<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 {
    map<tuple<int,int,char>,  pair<int,int> >dp;
    pair<int,int> f(vector<int>&piles,int idx,int m,char turn){
        if(idx>=piles.size()){
            return {0,0};
        }
        tuple<int,int,char>temp=make_tuple(idx,m,turn);
        auto it = dp.find(temp);
        if(it!=dp.end()){
            return it->second;
        }
        pair<int,int>mex={0,0};
        int pts=0;
        int m1=1;
        for(int i=idx;i<(idx+2*m) && i<piles.size();i++){
            pts+=piles[i];
            if(turn=='a'){
                // mex.first=max(mex.first,
                // pts+f(piles,i+1,max(m,piles[i]),'b').first);
                pair<int,int>n1=f(piles,i+1,max(m,m1),'b');
                n1.first+=pts;
                // cout<<"n1 first: "<<n1.first<<" "<<pts<<" idx: "<<i<<endl;
                if(mex.first<n1.first)mex=n1;
            }else{
                // mex.second=max(mex.second,
                // pts+f(piles,i+1,max(m,piles[i]),'a').second);
                pair<int,int>n2=f(piles,i+1,max(m,m1),'a');
                n2.second+=pts;
                if(mex.second<n2.second)mex=n2;
            }
            m1++;
        }
        // dp = mex;
        dp.insert({temp,mex});
        return mex;
    }   
public:
    int stoneGameII(vector<int>& piles) {
        pair<int,int>temp=f(piles,0,1,'a');
        cout<<temp.first<<" "<<temp.second<<endl;
        return temp.first;
    }
};
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