292. Nim Game

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.

Example:

Input: 4
Output: false 
Explanation: 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.

思路：

如果石头的个数是4的倍数，则不管先手取几块石头，另一个人后手补齐4颗，必输；如果不是4的倍数，则第一次取石头数除4的余数，后面与另一个人每次都补齐4颗，必胜。

Solution (C++):

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

性能：

Runtime: 4 ms  Memory Usage: 6.1 MB

思路：

Solution (C++):

性能：

Runtime: ms  Memory Usage: MB