<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:
    pair<int,int> find(int i , int x , int turn , vector<int>&arr,map<pair<int,pair<int,int>>,pair<int,int>>&dp){
        if(i==arr.size())return {0,0};
        if(dp.count({i,{x,turn}}))return dp[{i,{x,turn}}];
        if(turn){
            // alice turn
            pair<int,int>res;
            res.first = INT_MIN;
            for(int k = i;k<min((int)arr.size(),x+i);k++){
                int score = arr[k];
                if(i>0)score-=arr[i-1];
                int new_x = min((int)arr.size()-k-1,max(x,2*(k-i+1)));
                auto p = find(k+1,new_x,0,arr,dp);
                if(score+p.first>res.first){
                    res = p;
                    res.first+=score;
                }
            }
            return dp[{i,{x,turn}}]=res;
        }
        else{
            pair<int,int>res;
            res.second = INT_MIN;
            for(int k = i;k<min((int)arr.size(),x+i);k++){
                int score = arr[k];
                if(i>0)score-=arr[i-1];
                int new_x = min((int)arr.size()-k-1,max(x,2*(k-i+1)));
                auto p = find(k+1,new_x,1,arr,dp);
                if(score+p.second>res.second){
                    res = p;
                    res.second+=score;
                }
            }
            return dp[{i,{x,turn}}]=res;
        }
    }
    int stoneGameII(vector<int>& piles) {
        for(int i = 1;i<piles.size();i++)piles[i]+=piles[i-1];
        map<pair<int,pair<int,int>>,pair<int,int>>dp;
        auto ans = find(0,2,1,piles,dp);
        return ans.first;
    }
};
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