292. Nim Game

1. Question

You are playing the following Nim Game with your friend:

  • Initially, there is a heap of stones on the table.
  • You and your friend will alternate taking turns, and you go first.
  • On each turn, the person whose turn it is will remove 1 to 3 stones from the heap.

  • The one who removes the last stone is the winner.

Given n, the number of stones in the heap, return true if you can win the game assuming both you and your friend play optimally, otherwise return false.

2. Examples

Example 1:

Input: n = 4
Output: false
Explanation: These are the possible outcomes:

1. You remove 1 stone. Your friend removes 3 stones, including the last stone. Your friend wins.
2. You remove 2 stones. Your friend removes 2 stones, including the last stone. Your friend wins.
3. You remove 3 stones. Your friend removes the last stone. Your friend wins.
   In all outcomes, your friend wins.

Example 2:

Input: n = 1
Output: true

Example 3:

Input: n = 2
Output: true

3. Constraints

  • 1 <= n <= 231 - 1

4. References

来源:力扣(LeetCode) 链接:https://leetcode-cn.com/problems/nim-game 著作权归领扣网络所有。商业转载请联系官方授权,非商业转载请注明出处。

5. Solutions

如果数是4的余数必输

class Solution {
    public boolean canWinNim(int n) {
        return n % 4 != 0;
    }
}
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