Merge two sorted arrays

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/
#include<bits/stdc++.h>
using namespace std;

void mergeArrays(int arr1[], int arr2[], int n1,
                            int n2, int arr3[])
{
    int i = 0, j = 0, k = 0;
      // traverse the arr1 and insert its element in arr3
      while(i < n1){
      arr3[k++] = arr1[i++];
    }

      // now traverse arr2 and insert in arr3
      while(j < n2){
      arr3[k++] = arr2[j++];
    }

      // sort the whole array arr3
      sort(arr3, arr3+n1+n2);
}

// Driver code
int main()
{
    int arr1[] = {1, 3, 5, 7};
    int n1 = sizeof(arr1) / sizeof(arr1[0]);

    int arr2[] = {2, 4, 6, 8};
    int n2 = sizeof(arr2) / sizeof(arr2[0]);

    int arr3[n1+n2];
    mergeArrays(arr1, arr2, n1, n2, arr3);

    cout << "Array after merging" <<endl;
    for (int i=0; i < n1+n2; i++)
        cout << arr3[i] << " ";

    return 0;
}

Java

// Java program to merge two sorted arrays/
import java.util.*;

public class GFG {
    // Driver code
    public static void main(String[] args) {
        int arr1[] = {1, 3, 5, 7};
        int n1 = arr1.length;

        int arr2[] = {2, 4, 6, 8};
        int n2 = arr2.length;

        int arr3[] = new int[n1 + n2];
        mergeArrays(arr1, arr2, n1, n2, arr3);

        System.out.println("Array after merging");
        for (int i=0; i < n1+n2; i++)
            System.out.print(arr3[i] + " ");

    }

    public static void mergeArrays(int[] arr1, int[] arr2, int n1, int n2, int[] arr3){
        int i = 0;
        int j = 0;
        int k = 0;

        // traverse the arr1 and insert its element in arr3
        while(i < n1){
         arr3[k++] = arr1[i++];
        }

        // now traverse arr2 and insert in arr3
        while(j < n2){
         arr3[k++] = arr2[j++];
        }

        // sort the whole array arr3
        Arrays.sort(arr3);
    }
}

// This code is contributed by Tapesh(tapeshdua420)

Python3

# Python program to merge two sorted arrays/
def mergeArrays(arr1, arr2, n1, n2, arr3):
    i = 0
    j = 0
    k = 0

    # traverse the arr1 and insert its element in arr3
    while(i < n1):
        arr3[k] = arr1[i]
        k += 1
        i += 1

    # now traverse arr2 and insert in arr3
    while(j < n2):
        arr3[k] = arr2[j]
        k += 1
        j += 1

    # sort the whole array arr3
    arr3.sort()


# Driver code
if __name__ == '__main__':
    arr1 = [1, 3, 5, 7]
    n1 = len(arr1)

    arr2 = [2, 4, 6, 8]
    n2 = len(arr2)

    arr3 = [0 for i in range(n1+n2)]
    mergeArrays(arr1, arr2, n1, n2, arr3)

    print("Array after merging")
    for i in range(n1 + n2):
        print(arr3[i], end=" ")

# This code is contributed by Tapesh(tapeshdua420)

C#

// C# program to merge two sorted arrays
using System;
using System.Collections.Generic;

public class GFG
{
    public static void mergeArrays(int[] arr1, int[] arr2, int n1, int n2, int[] arr3) {
        int i = 0;
        int j = 0;
        int k = 0;

        // traverse the arr1 and insert its element in arr3
        while (i < n1) {
            arr3[k++] = arr1[i++];
        }

        // now traverse arr2 and insert in arr3
        while (j < n2) {
            arr3[k++] = arr2[j++];
        }

        // sort the whole array arr3
        Array.Sort(arr3);
    }

    public static void Main(string[] args)
    {
        int []arr1 = new int[] {1, 3, 5, 7};
        int n1 = arr1.Length;

        int []arr2 = new int[] {2, 4, 6, 8};
        int n2 = arr2.Length;

        int []arr3 = new int[n1 + n2];
        mergeArrays(arr1, arr2, n1, n2, arr3);

        Console.WriteLine("Array after merging");
        for (int i = 0; i < n1 + n2; i++)
            Console.Write(arr3[i] + " ");
    }
}

// This code is contributed by ajaymakavana.

Javascript

  // JavaScript program to merge two sorted arrays/
  function mergeArrays(arr1, arr2, n1, n2, arr3) {
      var i = 0, j = 0, k = 0;

      // traverse the arr1 and insert its element in arr3
      while (i < n1) {
          arr3[k++] = arr1[i++];
      }

      // now traverse arr2 and insert in arr3
      while (j < n2) {
          arr3[k++] = arr2[j++];
      }

      // sort the whole array arr3
      arr3.sort();
  }
  var arr1 = [1, 3, 5, 7];
  var n1 = arr1.length;
  var arr2 = [2, 4, 6, 8];
  var n2 = arr2.length;
  var arr3 = new Array(n1 + n2);
  mergeArrays(arr1, arr2, n1, n2, arr3);

  console.log("Array after merging");
  for (var i = 0; i < n1 + n2; i++)
      process.stdout.write(arr3[i] + " ");

// This code is contributed by tapeshdua420.

