Alice and Bob continue their games with piles of stones. There are several stones arranged in a row, and each stone has an associated value which is an integer given in the array stoneValue.

Alice and Bob take turns, with Alice starting first. On each player’s turn, that player can take 1, 2, or 3 stones from the first remaining stones in the row.

The score of each player is the sum of the values of the stones taken. The score of each player is 0 initially.

The objective of the game is to end with the highest score, and the winner is the player with the highest score and there could be a tie. The game continues until all the stones have been taken.

Assume Alice and Bob play optimally.

Return “Alice” if Alice will win, “Bob” if Bob will win, or “Tie” if they will end the game with the same score.

Example

Input: values = [1,2,3,7]
Output: "Bob"
Explanation: Alice will always lose. Her best move will be to take three piles and the score become 6. Now the score of Bob is 7 and Bob wins

Solution

Great solution found here

/**
 * @param {number[]} stoneValue
 * @return {string}
 */
var stoneGameIII = function (stoneValue) {
  // dp[i] is the max score the current player can get when playing piles[i:]
  const dp = new Array(stoneValue.length).fill(-Infinity);
  for (let i = stoneValue.length - 1; i >= 0; i--) {
    let points = 0;
    for (let numStones = 1; numStones <= 3; numStones++) {
      // if there are not enough stones left, break
      if (i + numStones > stoneValue.length) break;
      // add the points of the stones taken
      points += stoneValue[i + numStones - 1];
      // dp[i] is the max of the points taken and the points the other player can get
      dp[i] = Math.max(dp[i], points - (dp[i + numStones] || 0));
    }
  }
  if (dp[0] === 0) return "Tie";
  if (dp[0] > 0) return "Alice";
  return "Bob";
};