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It's the classic max subarray problem but you also have to track where the subarray begins and ends, not just the sum.
Start by clarifying the problem constraints (e.g., array size, possible negative numbers, whether the subarray can be empty). Then explain Kadane's algorithm, which tracks the maximum sum ending at each position and updates the global maximum, while also recording the start and end indices. Walk through a small example to demonstrate correctness and discuss time/space complexity.
Pro tip: Mention that you would handle edge cases like all negative numbers by initializing max_sum to the first element and updating indices accordingly, and note that Kadane's algorithm can be adapted to return indices without extra space.
Ask about array size, possible values (negative, zero, positive), and whether the subarray must be non-empty. Confirm the expected return format (e.g., 0-indexed vs 1-indexed).
Describe Kadane's algorithm: iterate through the array, maintaining current_sum and max_sum, and update start/end indices when a new maximum is found. Mention that it works in O(n) time and O(1) space.
Choose a small array (e.g., [-2,1,-3,4,-1,2,1,-5,4]) and step through the algorithm, showing how current_sum and max_sum change and how indices are updated.
Cover cases like all negative numbers, single element, and arrays with zeros. Explain how the algorithm handles them and mention that the same approach can be used to return the subarray itself.
State the time complexity O(n) and space complexity O(1). Summarize the solution and offer to code it if needed.
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