Solution: Cherry Pickup

Statement▼

You are given an $n \times n$ grid representing a field of cherries. Each cell in the grid can have one of three possible values:

Your task is to find the maximum number of cherries that can be collected while following these rules:

Start at the top-left corner $(0,0)$ and reach the bottom-right corner $(n-1,~n-1)$ by only moving right or down through valid cells ( $0$ or $1$ ).
After reaching the bottom-right corner, return to the starting point $(0, 0)$ by only moving left or up through valid cells.
When passing through a valid cell containing a cherry, pick it up, and the cell becomes empty (its value changes from $1$ to $0$ ).
If there is no valid path between $(0,0)$ and $(n-1,~n-1)$ , then no cherries can be collected. Return ...

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Problem

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Solution

You are given an $n \times n$ grid representing a field of cherries. Each cell in the grid can have one of three possible values:

Your task is to find the maximum number of cherries that can be collected while following these rules:

Start at the top-left corner $(0,0)$ and reach the bottom-right corner $(n-1,~n-1)$ by only moving right or down through valid cells ( $0$ or $1$ ).
After reaching the bottom-right corner, return to the starting point $(0, 0)$ by only moving left or up through valid cells.
When passing through a valid cell containing a cherry, pick it up, and the cell becomes empty (its value changes from $1$ to $0$ ).
If there is no valid path between $(0,0)$ and $(n-1,~n-1)$ , then no cherries can be collected. Return ...