LeetCode 292. Nim Game

Posted 2020-06-16

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：

当有1个石子时，我必赢。

当有2个石子时，我可以赢。

当有3个石子时，我可以赢。

当有4个石子时，我必输，因为第一轮无论我取几个石子，随后对方都会拿光剩余石子。这种情况值得注意，当面临剩余4个石子时，必输无疑。

当有5个石子时，我取走1个石子，则对方面临只有4个石子可取，必输。

当有6个石子时，我取走2个石子，则对方面临只有4个石子可取，必输。

当有7个石子时，我取走3个石子，则对方面临只有4个石子可取，必输。

当有8个石子时，无论第一轮我取走几个石子，对方都会使我在第二轮中面临4个石子，我必输。

由此推断，当石子个数为4的倍数时，我必输，其他情况都可以获胜。

1 bool canWinNim(int n) {
2     if (n%4==0) {
3         return false;
4     } else {
5         return true;
6     }
7 }