#leetcode#Nim Game

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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.

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尼姆游戏，咋一看没有头绪，可以从简单case开始分析，面试时也可以给面试官展示思考过程

n = 1, win

n = 2, win

n = 3, win

n = 4, lose

n = 5, win, 5 - 1 = 4

n = 6, win, 6 - 2 = 4

n = 7, win, 7 - 3 = 4

n = 8, lose

n = 9, win, 9 - 1 = 8

...

不难发现规律，如果你能让你的对手抽取时台面上剩下4的倍数个石头的话，你就赢了

其实对数字敏感的话，读题时每次可以取1，2，或3个石头就应该联想到他们都是4的余数

public class Solution {
    public boolean canWinNim(int n) {
        if(n <= 0 )
            return false;
        return n % 4 != 0; 
    }
}

时间复杂度O（1）