292. Nim Game[E]

题目

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.

分析

  1. 只要能被4整除，你就输了。因为不论你怎么拿，对方都会凑到4。
  2. 如果不能被4整除，那你第一次把余数拿了，然后你模仿上面的策略，你就赢了。

代码

  1. return bool(n%4)