292. Nim Game——策略

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最新推荐文章于 2022-08-17 22:00:58 发布

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本文介绍了一种名为Nim的游戏，玩家轮流从一堆石头中移除1到3个石头，最后一个移除石头的人获胜。文章提供了判断先手是否能赢得比赛的简单策略，并通过代码示例说明了这一策略。

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292. Nim Game ——策略
Difficulty: Easy

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.

bool canWinNim(int n) {
    return n%4 != 0;
}

一条语句完成。
因为每个人都取不到4个，假设自己后走，要保证每轮自己和对方取得数量的和是4，这样就能确保每轮完后都有4的倍数个石头被取走。这样，如果我们先走的话，先把n除4的余数个石头拿走，这样不管怎样，最后都会留4个下来，这样子就必赢了。