Classic problem, linear time solution with constant space.
Start by clarifying the problem constraints (e.g., array size, possible negative numbers) and then propose Kadane's algorithm, which scans the array once while tracking the maximum sum ending at the current position and the overall maximum. Walk through a small example to demonstrate correctness, then analyze time and space complexity.
Pro tip: Mention that Kadane's algorithm can be adapted to return the actual subarray indices if needed, and discuss how to handle edge cases like all-negative arrays by initializing with the first element rather than zero.
Ask about input size, whether the array can be empty, and if negative numbers are allowed. Confirm the expected return type (sum only or subarray).
Introduce Kadane's algorithm: iterate through the array, maintaining the maximum sum of a subarray ending at the current index, and update the global maximum.
Use a small array (e.g., [-2,1,-3,4,-1,2,1,-5,4]) to show how the algorithm works step by step, highlighting the decisions at each index.
State that the time complexity is O(n) and space is O(1). Discuss edge cases: empty array, all negatives, single element, and how to handle them.
Mention how to modify the algorithm to return the subarray itself, and compare with a divide-and-conquer approach (O(n log n)) if asked.
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