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 is the illustration of the above approach:

Take two sorted arrays Array1 and Array2 and an Empty Array3 . Take three pointers  ‘i’, ‘j’, and ‘k’ for comparisons, here ‘i’ pointer points towards 0th index of Array1, similarly ‘j’ and ‘k’ pointer point towards 0th index of Array2 and Array3

Initial Arrays

Step 1: Pick Smaller element which is 4 and insert in into Array3 and update the pointer ‘j ‘and ‘k’ after comparing ‘i’ and ‘j’.

Pick Smaller element which is 4

Step 2: Pick next smaller element which is 5 and insert in into Array3 and update the pointer ‘i’ and ‘k’ after comparing ‘i’ and ‘j’.

Pick next smaller element which is 5

Step 3: Pick next smaller element which is 7 and insert in into Array3 and update the pointer ‘j’ and ‘k ‘after comparing ‘i’ and ‘j’.

Pick next smaller element which is 7

Step 4: when ‘j’ pointer meets the length of Array2 then first while loop breaks and second while loop copies all elements from arr1 to arr3.

second while loop copies all elements from arr1 to arr3.

Step 5:  Pick adjacent element from Array1 and insert in into Array3 and update the pointer i and k

Pick adjacent element from Array1 and insert in into Array3

Step 6:     Pick remaining element from Array1 and insert in into Array3, when i pointer meets the length of Array1 that means k = n1+n2 and at last we have merge sorted Array3

ick remaining element from Array1 and insert in into Array3,

Below is the implementation of the above approach: 

C++

// C++ program to merge two sorted arrays/
#include<iostream>
using namespace std;

// Merge arr1[0..n1-1] and arr2[0..n2-1] into
// arr3[0..n1+n2-1]
void mergeArrays(int arr1[], int arr2[], int n1,
                             int n2, int arr3[])
{
    int i = 0, j = 0, k = 0;

    // Traverse both array
    while (i<n1 && j <n2)
    {
        // Check if current element of first
        // array is smaller than current element
        // of second array. If yes, store first
        // array element and increment first array
        // index. Otherwise do same with second array
        if (arr1[i] < arr2[j])
            arr3[k++] = arr1[i++];
        else
            arr3[k++] = arr2[j++];
    }

    // Store remaining elements of first array
    while (i < n1)
        arr3[k++] = arr1[i++];

    // Store remaining elements of second array
    while (j < n2)
        arr3[k++] = arr2[j++];
}

// Driver code
int main()
{
    int arr1[] = {1, 3, 5, 7};
    int n1 = sizeof(arr1) / sizeof(arr1[0]);

    int arr2[] = {2, 4, 6, 8};
    int n2 = sizeof(arr2) / sizeof(arr2[0]);

    int arr3[n1+n2];
    mergeArrays(arr1, arr2, n1, n2, arr3);

    cout << "Array after merging" <<endl;
    for (int i=0; i < n1+n2; i++)
        cout << arr3[i] << " ";

    return 0;
}

Java

// Java program to merge two sorted arrays
import java.util.*;
import java.lang.*;
import java.io.*;

class MergeTwoSorted
{
    // Merge arr1[0..n1-1] and arr2[0..n2-1]
    // into arr3[0..n1+n2-1]
    public static void mergeArrays(int[] arr1, int[] arr2, int n1,
                                int n2, int[] arr3)
    {
        int i = 0, j = 0, k = 0;

        // Traverse both array
        while (i<n1 && j <n2)
        {
            // Check if current element of first
            // array is smaller than current element
            // of second array. If yes, store first
            // array element and increment first array
            // index. Otherwise do same with second array
            if (arr1[i] < arr2[j])
                arr3[k++] = arr1[i++];
            else
                arr3[k++] = arr2[j++];
        }

        // Store remaining elements of first array
        while (i < n1)
            arr3[k++] = arr1[i++];

        // Store remaining elements of second array
        while (j < n2)
            arr3[k++] = arr2[j++];
    }

    public static void main (String[] args)
    {
        int[] arr1 = {1, 3, 5, 7};
        int n1 = arr1.length;

        int[] arr2 = {2, 4, 6, 8};
        int n2 = arr2.length;

        int[] arr3 = new int[n1+n2];

        mergeArrays(arr1, arr2, n1, n2, arr3);

        System.out.println("Array after merging");
        for (int i=0; i < n1+n2; i++)
            System.out.print(arr3[i] + " ");
    }
}

