g1801_1900.s1872_stone_game_viii

Class Solution

java.lang.Object

g1801_1900.s1872_stone_game_viii.Solution

public class Solution
extends Object

1872 - Stone Game VIII.

Hard

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, while the number of stones is more than one , they will do the following:

1. Choose an integer x > 1, and remove the leftmost x stones from the row.
2. Add the sum of the removed stones’ values to the player’s score.
3. Place a new stone , whose value is equal to that sum, on the left side of the row.

The game stops when only one stone is left in the row.

The score difference between Alice and Bob is (Alice's score - Bob's score). Alice’s goal is to maximize the score difference, and Bob’s goal is the minimize the score difference.

Given an integer array stones of length n where stones[i] represents the value of the ith stone from the left , return the score difference between Alice and Bob if they both play optimally.

Example 1:

Input: stones = [-1,2,-3,4,-5]

Output: 5

Explanation:

• Alice removes the first 4 stones, adds (-1) + 2 + (-3) + 4 = 2 to her score, and places a stone of value 2 on the left. stones = [2,-5].

• Bob removes the first 2 stones, adds 2 + (-5) = -3 to his score, and places a stone of value -3 on the left. stones = [-3].

The difference between their scores is 2 - (-3) = 5.

Example 2:

Input: stones = [7,-6,5,10,5,-2,-6]

Output: 13

Explanation:

• Alice removes all stones, adds 7 + (-6) + 5 + 10 + 5 + (-2) + (-6) = 13 to her score, and places a stone of value 13 on the left. stones = [13].

The difference between their scores is 13 - 0 = 13.

Example 3:

Input: stones = [-10,-12]

Output: -22

Explanation: - Alice can only make one move, which is to remove both stones. She adds (-10) + (-12) = -22 to her score and places a stone of value -22 on the left. stones = [-22].

The difference between their scores is (-22) - 0 = -22.

Constraints:

• n == stones.length
• 2 <= n <= 105
• -104 <= stones[i] <= 104

Constructor Summary

Constructors

Constructor and Description
Solution()

Method Summary

Modifier and Type	Method and Description
int	stoneGameVIII(int[] stones)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Solution

public Solution()

Method Detail

stoneGameVIII

public int stoneGameVIII(int[] stones)