Maximum sum in a 2 x n grid such that no two elements are adjacent

Given a rectangular grid of dimension 2 x n. We need to find out the maximum sum such that no two chosen numbers are adjacent, vertically, diagonally or horizontally.
Examples:

Input : 1 4 5
        2 0 0
Output : 7
If we start from 1 then we can add only 5 or 0. 
So max_sum = 6 in this case.
If we select 2 then also we can add only 5 or 0.
So max_sum = 7 in this case.
If we select from 4 or 0  then there is no further 
elements can be added.
So, Max sum is 7.

Input : 1 2 3 4 5
        6 7 8 9 10
Output : 24



This problem is an extension of Maximum sum such that no two elements are adjacent. Only thing to be changed is to take maximum element of both row of a particular column. We traverse column by column and maintain maximum sum considering two cases.
1) An element of current column is included. In this case we take maximum of two elements in current column.
2) An element of current column is excluded (or not included)

Below is the implementation of above steps.

C++

// C++ program to find maximum sum in a grid such that
// no two elements are adjacent.
#include<bits/stdc++.h>
#define MAX 1000
using namespace std;
  
// Function to find max sum without adjacent
int maxSum(int grid[2][MAX], int n)
{
    // Sum including maximum element of first column
    int incl = max(grid[0][0], grid[1][0]);
  
    // Not including first column's element
    int excl = 0, excl_new;
  
    // Traverse for further elements
    for (int i = 1; i<n; i++ )
    {
        // Update max_sum on including or excluding
        // of previous column
        excl_new = max(excl, incl);
  
        // Include current column. Add maximum element
        // from both row of current column
        incl = excl + max(grid[0][i], grid[1][i]);
  
        // If current column doesn't to be included
        excl = excl_new;
    }
  
    // Return maximum of excl and incl
    // As that will be the maximum sum
    return max(excl, incl);
}
  
// Driver code
int main()
{
    int grid[2][MAX] = {{ 1, 2, 3, 4, 5},
                        { 6, 7, 8, 9, 10}};
  
    int n = 5;
    cout << maxSum(grid, n);
  
    return 0;
}

Java

// JAVA Code for Maximum sum in a 2 x n grid
// such that no two elements are adjacent
import java.util.*;
  
class GFG {
      
    // Function to find max sum without adjacent
    public static int maxSum(int grid[][], int n)
    {
        // Sum including maximum element of first
        // column
        int incl = Math.max(grid[0][0], grid[1][0]);
       
        // Not including first column's element
        int excl = 0, excl_new;
       
        // Traverse for further elements
        for (int i = 1; i < n; i++ )
        {
            // Update max_sum on including or 
            // excluding of previous column
            excl_new = Math.max(excl, incl);
       
            // Include current column. Add maximum element
            // from both row of current column
            incl = excl + Math.max(grid[0][i], grid[1][i]);
       
            // If current column doesn't to be included
            excl = excl_new;
        }
       
        // Return maximum of excl and incl
        // As that will be the maximum sum
        return Math.max(excl, incl);
    }
      
    /* Driver program to test above function */
    public static void main(String[] args) 
    {
         int grid[][] = {{ 1, 2, 3, 4, 5},
                         { 6, 7, 8, 9, 10}};
  
         int n = 5;
         System.out.println(maxSum(grid, n));
    }
  }
// This code is contributed by Arnav Kr. Mandal.


Output:

24

Time Complexity : O(n)

This article is contributed by Sahil Chhabra. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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