<p>Alice and Bob play a game with piles of stones. There are an <strong>even</strong> number of piles arranged in a row, and each pile has a <strong>positive</strong> integer number of stones <code>piles[i]</code>.</p>

<p>The objective of the game is to end with the most stones. The <strong>total</strong> number of stones across all the piles is <strong>odd</strong>, so there are no ties.</p>

<p>Alice and Bob take turns, with <strong>Alice starting first</strong>. Each turn, a player takes the entire pile of stones either from the <strong>beginning</strong> or from the <strong>end</strong> of the row. This continues until there are no more piles left, at which point the person with the <strong>most stones wins</strong>.</p>

<p>Assuming Alice and Bob play optimally, return <code>true</code><em> if Alice wins the game, or </em><code>false</code><em> if Bob wins</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> piles = [5,3,4,5]
<strong>Output:</strong> true
<strong>Explanation:</strong> 
Alice starts first, and can only take the first 5 or the last 5.
Say she takes the first 5, so that the row becomes [3, 4, 5].
If Bob takes 3, then the board is [4, 5], and Alice takes 5 to win with 10 points.
If Bob takes the last 5, then the board is [3, 4], and Alice takes 4 to win with 9 points.
This demonstrated that taking the first 5 was a winning move for Alice, so we return true.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> piles = [3,7,2,3]
<strong>Output:</strong> true
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= piles.length &lt;= 500</code></li>
	<li><code>piles.length</code> is <strong>even</strong>.</li>
	<li><code>1 &lt;= piles[i] &lt;= 500</code></li>
	<li><code>sum(piles[i])</code> is <strong>odd</strong>.</li>
</ul>

class Solution {
public:
    // int Alice(vector<int> piles){
    //     int n=piles.size();
    //     if(n==2){
    //         return abs(piles[0]-piles[1]);
    //     }
    //     if(piles[0]>piles[n-1]){
    //         return piles[0]-Bob(vector<int>(piles.begin()+1,piles.end()));
    //     }
    //     else if(piles[n-1]>piles[0]){
    //         return piles[n-1]-Bob(vector<int>(piles.begin(),piles.begin()+n-1));
    //     }
    //     else{
    //         return piles[0]-min(Bob(vector<int>(piles.begin()+1,piles.end())),Bob(vector<int>(piles.begin(),piles.begin()+n-1)));
    //     }
    // }
    // int Bob(vector<int> piles){
    //     int n=piles.size();
    //     if(piles[0]>piles[n-1]){
    //         return piles[0]-Alice(vector<int>(piles.begin()+1,piles.end()));
    //     }
    //     else if(piles[n-1]>piles[0]){
    //         return piles[n-1]-Alice(vector<int>(piles.begin(),piles.begin()+n-1));
    //     }
    //     else{
    //         return piles[0]-min(Alice(vector<int>(piles.begin(),piles.begin()+n-1)),Alice(vector<int>(piles.begin()+1,piles.end())));
    //     }
    // }
    bool stoneGame(vector<int>& piles) {
        int n=piles.size();
        map<pair<int,int>,int> m;
        for(int i=0;i<n;i++){
            pair<int,int> p;
            p.first=i;
            p.second=i;
            m[p]=0;
        }
        for(int i=0;i<n;i++){
            for(int j=0;j<n-i;j++){
                pair<int,int> p;
                pair<int,int> q;
                pair<int,int> r;
                p.first=j;
                p.second=j+i;
                q.first=j;
                q.second=j+i-1;
                r.first=j+1;
                r.second=j+i;
                m[p]=max(piles[j]-m[r],piles[j+i]-m[q]);
            }
        }
        pair<int,int> p;
        p.first=0;
        p.second=n-1;
        if(m[p]>0) return true;
        return false;
    }
};
63068