Start by clarifying the problem constraints (e.g., array size, possible values) and then explain Kadane's algorithm, which efficiently finds the maximum sum in O(n) time. Walk through a small example to illustrate the algorithm and discuss edge cases like all negative numbers.
Pro tip: Mention that Kadane's algorithm can be adapted to return the subarray indices if needed, and that it's a classic example of dynamic programming with optimal substructure. This shows depth and awareness of variations.
Ask about constraints: array size, possible values (negative, zero, positive), and whether the subarray must be non-empty. Confirm the expected return type (sum only or indices).
Acknowledge that a brute force O(n^2) or O(n^3) solution exists but is inefficient. Then introduce Kadane's algorithm as an O(n) dynamic programming solution.
Define local_max as the maximum sum ending at the current index, and global_max as the overall maximum. Iterate through the array, updating local_max = max(num, local_max + num) and global_max = max(global_max, local_max).
Use a small array like [-2,1,-3,4,-1,2,1,-5,4] to demonstrate how the algorithm works step by step, showing updates to local_max and global_max.
Discuss edge cases: all negative numbers (return the maximum single element), empty array (return 0 or handle as per constraints). State time complexity O(n) and space complexity O(1).
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