<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 {
private:
    pair<int, int> pickStones(int i, int n, int M, bool isAlice,
                              vector<int>& piles, auto& dpAlice, auto& dpBob) {

        if (i >= n)
            return pair<int, int>{0, 0};

        if (isAlice && dpAlice[i].find(M) != dpAlice[i].end()) {
            return dpAlice[i][M];
        }

        if (!isAlice && dpBob[i].find(M) != dpBob[i].end()) {
            return dpBob[i][M];
        }

        pair<int, int> score = {INT_MIN, INT_MIN};
        int pickedStones = 0;

        for (int j = 1; j <= (2 * M) && (i + j - 1) < n; j++) {
            pickedStones += piles[i + j - 1];

            pair<int, int> tempScore = pickStones(i + j, n, max(M, j), !isAlice,
                                                  piles, dpAlice, dpBob);

            if (score.first == INT_MIN ||
                (isAlice && (score.first < (pickedStones + tempScore.first))) ||
                (!isAlice &&
                 (score.second < (pickedStones + tempScore.second)))) {
                score = {tempScore.first + (isAlice ? pickedStones : 0),
                         tempScore.second + (isAlice ? 0 : pickedStones)};
            }
        }

        if (isAlice)
            dpAlice[i][M] = score;
        else
            dpBob[i][M] = score;

        return score;
    }

public:
    int stoneGameII(vector<int>& piles) {
        int n = piles.size();

        vector<unordered_map<int, pair<int, int>>> dpAlice(n);
        vector<unordered_map<int, pair<int, int>>> dpBob(n);

        return pickStones(0, n, 1, true, piles, dpAlice, dpBob).first;
    }
};
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