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Check if two sorted arrays can be merged to form a sorted array with no adjacent pair from the same array
  • Last Updated : 23 Apr, 2021

Given two sorted arrays A[] and B[] of size N, the task is to check if it is possible to merge two given sorted arrays into a new sorted array such that no two consecutive elements are from the same array.

Examples:

Input: A[] = {3, 5, 8}, B[] = {2, 4, 6}
Output: Yes

Explanation: Merged array = {B[0], A[0], B[1], A[1], B[2], A[2]} 
Since the resultant array is sorted array, the required output is Yes. 

Input: A[] = {12, 4, 2, 5, 3}, B[] = {32, 13, 43, 10, 8}
Output: No



Approach: Follow the steps below to solve the problem:

  • Initialize a variable, say flag = true to check if it is possible to form a new sorted array by merging the given two sorted arrays such that no two consecutive elements are from the same array.
  • Initialize a variable, say prev to check if the previous element of the merge array are from the array A[] or the array B[]. If prev == 1 then the previous element are from the array A[] and if prev == 0 then the previous element are from the array B[].
  • Traverse both the array using variables, i and j and check the following conditions: 
    • If A[i] < B[j] and prev != 0 then increment the value of i and update the value of prev to 0.
    • If B[j] < A[i[ and prev != 1 then increment the value of j and update the value of prev to 1.
    • If A[i] == B[j] and prev != 1 then increment the value of j and update the value of prev to 1.
    • If A[i] == B[j] and prev != 0 then increment the value of i and update the value of prev to 0.
    • If none of the above condition satisfy then update flag = false.
  • Finally, print the value of flag.

Below is the implementation of the above approach:

C++




// C++ program to implement
// the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if it is possible to merge
// the two given arrays with given conditions
bool checkIfPossibleMerge(int A[], int B[], int N)
{
    // Stores index of
    // the array A[]
    int i = 0;
 
    // Stores index of
    // the array  B[]
    int j = 0;
 
    // Check if the previous element are from
    // the array A[] or from the array B[]
    int prev = -1;
 
    // Check if it is possible to merge the two
    // given sorted arrays with given conditions
    int flag = 1;
 
    // Traverse both the arrays
    while (i < N && j < N) {
 
        // If A[i] is less than B[j] and
        // previous element are not from A[]
        if (A[i] < B[j] && prev != 0) {
 
            // Update prev
            prev = 0;
 
            // Update i
            i++;
        }
 
        // If B[j] is less than A[i] and
        // previous element are not from B[]
        else if (B[j] < A[i] && prev != 1) {
 
            // Update prev
            prev = 1;
 
            // Update j
            j++;
        }
 
        // If A[i] equal to B[j]
        else if (A[i] == B[j]) {
 
            // If previous element
            // are not from B[]
            if (prev != 1) {
 
                // Update prev
                prev = 1;
 
                // Update j
                j++;
            }
 
            // If previous element is
            // not from A[]
            else {
 
                // Update prev
                prev = 0;
 
                // Update i
                i++;
            }
        }
 
        // If it is not possible to merge two
        // sorted arrays with given conditions
        else {
 
            // Update flag
            flag = 0;
            break;
        }
    }
 
    return flag;
}
 
// Driver Code
int main()
{
    int A[3] = { 3, 5, 8 };
    int B[3] = { 2, 4, 6 };
    int N = sizeof(A) / sizeof(A[0]);
 
    if (checkIfPossibleMerge(A, B, N)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java




// Java program to implement
// the above approach
import java.io.*;
 
class GFG{
 
// Function to check if it is possible to merge
// the two given arrays with given conditions
static boolean checkIfPossibleMerge(int[] A, int[] B,
                                    int N)
{
     
    // Stores index of
    // the array A[]
    int i = 0;
 
    // Stores index of
    // the array  B[]
    int j = 0;
 
    // Check if the previous element are from
    // the array A[] or from the array B[]
    int prev = -1;
 
    // Check if it is possible to merge the two
    // given sorted arrays with given conditions
    boolean flag = true;
 
    // Traverse both the arrays
    while (i < N && j < N)
    {
         
        // If A[i] is less than B[j] and
        // previous element are not from A[]
        if (A[i] < B[j] && prev != 0)
        {
             
            // Update prev
            prev = 0;
 
            // Update i
            i++;
        }
 
        // If B[j] is less than A[i] and
        // previous element are not from B[]
        else if (B[j] < A[i] && prev != 1)
        {
             
            // Update prev
            prev = 1;
 
            // Update j
            j++;
        }
 
        // If A[i] equal to B[j]
        else if (A[i] == B[j])
        {
             
            // If previous element
            // are not from B[]
            if (prev != 1)
            {
                 
                // Update prev
                prev = 1;
 
                // Update j
                j++;
            }
 
            // If previous element is
            // not from A[]
            else
            {
                 
                // Update prev
                prev = 0;
 
                // Update i
                i++;
            }
        }
 
        // If it is not possible to merge two
        // sorted arrays with given conditions
        else
        {
             
            // Update flag
            flag = false;
            break;
        }
    }
    return flag;
}
 
// Driver Code
public static void main(String[] args)
{
    int[] A = { 3, 5, 8 };
    int[] B = { 2, 4, 6 };
    int N = A.length;
 
    if (checkIfPossibleMerge(A, B, N))
    {
        System.out.println("Yes");
    }
    else
    {
        System.out.println("No");
    }
}
}
 
// This code is contributed by akhilsaini

Python3




# Python3 program to implement
# the above approach
 
# Function to check if it is possible
# to merge the two given arrays with
# given conditions
def checkIfPossibleMerge(A, B, N):
     
