292. Nim Game
Question
Total Accepted: 30675 Total
Submissions: 61031 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.
Hint:
- 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?
Credits:
Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.
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//思路首先：将问题规模缩小，找规律：
//桌子上只有1个我必赢，2个我必赢，3个我必赢，4个我必输，5个我必赢，6个必赢，7个必赢
//8个，就是两个4，我第一轮无论怎么摸石头都能让对手最后（以4为一个坎）摸完石头，所以必输
//也就是说n%4==0必输了哦？最后试了一下，的确是这样的。
class Solution {
public:
bool canWinNim(int n) {
return n%4!=0;//卧槽，此题代码可以如此简单，意义何在？
}
};