Leetcode #1686: Stone Game VI
In this guide, we solve Leetcode #1686 Stone Game VI in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Alice and Bob take turns playing a game, with Alice starting first. There are n stones in a pile.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Math, Game Theory, Sorting, Heap (Priority Queue)
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: aliceValues = [1,3], bobValues = [2,1]
Output: 1
Explanation:
If Alice takes stone 1 (0-indexed) first, Alice will receive 3 points.
Bob can only choose stone 0, and will only receive 2 points.
Alice wins.
Python Solution
class Solution:
def stoneGameVI(self, aliceValues: List[int], bobValues: List[int]) -> int:
vals = [(a + b, i) for i, (a, b) in enumerate(zip(aliceValues, bobValues))]
vals.sort(reverse=True)
a = sum(aliceValues[i] for _, i in vals[::2])
b = sum(bobValues[i] for _, i in vals[1::2])
if a > b:
return 1
if a < b:
return -1
return 0
Complexity
The time complexity is , and the space complexity is , where is the length of the arrays aliceValues and bobValues. The space complexity is , where is the length of the arrays aliceValues and bobValues.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.