3418 - Maximum Amount of Money Robot Can Earn.

Medium

You are given an m x n grid. A robot starts at the top-left corner of the grid (0, 0) and wants to reach the bottom-right corner (m - 1, n - 1). The robot can move either right or down at any point in time.

The grid contains a value coins[i][j] in each cell:

• If coins[i][j] >= 0, the robot gains that many coins.

• If coins[i][j] < 0, the robot encounters a robber, and the robber steals the absolute value of coins[i][j] coins.

The robot has a special ability to neutralize robbers in at most 2 cells on its path, preventing them from stealing coins in those cells.

Note: The robot's total coins can be negative.

Return the maximum profit the robot can gain on the route.

Example 1:

Input: coins = \[\[0,1,-1],1,-2,3,2,-3,4]

Output: 8

Explanation:

An optimal path for maximum coins is:

• Start at (0, 0) with 0 coins (total coins = 0).

• Move to (0, 1), gaining 1 coin (total coins = 0 + 1 = 1).

• Move to (1, 1), where there's a robber stealing 2 coins. The robot uses one neutralization here, avoiding the robbery (total coins = 1).

• Move to (1, 2), gaining 3 coins (total coins = 1 + 3 = 4).

• Move to (2, 2), gaining 4 coins (total coins = 4 + 4 = 8).

Example 2:

Input: coins = \[\[10,10,10],10,10,10]

Output: 40

Explanation:

An optimal path for maximum coins is:

• Start at (0, 0) with 10 coins (total coins = 10).

• Move to (0, 1), gaining 10 coins (total coins = 10 + 10 = 20).

• Move to (0, 2), gaining another 10 coins (total coins = 20 + 10 = 30).

• Move to (1, 2), gaining the final 10 coins (total coins = 30 + 10 = 40).

Constraints:

• m == coins.length

• n == coins[i].length

• 1 <= m, n <= 500

• -1000 <= coins[i][j] <= 1000