Stone Game II
Alice and Bob continue their games with piles of stones. There are a 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.
Alice and Bob take turns, with Alice starting first.
On each player's turn, that player can take all the stones in the first X remaining piles, where 1 <= X <= 2M. Then, set M = max(M, X). Initially, M = 1.
The game continues until all the stones have been taken.
Assuming Alice and Bob play optimally, return the maximum number of stones Alice can get.
Example 1
Input
piles = [2,7,9,4,4]Output
10If Alice takes one pile at the beginning, Bob takes two piles, then Alice takes two piles again, so Alice can get 10 stones total, which is better than taking two piles initially.
Example 2
Input
piles = [1,2,3,4,5,100]Output
104With optimal play, Alice can get a maximum of 104 stones.
Constraints
- 1 <= piles.length <= 100
- 1 <= piles[i] <= 10^4