<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 helper(bool alice, vector<int>& piles, int M, int idx, vector<vector<vector<int>>>& dp) {
    if (idx == piles.size())
        return 0;
    
    if (dp[alice][idx][M] != -1)
        return dp[alice][idx][M];

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

    for (int i = 1; i <= 2 * M; i++) {
        if (idx + i > piles.size())
            break;

        total += piles[idx + i - 1];

        if (alice) {
            res = max(res, total + helper(!alice, piles, max(M, i), idx + i, dp));
        } else {
            res = min(res, helper(!alice, piles, max(M, i), idx + i, dp));
        }
    }

    dp[alice][idx][M] = res;
    return res;
}

int stoneGameII(vector<int>& piles) {
    bool alice = true;
    int n = piles.size();
    vector<vector<vector<int>>> dp(2, vector<vector<int>>(n + 1, vector<int>(2 * n + 1, -1)));
    return helper(alice, piles, 1, 0, dp);
}
};
19776