Check if two sorted arrays can be merged to form a sorted array with no adjacent pair from the same array

Given two sorted arraysA[] 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:

Yes

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

Approach 2: Dynamic Programming:

The given problem can be solved using a dynamic programming approach. We can create a 2D boolean table dp[][] of size (N+1)x(N+1) where dp[i][j] represents if it is possible to merge the first i elements of array A and the first j elements of array B with given conditions.

• The base case is dp[0][0] = true, as we can merge 0 elements from both arrays.
• For each (i,j) such that i>0 and j>0, we can calculate dp[i][j] as follows:
• If A[i-1] == B[j-1], then we can merge both the elements into the resulting array, and the previous element can be from either array. So, dp[i][j] = dp[i-1][j-1].
• If A[i-1] < B[j-1], then we can only merge the element A[i-1] into the resulting array if the previous element is from array B. So, dp[i][j] = dp[i][j-1].
• If A[i-1] > B[j-1], then we can only merge the element B[j-1] into the resulting array if the previous element is from array A. So, dp[i][j] = dp[i-1][j].
  Finally, the answer is dp[N][N]. If dp[N][N] is true, it means it is possible to merge the entire arrays A and B with given conditions.

Yes

Time Complexity: O(N^2)
Auxiliary Space: O(N)