Cherry Pickup II
You are given a rows x cols matrix grid representing a field of cherries where grid[i][j] represents the number of cherries that you can collect from the (i, j) cell.
You have two robots that can collect cherries for you:
- Robot #1 is located at the top-left corner
(0, 0). - Robot #2 is located at the top-right corner
(0, cols - 1).
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 passes through a cell, it picks up all cherries, and the cell becomes an empty cell.
- When both robots stay in the same cell, only one takes the cherries.
- Both robots cannot move outside of the grid at any moment.
- Both robots should reach the bottom row in
grid.
Example 1
3 1 1 2 5 1 1 5 5 2 1 1
Input
grid = [[3,1,1],[2,5,1],[1,5,5],[2,1,1]]Output
24Robot #1 collects 12 cherries and Robot #2 collects 12 cherries, for a total of 24.
Example 2
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
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
28Robot #1 collects 17 cherries and Robot #2 collects 11 cherries, for a total of 28.
Constraints
- rows == grid.length
- cols == grid[i].length
- 2 <= rows, cols <= 70
- 0 <= grid[i][j] <= 100