parseInt(array.length / 2);
 
            // Split left part
            var left = Array(mid).fill(0);
            for (i = 0; i < mid; i++) {
                left[i] = array[i];
            }
 
            // Split right part
            var right = Array(array.length - mid).fill(0);
            for (i = mid; i < array.length; i++) {
                right[i - mid] = array[i];
            }
            mergeSort(left);
            mergeSort(right);
 
            var i = 0;
            var j = 0;
            var k = 0;
 
            // Merge left and right arrays
            while (i < left.length && j < right.length) {
                if (left[i] < right[j]) {
                    array[k] = left[i];
                    i++;
                } else {
                    array[k] = right[j];
                    j++;
                }
                k++;
            }
            // Collect remaining elements
            while (i < left.length) {
                array[k] = left[i];
                i++;
                k++;
            }
            while (j < right.length) {
                array[k] = right[j];
                j++;
                k++;
            }
        }
    }
 
    // Driver program to test above functions.
     
        var arr = [ 12, 11, 13, 5, 6, 7 ];
        var i = 0;
        document.write("Given array is<br/>");
 
        for (i = 0; i < arr.length; i++)
            document.write(arr[i] + " ");
 
        mergeSort(arr);
 
        document.write("<br/><br/>");
        document.write("Sorted array is<br/>");
 
        for (i = 0; i < arr.length; i++)
            document.write(arr[i] + " ");
 
// This code is contributed by umadevi9616 
 
</script>

PHP

<?php
// Recursive PHP program for merge sort
 
//Merge function
function merge($l_arr, $r_arr)
{
    $result = array();
 
    while (sizeof($l_arr) > 0 && sizeof($r_arr) > 0){
        if($l_arr[0] > $r_arr[0]){
            $result[] = $r_arr[0];
            $r_arr = array_slice($r_arr , 1);
        }
        else{
            $result[] = $l_arr[0];
            $l_arr = array_slice($l_arr, 1);
        }
    }
 
    while (sizeof($l_arr) > 0){
        $result[] = $l_arr[0];
        $l_arr = array_slice($l_arr, 1);
    }
 
    while (sizeof($r_arr) > 0){
        $result[] = $r_arr[0];
        $r_arr = array_slice($r_arr, 1);
    }
 
    return $result;
}
 
//Merge sort function
function mergeSort($arr){
    if(sizeof($arr) < 2)
        return $arr;
     
    $m = sizeof($arr) / 2;
    $l = array_slice($arr, 0, $m);
    $r = array_slice($arr, $m);
    $l = mergeSort($l);
    $r = mergeSort($r);
 
    return merge($l, $r);
}
 
// Function to print an array 
function printArray($A, $size)
{
    for($i = 0; $i < $size; $i++)
        echo $A[$i]." ";
         
    echo "\n";
}
 
// Driver code
$arr = array( 12, 11, 13, 5, 6, 7 );
$arr_size = sizeof($arr);
 
echo "Given array is \n";
printArray($arr, $arr_size);
 
$arr = mergeSort($arr, 0, $arr_size - 1);
 
echo "\nSorted array is \n";
printArray($arr, $arr_size);
// This code is contributed by Susobhan Akhuli
?>

Output

Given array is 
12 11 13 5 6 7 

Sorted array is 
5 6 7 11 12 13

Time complexity: O(n log n)
Auxiliary Space complexity: O(n)

Iterative Merge Sort:
The above function is recursive, so uses function call stack to store intermediate values of l and h. The function call stack stores other bookkeeping information together with parameters. Also, function calls involve overheads like storing activation record of the caller function and then resuming execution. Unlike Iterative QuickSort, the iterative MergeSort doesn’t require explicit auxiliary stack.

Note: In iterative merge sort, we do bottom up approach ie, start from 2 element sized array (we know that 1 element sized array is already sorted). Also the key point is that since we don’t know how to divide the array exactly as in top down approach, where the 2 element sized array may be of size sequence 2,1,2,2,1…we in bottom up approach assume the array was divided exactly by powers of 2 (n/2,n/4….etc) for an array size of powers of 2, ex: n=2,4,8,16.
So for other input sizes such as 5, 7, 11 we will have remaining sublist that didn’t go into the power of 2 width at each level as we keep on merging and go upwards, this unmerged sublist which is of size that is not exact power of 2, will remain isolated till the final merge.
To merge this unmerged list at final merge we need to force the mid to be at the start of unmerged list so that it is a candidate for merge.

The unmerged sublist element count that will be isolated until final merge call can be found out using the remainder (n % width). The final merge (when we have uneven lists) can be identified by (width>n/2).

Since width grows by powers of 2 when width == n/2 then it means the input was already of size in powers of 2, else if width < n/2 then we haven’t reached final merge yet, so when width > n/2 we must be having pending unmerged uneven list hence we reset mid only in such case.

