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

<p>Alice and Bob take turns, with Alice starting first.</p>

<p>On each player&#39;s turn, that player can take <strong>all the stones</strong> in the <strong>first</strong> <code>X</code> remaining piles, where <code>1 &lt;= X &lt;= 2M</code>. Then, we set <code>M = max(M, X)</code>. Initially, M = 1.</p>

<p>The game continues until all the stones have been taken.</p>

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

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">piles = [2,7,9,4,4]</span></p>

<p><strong>Output:</strong> <span class="example-io">10</span></p>

<p><strong>Explanation:</strong></p>

<ul>
	<li>If Alice takes one pile at the beginning, Bob takes two piles, then Alice takes 2 piles again. Alice can get <code>2 + 4 + 4 = 10</code> stones in total.</li>
	<li>If Alice takes two piles at the beginning, then Bob can take all three piles left. In this case, Alice get <code>2 + 7 = 9</code> stones in total.</li>
</ul>

<p>So we return 10 since it&#39;s larger.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">piles = [1,2,3,4,5,100]</span></p>

<p><strong>Output:</strong> <span class="example-io">104</span></p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= piles.length &lt;= 100</code></li>
	<li><code>1 &lt;= piles[i]&nbsp;&lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int solver(vector<int>& piles, int idx, int m, bool isAlice, map<pair<int, int>, int>& dpAlice, map<pair<int, int>, int>& dpBob) {
        int n = piles.size();

        if (idx == n) return 0;

        if (isAlice) {
            if (dpAlice.find({idx, m}) != dpAlice.end()) return dpAlice[{idx, m}];

            int maxi = 0;
            int sum = 0;
            for (int i = 1; i <= 2 * m; i++) {
                if (idx + i - 1 >= n) break;

                sum += piles[idx + i - 1];

                maxi = max(maxi, sum + solver(piles, idx + i, max(i, m), !isAlice, dpAlice, dpBob));
            }

            return dpAlice[{idx, m}] = maxi;
        } else {
            if (dpBob.find({idx, m}) != dpBob.end()) return dpBob[{idx, m}];

            int mini = INT_MAX;
            for (int i = 1; i <= 2 * m; i++) {
                if (idx + i - 1 >= n) break;

                mini = min(mini, solver(piles, idx + i, max(i, m), !isAlice, dpAlice, dpBob));
            }

            return dpBob[{idx, m}] = mini;
        }
    }

    int stoneGameII(vector<int>& piles) {
        map<pair<int, int>, int> dpAlice;
        map<pair<int, int>, int> dpBob;
        return solver(piles, 0, 1, true, dpAlice, dpBob);
    }
};

22498