/* This code is contributed by Mr. Somesh Awasthi */

Python 3

# Python program to merge
# two sorted arrays

# Merge arr1[0..n1-1] and
# arr2[0..n2-1] into
# arr3[0..n1+n2-1]
def mergeArrays(arr1, arr2, n1, n2):
    arr3 = [None] * (n1 + n2)
    i = 0
    j = 0
    k = 0

    # Traverse both array
    while i < n1 and j < n2:

        # Check if current element
        # of first array is smaller
        # than current element of
        # second array. If yes,
        # store first array element
        # and increment first array
        # index. Otherwise do same
        # with second array
        if arr1[i] < arr2[j]:
            arr3[k] = arr1[i]
            k = k + 1
            i = i + 1
        else:
            arr3[k] = arr2[j]
            k = k + 1
            j = j + 1


    # Store remaining elements
    # of first array
    while i < n1:
        arr3[k] = arr1[i];
        k = k + 1
        i = i + 1

    # Store remaining elements
    # of second array
    while j < n2:
        arr3[k] = arr2[j];
        k = k + 1
        j = j + 1
    print("Array after merging")
    for i in range(n1 + n2):
        print(str(arr3[i]), end = " ")

# Driver code
arr1 = [1, 3, 5, 7]
n1 = len(arr1)

arr2 = [2, 4, 6, 8]
n2 = len(arr2)
mergeArrays(arr1, arr2, n1, n2);

# This code is contributed
# by ChitraNayal

C#

// C# program to merge
// two sorted arrays
using System;

class GFG
{
    // Merge arr1[0..n1-1] and
    // arr2[0..n2-1] into
    // arr3[0..n1+n2-1]
    public static void mergeArrays(int[] arr1, int[] arr2,
                                   int n1, int n2, int[] arr3)
    {
        int i = 0, j = 0, k = 0;

        // Traverse both array
        while (i < n1 && j < n2)
        {
            // Check if current element
            // of first array is smaller
            // than current element
            // of second array. If yes,
            // store first array element
            // and increment first array
            // index. Otherwise do same
            // with second array
            if (arr1[i] < arr2[j])
                arr3[k++] = arr1[i++];
            else
                arr3[k++] = arr2[j++];
        }

        // Store remaining
        // elements of first array
        while (i < n1)
            arr3[k++] = arr1[i++];

        // Store remaining elements
        // of second array
        while (j < n2)
            arr3[k++] = arr2[j++];
    }

    // Driver code
    public static void Main()
    {
        int[] arr1 = {1, 3, 5, 7};
        int n1 = arr1.Length;

        int[] arr2 = {2, 4, 6, 8};
        int n2 = arr2.Length;

        int[] arr3 = new int[n1+n2];

        mergeArrays(arr1, arr2, n1, n2, arr3);

        Console.Write("Array after merging\n");
        for (int i = 0; i < n1 + n2; i++)
            Console.Write(arr3[i] + " ");
    }
}

// This code is contributed
// by ChitraNayal

PHP

<?php
// PHP program to merge
// two sorted arrays

// Merge $arr1[0..$n1-1] and
//       $arr2[0..$n2-1] into
//       $arr3[0..$n1+$n2-1]
function mergeArrays(&$arr1, &$arr2,
                      $n1, $n2, &$arr3)
{
    $i = 0;
    $j = 0;
    $k = 0;

    // Traverse both array
    while ($i < $n1 && $j < $n2)
    {
        // Check if current element
        // of first array is smaller
        // than current element of
        // second array. If yes,
        // store first array element
        // and increment first array
        // index. Otherwise do same
        // with second array
        if ($arr1[$i] < $arr2[$j])
            $arr3[$k++] = $arr1[$i++];
        else
            $arr3[$k++] = $arr2[$j++];
    }

    // Store remaining elements
    // of first array
    while ($i < $n1)
        $arr3[$k++] = $arr1[$i++];

    // Store remaining elements
    // of second array
    while ($j < $n2)
        $arr3[$k++] = $arr2[$j++];
}

// Driver code
$arr1 = array(1, 3, 5, 7);
$n1 = sizeof($arr1);

$arr2 = array(2, 4, 6, 8);
$n2 = sizeof($arr2);

$arr3[$n1 + $n2] = array();
mergeArrays($arr1, $arr2, $n1,
                   $n2, $arr3);

echo "Array after merging \n" ;
for ($i = 0; $i < $n1 + $n2; $i++)
    echo $arr3[$i] . " ";

// This code is contributed
// by ChitraNayal
?>

Javascript

<script>
// javascript program to merge two sorted arrays

    // Merge arr1[0..n1-1] and arr2[0..n2-1]
    // into arr3[0..n1+n2-1]
    function mergeArrays(arr1,  arr2 , n1 , n2,  arr3) {
        var i = 0, j = 0, k = 0;

