<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<pair<int,int>,int>m;
 int dp[101][101][2];
 int solve(int i,int M,vector<int>&piles,int ch){
    
    if(i>=piles.size())return 0;
    if(dp[i][M][ch]!=-1)return dp[i][M][ch];
    int ans=0;
    if(ch==0)ans=INT_MAX;
    for(int j=i;j<i+2*M;j++){
    
        if(ch)
         ans=max(ans,m[{i,j}]+solve(j+1,max(M,(j-i+1)),piles,0));
         else{
          ans=min(ans,solve(j+1,max(M,j-i+1),piles,1));
         }
         
    }
    return dp[i][M][ch]=ans;
 }
    int stoneGameII(vector<int>& piles) {
       
       for(int i=0;i<piles.size();i++){
        int sum=0;
        for(int j=i;j<piles.size();j++){
            sum+=piles[j];
            m[{i,j}]=sum;
        }
       }
       memset(dp,-1,sizeof(dp));
       
       return solve(0,1,piles,1);
    }
};
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