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)
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 email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Minimum product in a grid of adjacent elements
- Maximum sum such that no two elements are adjacent
- Maximum product of 4 adjacent elements in matrix
- Maximum sum in circular array such that no two elements are adjacent
- Maximum length subsequence with difference between adjacent elements as either 0 or 1
- Maximum length subsequence such that adjacent elements in the subsequence have a common factor
- Check if a grid can become row-wise and column-wise sorted after adjacent swaps
- Minimum difference between adjacent elements of array which contain elements from each row of a matrix
- Collect maximum points in a grid using two traversals
- Count of arrays in which all adjacent elements are such that one of them divide the another
- Number of ways to form an array with distinct adjacent elements
- Maximum sum of elements from each row in the matrix
- Sum of all maximum frequency elements in Matrix
- Maximum Subarray Sum Excluding Certain Elements
- Maximum sum subsequence with at-least k distant elements