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C++ Program to Merge Two Sorted Arrays

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Given two sorted arrays, the task is to merge them in a sorted manner.
Examples: 

Input: arr1[] = { 1, 3, 4, 5}, arr2[] = {2, 4, 6, 8} 
Output: arr3[] = {1, 2, 3, 4, 4, 5, 6, 8}

Input: arr1[] = { 5, 8, 9}, arr2[] = {4, 7, 8} 
Output: arr3[] = {4, 5, 7, 8, 8, 9} 

Naive Approach:

It is the brute force method to do the same. Take all the elements of arr1 and arr2 in arr3. Then simply sort the arr3.

The implementation of above approach is:

C++




// C++ program to merge two sorted arrays 
//using maps 
#include<bits/stdc++.h>
using namespace std;
  
// Function to merge arrays
void mergeArrays(int a[], int b[], int n, int m) 
{
    // Declaring a map.
    // using map as a inbuilt tool
    // to store elements in sorted order.
    map<int, int> mp;
      
    // Inserting values to a map.
    for(int i = 0; i < n; i++)mp[a[i]]++;
      
      
    for(int i = 0;i < m;i++)mp[b[i]]++;
  
      
    // Printing keys of the map.
    for(auto j: mp)
    {
         for(int i=0; i<j.second;i++)cout<<j.first<<" ";
    }
}
  
// Driver Code
int main()
    int a[] = {1, 3, 5, 7}, b[] = {2, 4, 6, 8};
      
    int size = sizeof(a)/sizeof(int);
    int size1 = sizeof(b)/sizeof(int);
      
    // Function call
    mergeArrays(a, b, size, size1);
      
    return 0;
}
  
//This code is contributed by yashbeersingh42


Output

Array after merging
1 2 3 4 5 6 7 8 

Time Complexity : O((m+n) log(m+n)) , the whole size of arr3 is m+n
Auxiliary Space: O(1), No extra space is used

Method 2 (O(n1 * n2) Time and O(n1+n2) Extra Space) 

  1. Create an array arr3[] of size n1 + n2.
  2. Copy all n1 elements of arr1[] to arr3[]
  3. Traverse arr2[] and one by one insert elements (like insertion sort) of arr3[] to arr1[]. This step take O(n1 * n2) time.

We have discussed implementation of above method in Merge two sorted arrays with O(1) extra space
Method 3 (O(n1 + n2) Time and O(n1 + n2) Extra Space) 
The idea is to use Merge function of Merge sort

  1. Create an array arr3[] of size n1 + n2.
  2. Simultaneously traverse arr1[] and arr2[]. 
    • Pick smaller of current elements in arr1[] and arr2[], copy this smaller element to next position in arr3[] and move ahead in arr3[] and the array whose element is picked.
  3. If there are remaining elements in arr1[] or arr2[], copy them also in arr3[].

Below image is a dry run of the above approach: 

Below is the implementation of the above approach: 

C++





Output

Array after merging
1 2 3 4 5 6 7 8 

Output: 

Array after merging
1 2 3 4 5 6 7 8

Time Complexity : O(n1 + n2) 
Auxiliary Space : O(n1 + n2)

Method 4: Using Maps (O(nlog(n) + mlog(m)) Time and O(N) Extra Space) 

  1. Insert elements of both arrays in a map as keys.
  2. Print the keys of the map.

Below is the implementation of above approach. 

CPP




// C++ program to merge two sorted arrays 
//using maps 
#include<bits/stdc++.h>
using namespace std;
  
// Function to merge arrays
void mergeArrays(int a[], int b[], int n, int m) 
{
    // Declaring a map.
    // using map as a inbuilt tool
    // to store elements in sorted order.
    map<int, int> mp;
      
    // Inserting values to a map.
    for(int i = 0; i < n; i++)mp[a[i]]++;
      
      
    for(int i = 0;i < m;i++)mp[b[i]]++;
  
      
    // Printing keys of the map.
    for(auto j: mp)
    {
         for(int i=0; i<j.second;i++)cout<<j.first<<" ";
    }
}
  
// Driver Code
int main()
    int a[] = {1, 3, 5, 7}, b[] = {2, 4, 6, 8};
      
    int size = sizeof(a)/sizeof(int);
    int size1 = sizeof(b)/sizeof(int);
      
    // Function call
    mergeArrays(a, b, size, size1);
      
    return 0;
}
  
//This code is contributed by yashbeersingh42


Output

1 2 3 4 5 6 7 8 

Time Complexity: O( nlog(n) + mlog(m) ) 
Auxiliary Space: O(N)
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Last Updated : 19 Sep, 2023
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