Leetcode #918: Maximum Sum Circular Subarray
In this guide, we solve Leetcode #918 Maximum Sum Circular Subarray 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
Given a circular integer array nums of length n, return the maximum possible sum of a non-empty subarray of nums. A circular array means the end of the array connects to the beginning of the array.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Queue, Array, Divide and Conquer, Dynamic Programming, Monotonic Queue
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: nums = [1,-2,3,-2]
Output: 3
Explanation: Subarray [3] has maximum sum 3.
Python Solution
class Solution:
def maxSubarraySumCircular(self, nums: List[int]) -> int:
pmi, pmx = 0, -inf
ans, s, smi = -inf, 0, inf
for x in nums:
s += x
ans = max(ans, s - pmi)
smi = min(smi, s - pmx)
pmi = min(pmi, s)
pmx = max(pmx, s)
return max(ans, s - smi)
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.