The above function can be easily converted to iterative version. Following is iterative Merge Sort.

C++

/* Iterative C program for merge sort */
#include <bits/stdc++.h>
using namespace std;
 
/* Function to merge the two haves arr[l..m] and arr[m+1..r] of array arr[] */
void merge(int arr[], int l, int m, int r);
 
// Utility function to find minimum of two integers
int min(int x, int y) { return (x<y)? x :y; }
 
 
/* Iterative mergesort function to sort arr[0...n-1] */
void mergeSort(int arr[], int n)
{
   int curr_size;  // For current size of subarrays to be merged
                   // curr_size varies from 1 to n/2
   int left_start; // For picking starting index of left subarray
                   // to be merged
 
   // Merge subarrays in bottom up manner.  First merge subarrays of
   // size 1 to create sorted subarrays of size 2, then merge subarrays
   // of size 2 to create sorted subarrays of size 4, and so on.
   for (curr_size=1; curr_size<=n-1; curr_size = 2*curr_size)
   {
       // Pick starting point of different subarrays of current size
       for (left_start=0; left_start<n-1; left_start += 2*curr_size)
       {
           // Find ending point of left subarray. mid+1 is starting 
           // point of right
           int mid = min(left_start + curr_size - 1, n-1);
 
           int right_end = min(left_start + 2*curr_size - 1, n-1);
 
           // Merge Subarrays arr[left_start...mid] & arr[mid+1...right_end]
           merge(arr, left_start, mid, right_end);
       }
   }
}
 
/* Function to merge the two haves arr[l..m] and arr[m+1..r] of array arr[] */
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;
    j = 0;
    k = l;
    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++;
    }
}
 
/* 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 n = sizeof(arr)/sizeof(arr[0]);
 
    cout <<"Given array is \n ";
    printArray(arr, n);
 
    mergeSort(arr, n);
 
    cout <<"\nSorted array is \n ";
    printArray(arr, n);
    return 0;
}
// This code is contributed shivanisinghss2110

C

/* Iterative C program for merge sort */
#include<stdlib.h>
#include<stdio.h>
 
/* Function to merge the two haves arr[l..m] and arr[m+1..r] of array arr[] */
void merge(int arr[], int l, int m, int r);
 
// Utility function to find minimum of two integers
int min(int x, int y) { return (x<y)? x :y; }
 
 
/* Iterative mergesort function to sort arr[0...n-1] */
void mergeSort(int arr[], int n)
{
   int curr_size;  // For current size of subarrays to be merged
                   // curr_size varies from 1 to n/2
   int left_start; // For picking starting index of left subarray
                   // to be merged
 
   // Merge subarrays in bottom up manner.  First merge subarrays of
   // size 1 to create sorted subarrays of size 2, then merge subarrays
   // of size 2 to create sorted subarrays of size 4, and so on.
   for (curr_size=1; curr_size<=n-1; curr_size = 2*curr_size)
   {
       // Pick starting point of different subarrays of current size
       for (left_start=0; left_start<n-1; left_start += 2*curr_size)
       {
           // Find ending point of left subarray. mid+1 is starting 
           // point of right
           int mid = min(left_start + curr_size - 1, n-1);
 
           int right_end = min(left_start + 2*curr_size - 1, n-1);
 
           // Merge Subarrays arr[left_start...mid] & arr[mid+1...right_end]
           merge(arr, left_start, mid, right_end);
       }
   }
}
 
/* Function to merge the two haves arr[l..m] and arr[m+1..r] of array arr[] */
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;
    j = 0;
    k = l;
    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++;
    }
}
 
/* 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};
    int n = sizeof(arr)/sizeof(arr[0]);
 
    printf("Given array is \n");
    printArray(arr, n);
 
    mergeSort(arr, n);
 
    printf("\nSorted array is \n");
    printArray(arr, n);
    return 0;
}

Java

/* Iterative Java program for merge sort */
import java.lang.Math.*;
 
class GFG {
 
    /* Iterative mergesort function to sort
     arr[0...n-1] */
    static void mergeSort(int arr[], int n)
    {
         
        // For current size of subarrays to
        // be merged curr_size varies from 
        // 1 to n/2
        int curr_size; 
                     
        // For picking starting index of 
        // left subarray to be merged
        int left_start;
                         
         
        // Merge subarrays in bottom up 
        // manner. First merge subarrays 
        // of size 1 to create sorted 
        // subarrays of size 2, then merge
        // subarrays of size 2 to create 
        // sorted subarrays of size 4, and
        // so on.
        for (curr_size = 1; curr_size <= n-1; 
                      curr_size = 2*curr_size)
        {
             
