<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:

    struct pair_hash
    {
        template<class T1, class T2>
        std::size_t operator() (const std::pair<T1, T2>& p) const {
            auto h1 = std::hash<T1>{}(p.first);
            auto h2 = std::hash<T2>{}(p.second);
            return h1 ^ h2;
        }
    };

    unordered_map<pair<int, int>, int, pair_hash> h[2];
    vector<int> prefix;

    int solve(int player, int i, int limit, int M)
    {
        if (i >= limit) {
            return 0;
        }

        auto p = make_pair(i, M);

        if (h[player].count(make_pair(i, M))) {
            return (!i) ? h[player][p] : prefix[limit] - prefix[i] - h[player][p];
        }

        int ans = 0;
        for (int j = 1; j <= 2*M && i + j <= limit; ++j) {
            ans = max(ans, prefix[i + j] - prefix[i] + solve(!player, i + j, limit, max(M, j)));
        }

        h[player][p] = ans;
        //cout << "[" << player << "][" << i << "]=" << ans << endl;
        return (!i) ? ans : prefix[limit] - prefix[i] - ans;
    }

    int stoneGameII(vector<int>& piles) {
        prefix = vector<int>(piles.size() + 1);
        for (int i = 1; i <= piles.size(); ++i) {
            prefix[i] = prefix[i - 1] + piles[i - 1];
        }
        h[0].reserve(piles.size() * piles.size());
        h[1].reserve(piles.size() * piles.size());
        return solve(0, 0, piles.size(), 1);
    }
};
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