<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 stoneGameII(const std::vector<int>& piles) {
        std::unordered_map<Nasral, std::pair<int, int>, Nasral::Hash> map;
        std::function<std::pair<int, int>(int, int, bool)> backtrack{
            [&piles, &map, &backtrack] (int index, int m, bool alice) -> std::pair<int, int> {
                std::pair<int, int> result{};
                if (index >= piles.size()) return result;
                if (map.contains({index, m, alice})) return map[{index, m, alice}];
                for (int i{1}; i <= (m * 2); ++i) {
                    if (index + i - 1 >= piles.size()) break;
                    int total{std::accumulate(piles.begin() + index, piles.begin() + index + i, 0)};
                    std::pair<int, int> nasral{backtrack(index + i, std::max(m, i), !alice)};
                    if (alice && (result.first < total + nasral.first)) {
                        result = {total + nasral.first, nasral.second};
                    } else if (!alice && (result.second < total + nasral.second)) {
                        result = {nasral.first, total + nasral.second};
                    }
                }
                map[{index, m, alice}] = result;
                return result;
            }
        };
        return backtrack({}, 1, true).first;
    }
private:
    struct Nasral {
        int index;
        int m;
        bool alice;
        
        bool operator==(const Nasral& other) const {
            return index == other.index && m == other.m && alice == other.alice;
        }
        struct Hash {
            std::size_t operator()(const Nasral& key) const {
                return std::hash<int>()(key.index) ^ std::hash<int>()(key.m) ^ std::hash<bool>()(key.alice);
            }
        };
    };
};
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