Stone Game — LeetCode 877 Python Solution

The problem

Alice and Bob play a game with piles of stones. There are an even number of piles arranged in a row, and each pile has a positive integer number of stones piles[i].

Example

Input

piles = [5,3,4,5]

Output

true

Explanation

Alice starts first, and can only take the first 5 or the last 5.

Python solution

class Solution:
    def stoneGame(self, piles: List[int]) -> bool:
        @cache
        def dfs(i: int, j: int) -> int:
            if i > j:
                return 0
            return max(piles[i] - dfs(i + 1, j), piles[j] - dfs(i, j - 1))

        return dfs(0, len(piles) - 1) > 0

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 877. Stone Game is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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