1463. Cherry Pickup II

https://leetcode.com/problems/cherry-pickup-ii

Description

Given a rows x cols matrix grid representing a field of cherries. Each cell in grid represents the number of cherries that you can collect.

You have two robots that can collect cherries for you, Robot #1 is located at the top-left corner (0,0) , and Robot #2 is located at the top-right corner (0, cols-1) of the grid.

Return the maximum number of cherries collection using both robots by following the rules below:

• From a cell (i,j), robots can move to cell (i+1, j-1) , (i+1, j) or (i+1, j+1).

• When any robot is passing through a cell, It picks it up all cherries, and the cell becomes an empty cell (0).

• When both robots stay on the same cell, only one of them takes the cherries.

• Both robots cannot move outside of the grid at any moment.

• Both robots should reach the bottom row in the grid.

Example 1:

**Input:** grid = [[3,1,1],[2,5,1],[1,5,5],[2,1,1]]
**Output:** 24
**Explanation:** Path of robot #1 and #2 are described in color green and blue respectively.
Cherries taken by Robot #1, (3 + 2 + 5 + 2) = 12.
Cherries taken by Robot #2, (1 + 5 + 5 + 1) = 12.
Total of cherries: 12 + 12 = 24.

Example 2:

**Input:** grid = [[1,0,0,0,0,0,1],[2,0,0,0,0,3,0],[2,0,9,0,0,0,0],[0,3,0,5,4,0,0],[1,0,2,3,0,0,6]]
**Output:** 28
**Explanation:** Path of robot #1 and #2 are described in color green and blue respectively.
Cherries taken by Robot #1, (1 + 9 + 5 + 2) = 17.
Cherries taken by Robot #2, (1 + 3 + 4 + 3) = 11.
Total of cherries: 17 + 11 = 28.

Example 3:

**Input:** grid = [[1,0,0,3],[0,0,0,3],[0,0,3,3],[9,0,3,3]]
**Output:** 22

Example 4:

**Input:** grid = [[1,1],[1,1]]
**Output:** 4

Constraints:

• rows == grid.length

• cols == grid[i].length

• 2 <= rows, cols <= 70

• 0 <= grid[i][j] <= 100

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