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C++ Program to Implement Merge Sort

C++ Program to Implement Merge Sort

The technique of merge sort is based on the strategy of divide and conquer. We divide the set of while data into smaller bits, arranged in sorted order followed by combining them into a larger item. It is also very good for the worst cases because, for the worst-case, this algorithm also has lower time complexity.

The complexity of Merge Sort Technique

  • Time Complexity: O(n log n) for all cases
  • Space Complexity: O(n)

Input ? the unsorted list: 14 20 78 98 20 45

Output ? Array after Sorting: 14 20 20 45 78 98


Merge (array, left, middle, right)

Input: The data set array, left, middle and right index

Output: The merged list

   nLeft := m - left+1
   nRight := right – m
   define arrays leftArr and rightArr of size nLeft and nRight respectively
   for i := 0 to nLeft do
      leftArr[i] := array[left +1]
   for j := 0 to nRight do
      rightArr[j] := array[middle + j +1]
   i := 0, j := 0, k := left
   while i < nLeft AND j < nRight do
      if leftArr[i] <= rightArr[j] then
         array[k] = leftArr[i]
         i := i+1
         array[k] = rightArr[j]
         j := j+1
         k := k+1
   while i < nLeft do
      array[k] := leftArr[i]
      i := i+1
      k := k+1
   while j < nRight do
      array[k] := rightArr[j]
      j := j+1
      k := k+1

mergeSort(array, left, right)

Input: An array of data, and lower and upper bound of the array

Output: The sorted Array

   if lower < right then
      mid := left + (right - left) /2
      mergeSort(array, left, mid)
      mergeSort (array, mid+1, right)
      merge(array, left, mid, right)

Example Code:

using namespace std;
void swapping(int &a, int &b) {     //swap the content of a and b
   int temp;
   temp = a;
   a = b;
   b = temp;
void display(int *array, int size) {
   for(int i = 0; i<size; i++)
      cout << array[i] << " ";
   cout << endl;
void merge(int *array, int l, int m, int r) {
   int i, j, k, nl, nr;
   //size of left and right sub-arrays
   nl = m-l+1; nr = r-m;
   int larr[nl], rarr[nr];
   //fill left and right sub-arrays
   for(i = 0; i<nl; i++)
      larr[i] = array[l+i];
   for(j = 0; j<nr; j++)
      rarr[j] = array[m+1+j];
   i = 0; j = 0; k = l;
   //marge temp arrays to real array
   while(i < nl && j<nr) {
      if(larr[i] <= rarr[j]) {
         array[k] = larr[i];
         array[k] = rarr[j];
   while(i<nl) {       //extra element in left array
      array[k] = larr[i];
      i++; k++;
   while(j<nr) {     //extra element in right array
      array[k] = rarr[j];
      j++; k++;
void mergeSort(int *array, int l, int r) {
   int m;
   if(l < r) {
      int m = l+(r-l)/2;
      // Sort first and second arrays
      mergeSort(array, l, m);
      mergeSort(array, m+1, r);
      merge(array, l, m, r);
int main() {
   int n;
   cout << "Enter the number of elements: ";
   cin >> n;
   int arr[n];     //create an array with given number of elements
   cout << "Enter elements:" << endl;
   for(int i = 0; i<n; i++) {
      cin >> arr[i];
   cout << "Array before Sorting: ";
   display(arr, n);
   mergeSort(arr, 0, n-1);     //(n-1) for last index
   cout << "Array after Sorting: ";
   display(arr, n);


CPP Program to Implement Merge Sort