<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:
    long long sum(int s, int e, vector<long long>& pre) {
        return pre[e] - pre[s - 1];
    }

    long long solve(int s, int e, vector<long long>& a, vector<long long>& pre,
                    vector<vector<long long>>& dp) {
        if (dp[s][e] != -1e18)
            return dp[s][e];
        if (s == e)
            return a[s-1];
        return dp[s][e] =
                   max(a[s-1] + sum(s + 1, e, pre) - solve(s + 1, e, a, pre, dp),
                       a[e-1] + sum(s, e - 1, pre) - solve(s, e - 1, a, pre, dp));
    }
    bool stoneGame(vector<int>& piles) {
        int n = piles.size();
        vector<long long> pre(n + 1), a(n + 1);
        for (int i = 1; i <= n; i++) {
            pre[i] = pre[i - 1] + piles[i-1];
        }
        vector<vector<long long>> dp(n + 1, vector<long long>(n + 1, -1e18));
        int alice = solve(1, n, a, pre, dp);
        int bob = pre[n] - alice;
        return alice>bob;
    }
};
26246