Maximum sum circular subarray

Array Divide and Conquer Dynamic Programming Queue Monotonic Queue

49.5% acceptance

Feb 25, 2026

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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. Formally, the next element of nums[i] is nums[(i + 1) % n] and the previous element of nums[i] is nums[(i - 1 + n) % n]. A subarray may only include each element of the fixed buffer nums at most once. Formally, for a subarray nums[i], nums[i + 1], ..., nums[j], there does not exist i <= k1, k2 <= j with k1 % n == k2 % n.

Solution

Rust

Time O(n)

Space O(1)

LeetCode

solution.rs

impl Solution {
  pub fn max_subarray_sum_circular(nums: Vec<i32>) -> i32 {
    let total: i32 = nums.iter().sum();
    let mut max_sum = nums[0]; let mut cur_max = 0;
    let mut min_sum = nums[0]; let mut cur_min = 0;
    for &x in &nums {
      cur_max = (cur_max + x).max(x); max_sum = max_sum.max(cur_max);
      cur_min = (cur_min + x).min(x); min_sum = min_sum.min(cur_min);
    }
    if max_sum < 0 { max_sum } else { max_sum.max(total - min_sum) }
  }
}