Stone Game IV

Problem Statement - link #

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.

Examples #

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 <= 10^5

Solutions #

class Solution {
public:
    bool winnerSquareGame(int n) {
    vector<int> dp(n+1,0);
        for (int i = 0; i <= n; i++) {
            if (dp[i]) {
                continue;
            }
            for (int k = 1; i + k * k <= n; k++) {
                dp[i + k * k] = true;
            }
        }
        return dp[n];   
    }
};