<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:
    map<string, int> dp;
    int recur_a(vector<int> &a, int k, int m, bool turn)
    {
        int n = a.size();
        if(k >= n)
        {
            return 0;
        }
        string s = to_string(turn) + "-" + to_string(k) + "-" + to_string(m);
        if(dp.find(s) != dp.end()) return dp[s];
        int ans = 0;
        int total = 0;
        if(turn == false) ans = 1e9;
        for(int i =0;i < 2*m && k+i < n;i++)
        {
            if (turn)
                total += a[i+k];
            if(turn)
                ans = max(ans, total+ recur_a(a, i+k+1, max(i+1,m), !(turn)));
            else
            {
                ans = min(ans, recur_a(a, i+k+1, max(i+1,m),  !(turn)));
            }

            
        }
        dp[s] = ans;
        return ans;
    }
    int stoneGameII(vector<int>& a) {
        int n = a.size();
        int alice = 0;
        int ans = recur_a(a, 0, 1, true);
        return ans;
    }
};
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