            // Pick starting point of different
            // subarrays of current size
            for (left_start = 0; left_start < n-1;
                        left_start += 2*curr_size)
            {
                // Find ending point of left 
                // subarray. mid+1 is starting 
                // point of right
                int mid = Math.min(left_start + curr_size - 1, n-1);
         
                int right_end = Math.min(left_start 
                             + 2*curr_size - 1, n-1);
         
                // Merge Subarrays arr[left_start...mid]
                // & arr[mid+1...right_end]
                merge(arr, left_start, mid, right_end);
            }
        }
    }
     
    /* Function to merge the two haves arr[l..m] and
    arr[m+1..r] of array arr[] */
    static 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[] = new int[n1];
        int R[] = new int[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;
        j = 0;
        k = l;
        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++;
        }
    }
     
    /* Function to print an array */
    static void printArray(int A[], int size)
    {
        int i;
        for (i=0; i < size; i++)
            System.out.printf("%d ", A[i]);
        System.out.printf("\n");
    }
     
    /* Driver program to test above functions */
    public static void main(String[] args)
    {
        int arr[] = {12, 11, 13, 5, 6, 7};
        int n = arr.length;
     
        System.out.printf("Given array is \n");
        printArray(arr, n);
     
        mergeSort(arr, n);
     
        System.out.printf("\nSorted array is \n");
        printArray(arr, n);
    }
}
 
// This code is contributed by Smitha

Python3

# Iterative Merge sort (Bottom Up) 
 
# Iterative mergesort function to 
# sort arr[0...n-1] 
 
# perform bottom up merge
def mergeSort(a):
    # start with least partition size of 2^0 = 1
    width = 1   
    n = len(a)                                          
    # subarray size grows by powers of 2 
    # since growth of loop condition is exponential, 
    # time consumed is logarithmic (log2n)
    while (width < n):
        # always start from leftmost
        l=0;
        while (l < n): 
            r = min(l+(width*2-1), n-1)         
            m = min(l+width-1,n-1)
            # final merge should consider 
            # unmerged sublist if input arr
            # size is not power of 2              
            merge(a, l, m, r)
            l += width*2
        # Increasing sub array size by powers of 2
        width *= 2
    return a
   
# Merge Function 
def merge(a, l, m, r): 
    n1 = m - l + 1
    n2 = r - m 
    L = [0] * n1 
    R = [0] * n2 
    for i in range(0, n1): 
        L[i] = a[l + i] 
    for i in range(0, n2): 
        R[i] = a[m + i + 1] 
 
    i, j, k = 0, 0, l 
    while i < n1 and j < n2: 
        if L[i] <= R[j]: 
            a[k] = L[i] 
            i += 1
        else: 
            a[k] = R[j] 
            j += 1
        k += 1
 
    while i < n1: 
        a[k] = L[i] 
        i += 1
        k += 1
 
    while j < n2: 
        a[k] = R[j] 
        j += 1
        k += 1
 
 
# Driver code 
a = [-74,48,-20,2,10,-84,-5,-9,11,-24,-91,2,-71,64,63,80,28,-30,-58,-11,-44,-87,-22,54,-74,-10,-55,-28,-46,29,10,50,-72,34,26,25,8,51,13,30,35,-8,50,65,-6,16,-2,21,-78,35,-13,14,23,-3,26,-90,86,25,-56,91,-13,92,-25,37,57,-20,-69,98,95,45,47,29,86,-28,73,-44,-46,65,-84,-96,-24,-12,72,-68,93,57,92,52,-45,-2,85,-63,56,55,12,-85,77,-39]
print("Given array is ") 
print(a) 
mergeSort(a) 
 
print("Sorted array is ") 
print(a) 
 
# Contributed by Madhur Chhangani [RCOEM] 
# corrected and improved by @mahee96

C#

/* Iterative C# program for merge sort */
using System;
public class GFG {
  
    /* Iterative mergesort function to sor
    t arr[0...n-1] */
    static void mergeSort(int []arr, int n)
    {
          
        // For current size of subarrays to
        // be merged curr_size varies from 
        // 1 to n/2
        int curr_size; 
                      
        // For picking starting index of 
        // left subarray to be merged
        int left_start;
                          
          
        // Merge subarrays in bottom up 
        // manner. First merge subarrays 
        // of size 1 to create sorted 
        // subarrays of size 2, then merge
        // subarrays of size 2 to create 
        // sorted subarrays of size 4, and
        // so on.
        for (curr_size = 1; curr_size <= n-1; 
                      curr_size = 2*curr_size)
        {
              
            // Pick starting point of different
            // subarrays of current size
            for (left_start = 0; left_start < n-1;
                        left_start += 2*curr_size)
            {
                // Find ending point of left 
                // subarray. mid+1 is starting 
                // point of right
                int mid = Math.Min(left_start + curr_size - 1,n-1);
          
                int right_end = Math.Min(left_start 
                             + 2*curr_size - 1, n-1);
          
