Start by clarifying the problem and edge cases, then propose an efficient O(n) solution using Kadane's algorithm. Explain the algorithm step-by-step, including how to handle negative numbers and all-negative arrays, and analyze its time and space complexity.
Pro tip: Mention that Kadane's algorithm can be adapted to return the subarray indices if needed, and discuss how to handle integer overflow if the array values were larger. This shows attention to detail and scalability.
Ask clarifying questions: Can the subarray be empty? What should be returned for an all-negative array? Are there any constraints on time/space complexity?
Acknowledge that a brute force O(n^2) solution exists by checking all subarrays, but aim for O(n) using Kadane's algorithm.
Initialize current_sum and max_sum to the first element. Iterate through the array, updating current_sum as max(current_sum + num, num) and max_sum as max(max_sum, current_sum).
For an all-negative array, Kadane's algorithm returns the maximum element (least negative), which is correct if the subarray must be non-empty. If empty subarray is allowed, max_sum can be initialized to 0.
Time complexity is O(n) since we traverse the array once. Space complexity is O(1) as we only use a few variables.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.