What is the time and space complexity of Maximum Sum Subarray of Size K?

Time complexity: O(n). Space complexity: O(1).

Maximum Sum Subarray of Size K

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Solution Guide: Maximum Sum Subarray of Size K

Approach

Build the initial window by summing the first k elements. Then slide the window one position at a time: add the new right element and subtract the element that falls off the left. Track the maximum sum seen across all window positions.

Complexity Analysis

Time: O(n)
Space: O(1)

Pattern

Sliding Window (Fixed Size)

Why It Works

Each window position differs from the previous by exactly one element added and one removed. By maintaining a running sum, we avoid recomputing the entire sum for each position, reducing the work from O(n*k) to O(n).

Updated Feb 2026