Nim Game

• Nim Game
  • 题目描述
  • 解法

Nim Game

题目描述

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.

解法

代码如下:

public static boolean canWinNim(int n) {
    return n % 4 != 0;
}

思考过程:

首先，得到数字4的一方肯定输，就像例子所解释的那样。

继续延伸思考，发现得到数字8的一方肯定输。

如此思考便会发现只要是数字4的倍数就肯定输了。

这样的思考就是通过样例来发现规律，是一种不错的思维方式。

时空复杂度: 时间复杂度是O(1), 空间复杂度是O(1)