Stone Game VII
Alice and Bob take turns playing a game, with Alice starting first.
There are n stones arranged in a row. On each player's turn, they can remove either the leftmost stone or the rightmost stone from the row and receive points equal to the sum of the remaining stones' values in the row. The winner is the one with the higher score when there are no stones left to remove.
Bob found that he will always lose this game, so he decided to minimize the score's difference. Alice's goal is to maximize the difference in the score.
Given an array of integers stones where stones[i] represents the value of the i^th stone from the left, return the difference in Alice and Bob's score if they both play optimally.
Example 1
Input
stones = [5,3,1,4,2]Output
6With optimal play, Alice ends with 18 points and Bob ends with 12 points, so the score difference is 6.
Example 2
Input
stones = [7,90,5,1,100,10,10,2]Output
122If both players play optimally, the final difference between Alice's and Bob's scores is 122.
Constraints
- n == stones.length
- 2 <= n <= 1000
- 1 <= stones[i] <= 1000