merge sort time complexity code example

Example 1: Merge sort in c++

#include <iostream>
using namespace std;
 

void merge(int arr[], int l, int m, int r)
{
    int n1 = m - l + 1;
    int n2 = r - m;
 
 
    int L[n1], R[n2];
 
   
    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];

 
    int i = 0;
 
    
    int j = 0;
 
    
    int k = l;
 
    while (i < n1 && j < n2) {
        if (L[i] <= R[j]) {
            arr[k] = L[i];
            i++;
        }
        else {
            arr[k] = R[j];
            j++;
        }
        k++;
    }
 
  
    while (i < n1) {
        arr[k] = L[i];
        i++;
        k++;
    }
 
   
    while (j < n2) {
        arr[k] = R[j];
        j++;
        k++;
    }
}
 

void mergeSort(int arr[],int l,int r){
    if(l>=r){
        return;
    }
    int m = (l+r-1)/2;
    mergeSort(arr,l,m);
    mergeSort(arr,m+1,r);
    merge(arr,l,m,r);
}
 

void printArray(int A[], int size)
{
    for (int i = 0; i < size; i++)
        cout << A[i] << " ";
}
 

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;
}

Example 2: time complexity of merge sort

O(n*Log n):

The time complexity of MergeSort is O(n*Log n) in all the 3 cases 
(worst, average and best).
As the mergesort always divides the array into two halves 
and takes linear time to merge two halves.

Example 3: merge sort algorithm

/*  
    a[] is the array, p is starting index, that is 0, 
    and r is the last index of array. 
*/

#include <stdio.h>

// lets take a[5] = {32, 45, 67, 2, 7} as the array to be sorted.

// merge sort function
void mergeSort(int a[], int p, int r)
{
    int q;
    if(p < r)
    {
        q = (p + r) / 2;
        mergeSort(a, p, q);
        mergeSort(a, q+1, r);
        merge(a, p, q, r);
    }
}

// function to merge the subarrays
void merge(int a[], int p, int q, int r)
{
    int b[5];   //same size of a[]
    int i, j, k;
    k = 0;
    i = p;
    j = q + 1;
    while(i <= q && j <= r)
    {
        if(a[i] < a[j])
        {
            b[k++] = a[i++];    // same as b[k]=a[i]; k++; i++;
        }
        else
        {
            b[k++] = a[j++];
        }
    }
  
    while(i <= q)
    {
        b[k++] = a[i++];
    }
  
    while(j <= r)
    {
        b[k++] = a[j++];
    }
  
    for(i=r; i >= p; i--)
    {
        a[i] = b[--k];  // copying back the sorted list to a[]
    } 
}

// function to print the array
void printArray(int a[], int size)
{
    int i;
    for (i=0; i < size; i++)
    {
        printf("%d ", a[i]);
    }
    printf("\n");
}
 
int main()
{
    int arr[] = {32, 45, 67, 2, 7};
    int len = sizeof(arr)/sizeof(arr[0]);
 
    printf("Given array: \n");
    printArray(arr, len);
    
    // calling merge sort
    mergeSort(arr, 0, len - 1);
 
    printf("\nSorted array: \n");
    printArray(arr, len);
    return 0;
}