How would you solve the maximum subarray sum problem using Kadane's Algorithm?
This classic dynamic programming question asks for the contiguous subarray with the largest sum. It tests DP and greedy strategy understanding.
Why Interviewers Ask This
Kadane's Algorithm is a staple in technical interviews because it bridges the gap between brute force and dynamic programming. Interviewers want to see if candidates can recognize overlapping subproblems and make optimal local choices. It demonstrates the ability to transform an O(n^2) problem into an O(n) solution efficiently.
How to Answer This Question
Define the core recurrence relation where the maximum sum ending at a position is either the current element or the current element added to the previous max sum. Explain how tracking the global maximum throughout the iteration yields the answer. Provide a clear example with mixed positive and negative numbers to illustrate the logic. Conclude with complexity analysis.
Key Points to Cover
- Track current subarray sum
- Reset if sum becomes negative
- Update global maximum continuously
- Linear time complexity
Sample Answer
Kadane's Algorithm maintains a running sum of the subarray ending at the current position. At each step, we decide whether to extend the existing subarray or start a new one with the current element. We update the global maximum whenever the running sum exceeds it. This greedy approach works because a negative prefix will only decrease the total sum. The algorithm runs in linear time O(n) and uses constant space O(1).
Common Mistakes to Avoid
- Initializing global max to zero instead of first element
- Failing to handle all-negative arrays
- Confusing subarray with subset
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