<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>

#include <bits/stdc++.h>
using namespace std;

class Solution {
    std::vector<std::unordered_map<size_t, std::pair<int, int>>> cache;

  public:
    int stoneGameII(vector<int>& piles) {
        for (int i = piles.size() - 2; i >= 0; --i) {
            piles[i] += piles[i + 1];
        }
        cache.resize(piles.size());
        return play(piles, 0, 1).first;
    }

    std::pair<int, int> play(const vector<int>& piles_sum, size_t cur, size_t M) {
        auto [it, inserted] = cache[cur].try_emplace(M, 0, 0);
        if (!inserted) {
            return it->second;
        }
        auto maxTake = 2 * M;
        if (maxTake >= piles_sum.size() - cur) {
            it->second = {piles_sum[cur], 0};
            return it->second;
        }
        int maxScore = 0;
        int other = 0;
        for (size_t take = 1; take <= maxTake; ++take) {
            auto take_sum = piles_sum[cur] - piles_sum[cur + take];
            auto [player1, player2] = play(piles_sum, cur + take, std::max(M, take));
            if (maxScore < player2 + take_sum) {
                maxScore = player2 + take_sum;
                other = player1;
            }
        }
        it->second = {maxScore, other};
        return it->second;
    }
};
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