LeetCode292. 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.

1个石子，先手全部拿走；2个石子，先手全部拿走；3个石子，先手全部拿走；4个石子，后手面对的是先手的第1，2，3情况，后手必胜；5个石子，先手拿走1个让后手面对第4种情况，后手必败；6个石子，先手拿走2个让后手面对第4种情况，后手必败；…… 容易看出来，只有当出现了4的倍数，先手无可奈何，其余情况先手都可以获胜。 （石子数量为4的倍数）后手的获胜策略十分简单，每次取石子的数量，与上一次先手取石子的数量和为4即可； （石子数量不为4的倍数）先手的获胜策略也十分简单，每次都令取之后剩余的石子数量为4的倍数，他就处于后手的位置上，利用以上的策略获胜。

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