<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:
    unordered_map<string,int>um;
    int solve(int curri,vector<int>&presum,int x,int n){
        if(curri>=n)
            return 0;
        string cmb=to_string(curri)+"_"+to_string(x);
        if(um.find(cmb)!=um.end())
            return um[cmb];
        int ans=INT_MIN;
        for(int i=1;i<=2*x and curri+i<=n;i++){
            int end=min(curri+i,n); // next find sum-arr[curr to curr+i-1]
            int first=0;
            if(curri-1>=0)
                first=presum[curri-1];

            int next =solve(curri+i,presum,max(x,i),n);
            ans=max(ans,presum[curri+(i-1)]-first +(presum[n-1]-presum[curri+(i-1)])-next);
        }
        return um[cmb]=ans;
    }
    int stoneGameII(vector<int>& arr) {
        int n=arr.size();
        vector<int>presum(n,0);
        presum[0]=arr[0];
        for(int i=1;i<n;i++){
            presum[i]+=(presum[i-1]+arr[i]);
        }
        return solve(0,presum,1,n);
    }
};
/*

*/
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