1510. Stone Game IV

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.

class Solution {
    int dp[100001][2];
    bool solution(int stones, bool alice) {
        if(!stones) return !alice;
        if(dp[stones][alice] != -1) return dp[stones][alice];
        dp[stones][alice] = !alice;
        for(int i = 1; i*i <= stones and dp[stones][alice] == !alice; i++) {
            if(alice) {
                dp[stones][alice] |= solution(stones - i*i, !alice);
            } else {
                dp[stones][alice] &= solution(stones - i*i, !alice);
            }
        }
        return dp[stones][alice];
    }
public:
    bool winnerSquareGame(int n) {
        memset(dp,-1,sizeof(dp));
        return solution(n, true);
    }
};