#1140 - Stone Game II - LeetCode JavaScript Solutions

#1140 - Stone Game II

Problem Description

Alice and Bob continue their games with piles of stones. There are a number of piles arranged in a row, and each pile has a positive integer number of stones piles[i]. The objective of the game is to end with the most stones.

Alice and Bob take turns, with Alice starting first.

On each player's turn, that player can take all the stones in the first X remaining piles, where 1 <= X <= 2M. Then, we set M = max(M, X). Initially, M = 1.

The game continues until all the stones have been taken.

Assuming Alice and Bob play optimally, return the maximum number of stones Alice can get.

Solution

/**
 * @param {number[]} piles
 * @return {number}
 */
var stoneGameII = function(piles) {
  const n = piles.length;
  const cache = new Map();
  const suffixSums = new Array(n + 1).fill(0);

  for (let i = n - 1; i >= 0; i--) {
    suffixSums[i] = suffixSums[i + 1] + piles[i];
  }

  return maxStones(0, 1);

  function maxStones(index, m) {
    if (index >= n) return 0;
    if (2 * m >= n - index) return suffixSums[index];

    const key = `${index},${m}`;
    if (cache.has(key)) return cache.get(key);

    let opponentMin = Infinity;
    for (let x = 1; x <= 2 * m; x++) {
      opponentMin = Math.min(opponentMin, maxStones(index + x, Math.max(m, x)));
    }

    const result = suffixSums[index] - opponentMin;
    cache.set(key, result);
    return result;
  }
};