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.
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.
Time Complexity: O(n)
Space Complexity: O(2n) which is equal to O(n)
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