<p>Alice and Bob take turns playing a game, with <strong>Alice starting first</strong>.</p>

<p>There are <code>n</code> stones arranged in a row. On each player&#39;s turn, they can <strong>remove</strong> either the leftmost stone or the rightmost stone from the row and receive points equal to the <strong>sum</strong> of the remaining stones&#39; values in the row. The winner is the one with the higher score when there are no stones left to remove.</p>

<p>Bob found that he will always lose this game (poor Bob, he always loses), so he decided to <strong>minimize the score&#39;s difference</strong>. Alice&#39;s goal is to <strong>maximize the difference</strong> in the score.</p>

<p>Given an array of integers <code>stones</code> where <code>stones[i]</code> represents the value of the <code>i<sup>th</sup></code> stone <strong>from the left</strong>, return <em>the <strong>difference</strong> in Alice and Bob&#39;s score if they both play <strong>optimally</strong>.</em></p>

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

<pre>
<strong>Input:</strong> stones = [5,3,1,4,2]
<strong>Output:</strong> 6
<strong>Explanation:</strong> 
- Alice removes 2 and gets 5 + 3 + 1 + 4 = 13 points. Alice = 13, Bob = 0, stones = [5,3,1,4].
- Bob removes 5 and gets 3 + 1 + 4 = 8 points. Alice = 13, Bob = 8, stones = [3,1,4].
- Alice removes 3 and gets 1 + 4 = 5 points. Alice = 18, Bob = 8, stones = [1,4].
- Bob removes 1 and gets 4 points. Alice = 18, Bob = 12, stones = [4].
- Alice removes 4 and gets 0 points. Alice = 18, Bob = 12, stones = [].
The score difference is 18 - 12 = 6.
</pre>

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

<pre>
<strong>Input:</strong> stones = [7,90,5,1,100,10,10,2]
<strong>Output:</strong> 122</pre>

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

<ul>
	<li><code>n == stones.length</code></li>
	<li><code>2 &lt;= n &lt;= 1000</code></li>
	<li><code>1 &lt;= stones[i] &lt;= 1000</code></li>
</ul>

class Solution {
public:
int solve(vector<int> &v,int i,int j,int turn,int sum,vector<vector<vector<int>>> &dp)
    {
        if(i>j || sum<0)
        {
            return 0;
        }

        if(dp[i][j][turn]!=-1)
        return dp[i][j][turn];

        int ans;
        if(turn==0)
        {
            ans=-1e9;
            ans=max(ans,sum-v[i]+solve(v,i+1,j,!turn,sum-v[i],dp));
            ans=max(ans,sum-v[j]+solve(v,i,j-1,!turn,sum-v[j],dp));
        }
        else
        {
            ans=1e9;
            ans=min(ans,-(sum-v[i])+solve(v,i+1,j,!turn,sum-v[i],dp));
            ans=min(ans,-(sum-v[j])+solve(v,i,j-1,!turn,sum-v[j],dp));
        }

        return dp[i][j][turn]=ans;
    }
    int stoneGameVII(vector<int>& v) {
        int i=0,j=v.size()-1;
        int turn=0;

        int sum=0;
        for(int k=0;k<v.size();k++)
        sum+=v[k];

        vector<vector<vector<int>>> dp(v.size()+1,vector<vector<int>>(v.size()+1,vector<int>(2,-1)));
        return solve(v,i,j,turn,sum,dp);
    }
};
328694