    # Stores index of
    # the array A[]
    i = 0
 
    # Stores index of
    # the array  B[]
    j = 0
 
    # Check if the previous element
    # are from the array A[] or from
    # the array B[]
    prev = -1
 
    # Check if it is possible to merge
    # the two given sorted arrays with
    # given conditions
    flag = 1
 
    # Traverse both the arrays
    while (i < N and j < N):
 
        # If A[i] is less than B[j] and
        # previous element are not from A[]
        if (A[i] < B[j] and prev != 0):
 
            # Update prev
            prev = 0
 
            # Update i
            i += 1
 
        # If B[j] is less than A[i] and
        # previous element are not from B[]
        elif (B[j] < A[i] and prev != 1):
 
            # Update prev
            prev = 1
 
            # Update j
            j += 1
 
        # If A[i] equal to B[j]
        elif (A[i] == B[j]):
 
            # If previous element
            # are not from B[]
            if (prev != 1):
                 
                # Update prev
                prev = 1
 
                # Update j
                j += 1
 
            # If previous element is
            # not from A[]
            else:
 
                # Update prev
                prev = 0
 
                # Update i
                i += 1
 
        # If it is not possible to merge two
        # sorted arrays with given conditions
        else:
 
            # Update flag
            flag = 0
            break
 
    return flag
 
# Driver Code
if __name__ == '__main__':
 
    A = [ 3, 5, 8 ]
    B = [ 2, 4, 6 ]
    N = len(A)
 
    if (checkIfPossibleMerge(A, B, N)):
        print("Yes")
    else:
        print("No")
 
# This code is contributed by akhilsaini

C#




// C# program to implement
// the above approach
using System;
 
class GFG{
 
// Function to check if it is possible to merge
// the two given arrays with given conditions
static bool checkIfPossibleMerge(int[] A, int[] B,
                                 int N)
{
     
    // Stores index of
    // the array A[]
    int i = 0;
 
    // Stores index of
    // the array  B[]
    int j = 0;
 
    // Check if the previous element are
    // from the array A[] or from the
    // array B[]
    int prev = -1;
 
    // Check if it is possible to merge
    // the two given sorted arrays with
    // given conditions
    bool flag = true;
 
    // Traverse both the arrays
    while (i < N && j < N)
    {
         
        // If A[i] is less than B[j] and
        // previous element are not from A[]
        if (A[i] < B[j] && prev != 0)
        {
             
            // Update prev
            prev = 0;
 
            // Update i
            i++;
        }
 
        // If B[j] is less than A[i] and
        // previous element are not from B[]
        else if (B[j] < A[i] && prev != 1)
        {
             
            // Update prev
            prev = 1;
 
            // Update j
            j++;
        }
 
        // If A[i] equal to B[j]
        else if (A[i] == B[j])
        {
             
            // If previous element
            // are not from B[]
            if (prev != 1)
            {
                 
                // Update prev
                prev = 1;
 
                // Update j
                j++;
            }
 
            // If previous element is
            // not from A[]
            else
            {
                 
                // Update prev
                prev = 0;
 
                // Update i
                i++;
            }
        }
 
        // If it is not possible to merge two
        // sorted arrays with given conditions
        else
        {
             
            // Update flag
            flag = false;
            break;
        }
    }
    return flag;
}
 
// Driver Code
public static void Main()
{
    int[] A = { 3, 5, 8 };
    int[] B = { 2, 4, 6 };
    int N = A.Length;
 
    if (checkIfPossibleMerge(A, B, N))
    {
        Console.WriteLine("Yes");
    }
    else
    {
        Console.WriteLine("No");
    }
}
}
 
// This code is contributed by akhilsaini

Javascript




<script>
 
// Javascript program to implement
// the above approach
 
// Function to check if it is possible to merge
// the two given arrays with given conditions
function checkIfPossibleMerge(A, B, N)
{
      
    // Stores index of
    // the array A[]
    let i = 0;
  
    // Stores index of
    // the array  B[]
    let j = 0;
  
    // Check if the previous element are from
    // the array A[] or from the array B[]
    let prev = -1;
  
    // Check if it is possible to merge the two
    // given sorted arrays with given conditions
    let flag = true;
  
    // Traverse both the arrays
    while (i < N && j < N)
    {
          
        // If A[i] is less than B[j] and
        // previous element are not from A[]
        if (A[i] < B[j] && prev != 0)
        {
              
            // Update prev
            prev = 0;
  
            // Update i
            i++;
        }
  
        // If B[j] is less than A[i] and
        // previous element are not from B[]
        else if (B[j] < A[i] && prev != 1)
        {
              
            // Update prev
            prev = 1;
  
            // Update j
            j++;
        }
  
        // If A[i] equal to B[j]
        else if (A[i] == B[j])
        {
              
            // If previous element
            // are not from B[]
            if (prev != 1)
            {
                  
                // Update prev
                prev = 1;
  
                // Update j
                j++;
            }
  
            // If previous element is
            // not from A[]
            else
            {
                  
                // Update prev
                prev = 0;
  
                // Update i
                i++;
            }
        }
  
        // If it is not possible to merge two
        // sorted arrays with given conditions
        else
        {
              
            // Update flag
            flag = false;
            break;
        }
    }
    return flag;
}
 
    // Driver Code
     
    let A = [ 3, 5, 8 ];
    let B = [ 2, 4, 6 ];
    let N = A.length;
  
    if (checkIfPossibleMerge(A, B, N))
    {
        document.write("Yes");
    }
    else
    {
        document.write("No");
    }
 
// This code is contributed by splevel62.
</script>
Output: 
Yes

 

Time Complexity: O(N)
Auxiliary Space: O(1)

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