1510. Stone Game IV

Hard

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Alice and Bob take turns playing a game, with Alice starting first.

Initially, there are n stones in a pile. On each player's turn, that player makes a move consisting of removing any non-zero square number of stones in the pile.

Also, if a player cannot make a move, he/she loses the game.

Given a positive integer n, return true if and only if Alice wins the game otherwise return false, assuming both players play optimally.

Example 1:

Input: n = 1
Output: true
Explanation: Alice can remove 1 stone winning the game because Bob doesn't have any moves.

Example 2:

Input: n = 2
Output: false
Explanation: Alice can only remove 1 stone, after that Bob removes the last one winning the game (2 -> 1 -> 0).

Example 3:

Input: n = 4
Output: true
Explanation: n is already a perfect square, Alice can win with one move, removing 4 stones (4 -> 0).

Constraints:

• 1 <= n <= 105

class Solution:
    def winnerSquareGame(self, n: int) -> bool:
        return self.recursion(n)
    
    @lru_cache(None)
    def recursion(self, n):
        if n == 0:
            return False
        for i in range(1, int(sqrt(n)) + 1):
            if not self.recursion(n-pow(i,2)): # Since We can remove sqaure of numbers
                return True
        return False