LeetCode 292 Nim Game

Posted 2020-08-15 SillyVicky

Problem: 

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.

Summary: 

双人游戏，两个人依次从一堆石头中拿走1-3块，最后一次拿石头的人胜利。给出石头总数n，若先方可胜返回true，否则返回false。

Analysis:

若石头有1-3块，则先方必胜。

若石头有4块，则无论先方怎么拿，后方必胜。

若石头有5-7块，则先方首先可拿成4块，先方必胜。

若石头有8块，则无论先方怎么拿，后方可拿成4块的状态，后方必胜。

故：n%4 == 0时，后方必胜，否则，先方必胜。

 1 class Solution {
 2 public:
 3     bool canWinNim(int n) {
 4         if (n % 4) {
 5             return true;
 6         }
 7         else {
 8             return false;
 9         }
10     }
11 };