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
.
Example 1:
Input: n = 4
Output: false
Explanation: These are the possible outcomes:
- You remove 1 stone. Your friend removes 3 stones, including the last stone. Your friend wins.
- You remove 2 stones. Your friend removes 2 stones, including the last stone. Your friend wins.
- 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
Constraints:
-
1 <= n <= 231 - 1
SOLUTION:
class Solution:
def canWinNim(self, n: int) -> bool:
return n != (n >> 2) << 2
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