Kadane's algorithm is the move here and I knew it, but I second-guessed myself for a solid two minutes staring at the negative numbers.
Start by clarifying the problem constraints and edge cases, then explain the optimal O(n) Kadane's algorithm. Walk through a small example to demonstrate understanding, and finally discuss potential optimizations or variations.
Pro tip: Mention that Kadane's algorithm can be adapted to return the subarray itself, and highlight its linear time complexity as optimal for this problem. Also, briefly note how you would handle all-negative arrays.
Ask about input size, possible values (negative, zero, positive), and whether the subarray must be non-empty. Confirm the expected return type.
Briefly mention the O(n^2) or O(n^3) solution to show you understand the problem, then transition to the optimal approach.
Describe the dynamic programming approach: maintain current sum and max sum, resetting current sum to 0 when it becomes negative. Emphasize O(n) time and O(1) space.
Use a small array (e.g., [-2,1,-3,4,-1,2,1,-5,4]) to illustrate how the algorithm works step by step, showing updates to current and max sums.
Mention how to return the subarray indices, handle all-negative arrays, and note that this is optimal for the problem.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.