<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:
    int size;
    map<pair<int,int>, pair<int,int>> cache;
    vector<int> prefixSum;
    int stoneGameII(vector<int>& piles) {
        size = piles.size();
        int sum=0;
        for (int i=0;i<size;i++) {
            sum+=piles[i];
            prefixSum.push_back(sum);
        }
        return dfs(0,1,piles).first;
    }

    pair<int,int> dfs(int idx, int m, vector<int>& piles) {
        if (idx>=size) {
            return make_pair(0,0);
        }
        pair<int,int> result, temp;
        for (int i=1;i<=2*m;i++) {
            int sum = prefixSum[min(idx+i-1, size-1)];
            if (idx>0) {
                sum-=prefixSum[idx-1];
            }
            /*for (int j=idx;j<idx+i && j<size;j++) {
                sum+=piles[j];
            }*/
            if (cache.find(make_pair(idx+i, max(m,i))) != cache.end())  {
                temp = cache[make_pair(idx+i, max(m,i))];
            } else {
                temp = dfs(idx+i, max(m,i), piles);
            }
            if (i==0) {
                result = make_pair(sum+temp.second, temp.first);
            } else {
                if (sum+temp.second > result.first) {
                    result = make_pair(sum+temp.second, temp.first);
                }
            }
        }
        cache[make_pair(idx,m)] = result;
        return result;
    }
};
17053