Leetcode Nim Game

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.

Hint:

1. If there are 5 stones in the heap, could you figure out a way to remove the stones such that you will always be the winner?

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解题思路：

I think this thinking way can help us to solve and understand this problem quickly.

First,Let's begin with some tries.
when the rock is 1(win) 2(win) 3(win) 4(lose) I think everyone can do this,then we stop and think.

After you take rock and your friend becomes "you" think it carefully for example. when there are 4 rocks,after your taking ,there are three situations.so your friend begin with 1,2,or 3 you lose(when there are 4 rocks) = your friend win = start with(4-1),(4-2),(4-3) win

so there must be 3 win before 1 lose

so 4 is a group.

in c language we just return n%4

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Java code:

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

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Reference:

1. https://leetcode.com/discuss/64188/an-easy-thinking-to-analysis-this-problem