Stone Game II — LeetCode 1140 Python Solution

The problem

Alice and Bob continue their games with piles of stones. There are a number of piles arranged in a row, and each pile has a positive integer number of stones piles[i].

Python solution

class Solution:
    def stoneGameII(self, piles: List[int]) -> int:
        @cache
        def dfs(i, m):
            if m * 2 >= n - i:
                return s[n] - s[i]
            return max(
                s[n] - s[i] - dfs(i + x, max(m, x)) for x in range(1, m << 1 | 1)
            )

        n = len(piles)
        s = list(accumulate(piles, initial=0))
        return dfs(0, 1)

Complexity

Pattern: Prefix Sum

Precompute running totals once so any range query becomes a single subtraction. LeetCode 1140. Stone Game II is filed here because LeetCode tags it Prefix Sum, which is the vocabulary this hub collects.

The prefix sum guide has the Python template for the pattern and the 157 LeetCode problems that use it.

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