m0877.py

"""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: piles = [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.

Constraints:

* 2 <= piles.length <= 500
* piles.length is even.
* 1 <= piles[i] <= 500
* sum(piles) is odd.
"""