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# Iterative Merge Sort

Following is a typical recursive implementation of Merge Sort

## C++

 `// Recursive C++ program for merge sort``#include``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``#include` `/* 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

## 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

 ``

## PHP

 ` 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 ``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

## C

 `/* Iterative C program for merge sort */``#include``#include` `/* 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

## 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

 ``

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