#1510 - Stone Game IV

Hard • View on LeetCode • View on GitHub

Problem 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.

Solution

/**
 * @param {number} n
 * @return {boolean}
 */
var winnerSquareGame = function(n) {
  const dp = new Array(n + 1).fill(false);

  for (let stones = 1; stones <= n; stones++) {
    for (let square = 1; square * square <= stones; square++) {
      if (!dp[stones - square * square]) {
        dp[stones] = true;
        break;
      }
    }
  }

  return dp[n];
};