How a failed coding interview sparked a shift from brute force to optimal thinking

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A developer recounts struggling with the maximum subarray sum problem during a coding interview, initially writing an O(n³) brute-force solution that failed on large inputs. The experience prompted deeper study into how experienced programmers identify efficient algorithmic shortcuts. The key insight was reframing the problem: instead of recomputing every possible subarray, maintain just two running values — the best sum ending at the current position and the overall best seen so far. This approach, known as Kadane's algorithm, solves the problem in a single pass with O(n) time and O(1) space. The article also highlights common implementation pitfalls, such as incorrectly resetting state to zero when all array elements are negative.

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