What is Kadane's Algorithm and how does it work?
Candidates must explain the dynamic programming technique used to find the maximum sum contiguous subarray. It tests understanding of DP and greedy approaches.
Why Interviewers Ask This
Kadane's Algorithm is a staple interview question because it elegantly demonstrates the power of dynamic programming. Interviewers want to verify if you can identify overlapping subproblems and make locally optimal choices that lead to a global optimum. It also checks your ability to implement the solution concisely and correctly handle all-negative number arrays.
How to Answer This Question
Explain that the algorithm maintains two variables: current_max (maximum sum ending at current position) and global_max. Iterate through the array, adding the current element to current_max. If current_max becomes negative, reset it to zero. Update global_max whenever current_max exceeds it. Discuss the edge case where all numbers are negative.
Key Points to Cover
- Running sum maintenance
- Resetting negative sums
- Tracking global maximum
- Handling all-negative inputs
Sample Answer
Kadane's Algorithm solves the Maximum Subarray Problem by iterating through the array once. We maintain a running sum, resetting it to zero whenever it drops below zero, because a negative sum would only decrease the total of any subsequent subarray. Simultaneously, we track the highest sum encountered so far. This greedy approach works because at any point, if the current subarray sum is negative, starting fresh from the next element is always better. The algorithm runs in O(N) time with O(1) space.
Common Mistakes to Avoid
- Not resetting negative sums correctly
- Failing to handle all-negative arrays
- Using nested loops unnecessarily
- Confusing subarray with subsequence
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