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# Stone Game

Alex and Lee play a game with piles of stones.  There are an even number of piles **arranged in a row**, and each pile has a positive integer number of stones `piles[i]`.

The objective of the game is to end with the most stones.  The total number of stones is odd, so there are no ties.

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

Assuming Alex and Lee play optimally, return `True` if and only if Alex wins the game.

**Example 1:**

```
Input: [5,3,4,5]
Output: true
Explanation: 
Alex starts first, and can only take the first 5 or the last 5.
Say he takes the first 5, so that the row becomes [3, 4, 5].
If Lee takes 3, then the board is [4, 5], and Alex takes 5 to win with 10 points.
If Lee takes the last 5, then the board is [3, 4], and Alex takes 4 to win with 9 points.
This demonstrated that taking the first 5 was a winning move for Alex, so we return true.
```

**Note:**

1. `2 <= piles.length <= 500`
2. `piles.length` is even.
3. `1 <= piles[i] <= 500`
4. `sum(piles)` is odd.

```java
class Solution {
    public boolean stoneGame(int[] piles) {
        // dp[i][j]: scores of Alex and Lee given piles[i:j], Alex picks first
        int dp[][][] = new int[piles.length][piles.length][], N = piles.length;
        // If only 1 pile is available then alex will take it
        // Diagonal base case
        for (int i = 0; i < N; i++)
            dp[i][i] = new int[] { piles[i], 0 };
        for (int i = piles.length - 1; i >= 0; i--) {
            // piles[i, ..., j] i and j are basically start and end pointers between which
            // we are picking stones
            for (int j = i + 1; j < piles.length; j++) {
                // Alex picks first , then he will get other pick after Lee has taken from
                // remaining,That means lee will take best possible now -> (I,J,0)
                // And Alex gets -> (I,J,1) score if Alex picks piles[i] (left pile)
                int pickLeftScore = piles[i] + dp[i + 1][j][1];
                // score if Alex picks piles[j] (right pile)
                int pickRightScore = piles[j] + dp[i][j - 1][1];
                if (pickLeftScore > pickRightScore) {
                    int leeScore = dp[i + 1][j][0];
                    dp[i][j] = new int[] { pickLeftScore, leeScore };
                } else {
                    int leeScore = dp[i][j - 1][0];
                    dp[i][j] = new int[] { pickRightScore, leeScore };
                }
            }
        }
        return dp[0][N - 1][0] > dp[0][N - 1][1];
    }
}
```


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