<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 n;
    vector<vector<vector<int>>>dp;

    int f(int i,int chance,int m,vector<int>&piles)
    {
        if(i>=n)
        {
            return 0;
        }
        if(dp[i][chance][m]!=-1)
        {
            return dp[i][chance][m];
        }

        int maxiAlice=(chance==1)?0:INT_MAX;

        int sum=0;
        // int maxiIdx=min(2*m,n-)
        for(int j=1;j<=2*m;j++)
        {
            int idx=i+j-1;

            if(idx>=n)
            {
                continue;
            }

            sum+=piles[idx];

            if(chance)
            {
                maxiAlice=max(maxiAlice,sum+f(idx+1,0,max(m,j),piles));
            }
            else
            {
                maxiAlice=min(maxiAlice,f(idx+1,1,max(m,j),piles));
            }

        }

        return dp[i][chance][m]=maxiAlice;
    }


    int stoneGameII(vector<int>& piles) 
    {

        n=piles.size();
        dp=vector<vector<vector<int>>>(n+1,vector<vector<int>>(2,vector<int>(200,-1)));
        int result=f(0,1,1,piles);
        return result;
    }
};
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