Description
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
Solutions
Possible to pre-calculate for every single possible value.
Language: javascript(2026-08-10 06:47)DONE
CPU Performance100.00%
Memory Performance96.04%
const LIMIT = 100_000;
const res = Array(LIMIT + 1).fill(false);
res[0] = false;
res[1] = true;
for (let i = 2; i <= LIMIT; i++) {
let canWin = false;
for (let j = 1; j * j <= i; j++) {
if (!res[i - j * j]) {
canWin = true;
break;
}
}
res[i] = canWin;
}
/**
* @param {number} n
* @return {boolean}
*/
var winnerSquareGame = function(n) {
return res[n];
};