Package g1801_1900.s1872_stone_game_viii

Class Solution

java.lang.Object
g1801_1900.s1872_stone_game_viii.Solution
public class Solution extends java.lang.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
    Description
    Solution()
     

  • Method Summary

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

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • stoneGameVIII

      public int stoneGameVIII(int[] stones)