Game of Nim — LeetCode 1908 Python Solution

The problem

Alice and Bob take turns playing a game with Alice starting first. In this game, there are n piles of stones.

Example

Input

piles = [1]

Output

true

Explanation

There is only one possible scenario:

Python solution

class Solution:
    def nimGame(self, piles: List[int]) -> bool:
        @cache
        def dfs(st):
            lst = list(st)
            for i, x in enumerate(lst):
                for j in range(1, x + 1):
                    lst[i] -= j
                    if not dfs(tuple(lst)):
                        return True
                    lst[i] += j
            return False

        return dfs(tuple(piles))

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 1908. Game of Nim is filed here because LeetCode tags it Bit Manipulation, which is the vocabulary this hub collects.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

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