<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:

    vector<int> piles;
    
    struct tuple_hash {
        template <class T1, class T2, class T3>
        std::size_t operator() (const std::tuple<T1, T2, T3>& t) const {
            auto hash1 = std::hash<T1>{}(std::get<0>(t));
            auto hash2 = std::hash<T2>{}(std::get<1>(t));
            auto hash3 = std::hash<T3>{}(std::get<2>(t));
            return hash1 ^ (hash2 << 1) ^ (hash3 << 2); // Combine the three hash values
        }
    };

    unordered_map<tuple<bool, int, int>, int, tuple_hash> cache;

    int dfs(bool alice, int i, int M) {
        //cout << "start: alice=" << alice << ", i=" << i << ", M=" << M << endl;
        if (i >= piles.size())
        {
            return 0;
        }

        auto it = cache.find(make_tuple(alice, i, M));
        if (it != cache.end())
        {
            return it->second;
        }

        //cout << "after dp check" << endl;

        
        int res = alice ? 0 : INT_MAX;
        int total = 0;

        for (int x = 1; x < 2 * M + 1; x++)
        {
            //cout << "for loop: i=" << i << ", x=" << x << endl;

            if (i + x > piles.size())
            {
                break;
            }

            total += piles[i + x - 1];
            //cout << "total updated: " << total << endl;


            if (alice) {
                int new_res = total + dfs(!alice, i + x, max(M, x));
                //cout << "alice: new_res=" << new_res << ", res=" << res << endl;
                res = max(res, new_res);
            } else {
                int new_res = dfs(!alice, i + x, max(M, x));
                //cout << "not alice: new_res=" << new_res << ", res=" << res << endl;
                res = min(res, new_res);
            }
        }

        //cout << "res: " << res << endl;

        cache.emplace(make_tuple(alice, i, M), res);
                //cout << "Cache updated: " << res << endl;

        
        return res;
    }

    int stoneGameII(vector<int>& piles) {
        this->piles = piles;

        return dfs(true, 0, 1);
    }
};

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