LeetCode: 292 Nim Game(easy)

原创于 2019-04-18 10:20:38 发布 · 146 阅读

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本文探讨了Nim游戏的胜负策略，通过分析游戏规则，得出了一种简洁的判断方法。只要堆中石头的数量不是4的倍数，先手玩家就有机会赢得比赛。此策略适用于所有Nim游戏变体，为玩家提供了明确的胜算判断依据。

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题目：

You are playing the following Nim Game with your friend: There is a heap of stones on the table, each time one of you take turns to remove 1 to 3 stones. The one who removes the last stone will be the winner. You will take the first turn to remove the stones.

Both of you are very clever and have optimal strategies for the game. Write a function to determine whether you can win the game given the number of stones in the heap.

For example, if there are 4 stones in the heap, then you will never win the game: no matter 1, 2, or 3 stones you remove, the last stone will always be removed by your friend.

Credits:
Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.

代码：

class Solution {
public:
    bool canWinNim(int n) {
        return (n%4 != 0);
    }
};