<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:
    def stoneGame(self, piles: List[int]) -> bool:
        ts=sum(piles)
        n=len(piles)
        dp=[[0 for i in range(n)]for j in range(n)]
        for i in range(0,n-1):
            dp[i][i+1]=max(piles[i],piles[i+1])
        for gap in range(3,n,2):
            for i in range(0,n-gap):
                j=i+gap
                dp[i][j]=max(piles[i]+min(dp[i+2][j],dp[i+1][j-1]),piles[j]+min(dp[i+1][j-1],dp[i][j-2]))
        alice_sum=dp[0][n-1]
        bob_sum=ts-alice_sum
        if(alice_sum>bob_sum):
            return True
        return False

        '''n=len(piles)
        s=0
        e=n-1
        p=self.alice_score(piles,s,e)
        return p

    def alice_score(self,piles,s,e):
        if(s==e):
            return piles[s]
        if(s>e):
            return 0
        return max(piles[0]+min(self.alice_score(piles,s+2,e),self.alice_score(piles,s+1,e-1)),piles[e-1]+min(self.alice_score(piles,s+1,e-1),self.alice_score(piles,s,e-2)))'''

        

        
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