<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 sz;
    vector<vector<int>> aliceMemo;
    vector<vector<int>> bobMemo;
    int solveBob(int m, vector<int>& piles, int cur) {
        if(cur == sz) {
            return 0;
        }
        else if(bobMemo[m][cur] != -1) {
            return bobMemo[m][cur];
        }

        int minStones = INT_MAX;

        for(int i = cur; i < 2*m + cur && i < sz; ++i) {
            minStones = min(minStones, solveAlice(max(m, i-cur+1), piles, i+1));
        }
       
        return bobMemo[m][cur] = minStones;
    }

    int solveAlice(int m, vector<int>& piles, int cur) {
        if(cur == sz) {
            return 0;
        }
        else if(aliceMemo[m][cur] != -1) {
            return aliceMemo[m][cur];
        }
        int maxStones = 0;
        int sum = 0;
        for(int i = cur; i < 2*m + cur && i < sz; ++i) {
            sum += piles[i];
            maxStones = max(maxStones, solveBob(max(m, i-cur+1), piles, i+1) + sum);
        }


        return aliceMemo[m][cur] = maxStones;
        

    }

    int stoneGameII(vector<int>& piles) {
        sz = piles.size();
        aliceMemo.resize(sz + 1, vector<int>(sz, -1));
        bobMemo.resize(sz + 1, vector<int>(sz, -1));
        return solveAlice(1, piles, 0);
    }
};
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