leetcode–877: 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.

解题思路:
先手必胜,比较奇数位和以及偶数位和的大小,先手一定会选择大的那个,确保只拿奇数位或者偶数位。
如[4,5,5,6]
奇数位和:4,+ 5 = 9
偶数位和:5 + 6 = 11
假如我是先手,则我先拿偶数位的6,对方拿4或者5,我接着拿5,那么我必胜。
又如[[4,2,5,8]]
奇数位和:4,+ 5 = 9
偶数位和:2 + 8= 10
假如我是先手,则我先拿偶数位的8,对方拿4或者5,我接着拿2,那么我必胜。
代码:直接返回true

class Solution(object):
    def stoneGame(self, piles):
        """
        :type piles: List[int]
        :rtype: bool
        """
        return True

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