<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 {

    int sum (vector<int>&piles , int index1 , int index2){

        if( index1 -1 >= 0)
        return piles[index2] - piles[index1-1];

        else return piles[index2];
    }
    int helper(vector<int>&piles , int index , int m , bool IsAlice , vector<int>&arr, unordered_map<string,int>&um){

        string hash = to_string(index) + " " + to_string(m) + " " + to_string(int(IsAlice));

        if( um.find(hash) != um.end()) return um[hash];
        // base case
        if( m >= piles.size()-index) {

            if(IsAlice) return sum(arr, index , piles.size()-1);
            else return 0;
        }

        // smaller problem
        
        int x = -1;
        if( !IsAlice) x = INT_MAX;

        for(int i = 1 ; i <= 2*m && index+i-1 < piles.size() ; i++){

            if(IsAlice)
            x = max(x , sum(arr , index , index+i-1)+ helper(piles, index+i, max(m,i) , !IsAlice , arr , um));

            else
            x = min(x , helper(piles, index+i, max(m,i) , !IsAlice , arr, um ) );
        }

        return um[hash] = x;

        // solve

    }
public:
    int stoneGameII(vector<int>& piles) {

        vector<int>arr = piles;
        unordered_map<string,int>um;
        for(int i = 1 ; i < piles.size() ; i++) arr[i] += arr[i-1];
        return helper(piles , 0 , 1 , true , arr, um);
        
    }

};
24478