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:
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.
Examples
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
1872. Stone Game VIII
Hard
50 Points
Array
Math
Dynamic Programming
Prefix Sum
Game Theory
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:
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.
Examples
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.