        // Traverse both array
        while (i < n1 && j < n2) {
            // Check if current element of first
            // array is smaller than current element
            // of second array. If yes, store first
            // array element and increment first array
            // index. Otherwise do same with second array
            if (arr1[i] < arr2[j])
                arr3[k++] = arr1[i++];
            else
                arr3[k++] = arr2[j++];
        }

        // Store remaining elements of first array
        while (i < n1)
            arr3[k++] = arr1[i++];

        // Store remaining elements of second array
        while (j < n2)
            arr3[k++] = arr2[j++];
    }


        var arr1 = [ 1, 3, 5, 7 ];
        var n1 = arr1.length;

        var arr2 = [ 2, 4, 6, 8 ];
        var n2 = arr2.length;

        var arr3 = Array(n1 + n2).fill(0);

        mergeArrays(arr1, arr2, n1, n2, arr3);

        document.write("Array after merging<br/>");
        for (i = 0; i < n1 + n2; i++)
            document.write(arr3[i] + " ");

// This code contributed by Rajput-Ji
</script>

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

Java

// Java program to merge two sorted arrays
//using maps
import java.io.*;
import java.util.*;

class GFG {

    // Function to merge arrays
    static 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<Integer,Boolean> mp = new TreeMap<Integer,Boolean>();

        // Inserting values to a map.
        for(int i = 0; i < n; i++)
        {
            mp.put(a[i], true);
        }
        for(int i = 0;i < m;i++)
        {
            mp.put(b[i], true);
        }

        // Printing keys of the map.
        for (Map.Entry<Integer,Boolean> me : mp.entrySet())
        {
            System.out.print(me.getKey() + " ");
        }
    }

    // Driver Code
    public static void main (String[] args)
    {
        int a[] = {1, 3, 5, 7}, b[] = {2, 4, 6, 8};
        int size = a.length;
        int size1 = b.length;

        // Function call
        mergeArrays(a, b, size, size1);
    }
}

// This code is contributed by rag2127

Python3

# Python program to merge two sorted arrays
# using maps
import bisect

# Function to merge arrays
def mergeArrays(a, b, n, m):
    # Declaring a map.
    # using map as a inbuilt tool
    # to store elements in sorted order.
    mp=[]

    # Inserting values to a map.
    for i in range(n):
        bisect.insort(mp, a[i])

    for i in range(m):
        bisect.insort(mp, b[i])

    # Printing keys of the map.
    for i in mp:
        print(i,end=' ')

# Driver code
arr1 = [1, 3, 5, 7]
arr2 = [2, 4, 6, 8]
size = len(arr1)
size1 = len(arr2)

# Function call
mergeArrays(arr1, arr2, size, size1)

# This code is contributed by Pushpesh Raj

C#

// C# program to merge two sorted arrays
//using maps
using System;
using System.Collections.Generic;

public class GFG {

  // Function to merge arrays
  static 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.
    SortedDictionary<int, Boolean> mp = new SortedDictionary<int, Boolean>();

    // Inserting values to a map.
    for (int i = 0; i < n; i++) {
      mp.Add(a[i], true);
    }
    for (int i = 0; i < m; i++) {
      mp.Add(b[i], true);
    }

    // Printing keys of the map.
    foreach (KeyValuePair<int, Boolean> me in mp) {
      Console.Write(me.Key + " ");
    }
  }

  // Driver Code
  public static void Main(String[] args) {
    int []a = { 1, 3, 5, 7 };
    int []b = { 2, 4, 6, 8 };
    int size = a.Length;
    int size1 = b.Length;

    // Function call
    mergeArrays(a, b, size, size1);
  }
}

// This code is contributed by gauravrajput1

Javascript

<script>
// javascript program to merge two sorted arrays
//using maps

    // Function to merge arrays
    function mergeArrays(a , b , n , m)
    {

        // Declaring a map.
        // using map as a inbuilt tool
        // to store elements in sorted order.
        var mp = new Map();

        // Inserting values to a map.
        for (i = 0; i < n; i++) {
            mp.set(a[i], true);
        }
        for (i = 0; i < m; i++) {
            mp.set(b[i], true);
        }
        var a = [];

        // Printing keys of the map.
        for ( me of mp.keys()) {
            a.push(me);
        }
        a.sort();
        for ( me of a) {
            document.write(me + " ");
        }
    }

    // Driver Code
        var a = [ 1, 3, 5, 7 ], b = [ 2, 4, 6, 8 ];
        var size = a.length;
        var size1 = b.length;

        // Function call
        mergeArrays(a, b, size, size1);

// This code is contributed by gauravrajput1
</script>

Output

1 2 3 4 5 6 7 8 

Time Complexity: O( nlog(n) + mlog(m) ) 
Auxiliary Space: O(N)
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