<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 dp[101][101][101];
    int helper(vector<int> & piles,int start,int end,int m)
    {
        if(start>end)return 0;    
        if(start==end)return piles[start];
        if(dp[start][end][m]!=-1)return dp[start][end][m];
        if(start+(2*m)-1>=end)
        {
            int sum=0;
            for(int i=start;i<=end;i++)sum+=piles[i];
            return dp[start][end][m]=sum;
        }
        long long sum=0;
        int maxi=-1000000;
        for(int i=0;i<2*m;i++)
        {
            sum+=piles[start+i];
            int score=1000000;
            int range=max(i+1,m);
            for(int j=0;j<2*range;j++)
            {
                score=min(score,helper(piles,start+i+2+j,end,max(range,j+1)));
            }
            score+=sum;
            maxi=max(maxi,score);
        }
        return dp[start][end][m]=maxi;
    }
    int stoneGameII(vector<int>& piles) 
    {
        memset(dp,-1,sizeof(dp));
        return helper(piles,0,piles.size()-1,1);    
    }
};
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