2.Nim Game(尼姆博弈)

题目原文:

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

分析: 尼姆博弈

    分析题目的意思就是你和你朋友两个人都是很聪明的人,两个人做尼姆博弈的游戏。给一堆石头,两人轮流拿1--3个中的石头,最后一个拿石头的获胜。

给的提示是如果最后剩4个石头,则先拿的那个一定输给后拿的那个人。题目要求是你先拿,并且当已知石头总数的时候判断你自己是否能赢。

所以按照这个提示可以分析得到在石头的个数是4的倍数的时候后拿的那个人赢(因为 两个人都是足够聪明,开始那个人拿了x之后,第二个人再拿4-x,每次这样循环,那么最后一轮肯定剩4,则后拿的那个人赢)。故按照题目的意思,当石头的总数是4的倍数的时候先拿的人输,后拿的那个人赢。

最后给出我的源代码:

public boolean canWinNim(int n) {
        if(n%4==0)
            return false;
        else
            return true;
    }


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