Alice and Bob take turns playing a game, with Alice starting first.
Initially, there is a number n
on the chalkboard. On each player's turn, that player makes a move consisting of:
- Choosing any
x
with0 < x < n
andn % x == 0
. - Replacing the number
n
on the chalkboard withn - x
.
Also, if a player cannot make a move, they lose the game.
Return true
if and only if Alice wins the game, assuming both players play optimally.
Example 1:
Input: n = 2
Output: true
Explanation: Alice chooses 1, and Bob has no more moves.
Example 2:
Input: n = 3
Output: false
Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.
Constraints:
-
1 <= n <= 1000
SOLUTION:
class Solution:
def DG(self, n: int) -> bool:
if n in self.cache:
return self.cache[n]
for x in range(1, n):
if n % x == 0 and not self.DG(n - x):
self.cache[n] = True
return True
self.cache[n] = False
return False
def divisorGame(self, n: int) -> bool:
self.cache = {}
return self.DG(n)
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