Leetcode #2029: Stone Game IX
In this guide, we solve Leetcode #2029 Stone Game IX 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 continue their games with stones. There is a row of n stones, and each stone has an associated value.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Math, Counting, Game Theory
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: stones = [2,1]
Output: true
Explanation: The game will be played as follows:
- Turn 1: Alice can remove either stone.
- Turn 2: Bob removes the remaining stone.
The sum of the removed stones is 1 + 2 = 3 and is divisible by 3. Therefore, Bob loses and Alice wins the game.
Python Solution
class Solution:
def stoneGameIX(self, stones: List[int]) -> bool:
def check(cnt: List[int]) -> bool:
if cnt[1] == 0:
return False
cnt[1] -= 1
r = 1 + min(cnt[1], cnt[2]) * 2 + cnt[0]
if cnt[1] > cnt[2]:
cnt[1] -= 1
r += 1
return r % 2 == 1 and cnt[1] != cnt[2]
c1 = [0] * 3
for x in stones:
c1[x % 3] += 1
c2 = [c1[0], c1[2], c1[1]]
return check(c1) or check(c2)
Complexity
The time complexity is , where is the length of the array . The space complexity is .
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.