                // Merge Subarrays arr[left_start...mid]
                // & arr[mid+1...right_end]
                merge(arr, left_start, mid, right_end);
            }
        }
    }
      
    /* Function to merge the two haves arr[l..m] and
    arr[m+1..r] of array arr[] */
    static 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 = new int[n1];
        int []R = new int[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;
        j = 0;
        k = l;
        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++;
        }
    }
      
    /* Function to print an array */
    static void printArray(int []A, int size)
    {
        int i;
        for (i=0; i < size; i++)
            Console.Write(A[i]+" ");
        Console.WriteLine("");
    }
      
    /* Driver program to test above functions */
    public static void Main()
    {
        int []arr = {-74,48,-20,2,10,-84,-5,-9,11,-24,-91,2,-71,64,63,80,28,-30,-58,-11,-44,-87,-22,54,-74,-10,-55,-28,-46,29,10,50,-72,34,26,25,8,51,13,30,35,-8,50,65,-6,16,-2,21,-78,35,-13,14,23,-3,26,-90,86,25,-56,91,-13,92,-25,37,57,-20,-69,98,95,45,47,29,86,-28,73,-44,-46,65,-84,-96,-24,-12,72,-68,93,57,92,52,-45,-2,85,-63,56,55,12,-85,77,-39};
        int n = arr.Length;
      
        Console.Write("Given array is \n");
        printArray(arr, n);
      
        mergeSort(arr, n);
      
        Console.Write("\nSorted array is \n");
        printArray(arr, n);
    }
}
// This code is contributed by Rajput-Ji

Javascript

<script>
/* Iterative javascript program for merge sort */
 
    /*
     * Iterative mergesort function to sor t arr[0...n-1]
     */
    function mergeSort(arr , n) {
 
        // For current size of subarrays to
        // be merged curr_size varies from
        // 1 to n/2
        var curr_size;
 
        // For picking starting index of
        // left subarray to be merged
        var left_start;
 
        // Merge subarrays in bottom up
        // manner. First merge subarrays
        // of size 1 to create sorted
        // subarrays of size 2, then merge
        // subarrays of size 2 to create
        // sorted subarrays of size 4, and
        // so on.
        for (curr_size = 1; curr_size <= n - 1; curr_size = 2 * curr_size) {
 
            // Pick starting point of different
            // subarrays of current size
            for (left_start = 0; left_start < n - 1; left_start += 2 * curr_size) {
                // Find ending point of left
                // subarray. mid+1 is starting
                // point of right
                var mid = Math.min(left_start + curr_size - 1, n - 1);
 
                var right_end = Math.min(left_start + 2 * curr_size - 1, n - 1);
 
                // Merge Subarrays arr[left_start...mid]
                // & arr[mid+1...right_end]
                merge(arr, left_start, mid, right_end);
            }
        }
    }
 
    /*
     * Function to merge the two haves arr[l..m] and arr[m+1..r] of array arr
     */
    function merge(arr , l , m , r) {
        var i, j, k;
        var n1 = m - l + 1;
        var n2 = r - m;
 
        /* create temp arrays */
        var L = Array(n1).fill(0);
        var R = Array(n2).fill(0);
 
        /*
         * 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;
        j = 0;
        k = l;
        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++;
        }
    }
 
    /* Function to print an array */
    function printArray(A , size) {
        var i;
        for (i = 0; i < size; i++)
            document.write( A[i]+" ");
        document.write("<br/>");
    }
 
    /* Driver program to test above functions */
     
        var arr = [-74,48,-20,2,10,-84,-5,-9,11,-24,-91,2,-71,64,63,80,28,-30,-58,-11,-44,-87,-22,54,-74,-10,-55,-28,-46,29,10,50,-72,34,26,25,8,51,13,30,35,-8,50,65,-6,16,-2,21,-78,35,-13,14,23,-3,26,-90,86,25,-56,91,-13,92,-25,37,57,-20,-69,98,95,45,47,29,86,-28,73,-44,-46,65,-84,-96,-24,-12,72,-68,93,57,92,52,-45,-2,85,-63,56,55,12,-85,77,-39];
        var n = arr.length;
 
        document.write("Given array is <br/>");
        printArray(arr, n);
 
        mergeSort(arr, n);
 
        document.write("<br/>Sorted array is <br/>");
        printArray(arr, n);
 
// This code contributed by umadevi9616 
</script>

Output:

Given array is
12 11 13 5 6 7

Sorted array is
5 6 7 11 12 13

Time complexity of above iterative function is same as recursive, i.e., O(nLogn).

Space Complexity: O(n)

References:
http://csg.sph.umich.edu/abecasis/class/2006/615.09.pdf
This article is contributed by Shivam Agrawal. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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