How do you solve Stone Game VIII on LeetCode?

Stone Game VIII (LeetCode #1872) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The game is about strategic removal of stones to maximize score differences.

What is the brute force solution for Stone Game VIII?

The brute force approach for Stone Game VIII is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we simulate all possible moves Alice and Bob can make. We recursively calculate the scores for each possible removal of stones and keep track of the maximum score difference. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Stone Game VIII?

Stone Game VIII uses the following concepts: Array, Math, Dynamic Programming, Prefix Sum, Game Theory. The recommended patterns to study are: Dynamic Programming, Prefix Sum.

What are the interview tips for Stone Game VIII?

Understand the game theory aspect of the problem. Practice prefix sums and dynamic programming concepts. Think about how both players will play optimally.

What are common mistakes when solving Stone Game VIII?

Not considering the optimal strategy for both players. Overcomplicating the recursive solution without realizing a linear approach is possible.

#1872

Stone Game VIII

Hard

ArrayMathDynamic ProgrammingPrefix SumGame TheoryDynamic ProgrammingPrefix Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution leverages dynamic programming and prefix sums to compute the maximum score difference in linear time. We can maintain a running total of the scores and use it to calculate the best possible outcome for Alice and Bob.

⚙️

Algorithm

3 steps

1Step 1: Calculate the prefix sums for the stones array.
2Step 2: Initialize a variable to keep track of the maximum score difference.
3Step 3: Iterate through the stones array, updating the maximum score difference based on the prefix sums.

solution.py8 lines

1def stoneGameVIII(stones):
2    n = len(stones)
3    for i in range(1, n):
4        stones[i] += stones[i - 1]
5    max_diff = stones[0]
6    for i in range(1, n - 1):
7        max_diff = max(max_diff, stones[i])
8    return max_diff

ℹ

Complexity note: The time complexity is O(n) because we only make a single pass through the stones array to compute the prefix sums and another pass to find the maximum score difference.

1The game is about strategic removal of stones to maximize score differences.
2Prefix sums help in calculating scores efficiently.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.