The core Kadane's logic came back to me pretty fast: track the max sum ending at the current position and decide whether to extend the running total or restart from the current element.
Use Kadane's algorithm to scan the array once, maintaining the maximum sum of a subarray ending at the current position and the overall maximum sum seen so far. At each step, decide whether to extend the previous subarray or start a new one from the current element. This yields an O(n) time and O(1) space solution.
Pro tip: Clearly state the recurrence relation and handle edge cases like all negative numbers upfront. Mention that this is a classic dynamic programming problem and that you can also return the subarray indices if needed.
Confirm that the array can contain negative numbers, that the subarray must be contiguous and non-empty, and that you need to return the sum (not the subarray itself).
Briefly mention that a naive solution would check all O(n^2) subarrays, but that we can do better with a linear-time algorithm.
Define two variables: current_sum (max sum ending at current index) and max_sum (overall max). Initialize both to the first element or to 0 depending on handling of negatives.
Iterate through the array, updating current_sum = max(nums[i], current_sum + nums[i]) and max_sum = max(max_sum, current_sum). Explain the intuition behind the recurrence.
State that time complexity is O(n) and space is O(1). Discuss edge cases: all negative numbers, single element, empty array (if allowed), and how to handle them.
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This tripped me up more than the main question.
First, briefly restate your original solution (e.g., Kadane's algorithm) to show continuity. Then, explain how to augment it with two index variables to track the start and end of the current subarray and the best subarray found so far. Finally, walk through a small example to demonstrate correctness and discuss edge cases.
Pro tip: Emphasize that the key is to update the start index only when the current sum resets to a single element, and to update the best indices only when a new maximum is found. This shows you understand the subtlety of index tracking.
Briefly explain your initial approach (e.g., Kadane's algorithm) to set the context and show you can build on it.
Describe adding variables: current_start, best_start, best_end. Explain their roles and initialization.
Explain how to update current_start when the current sum resets, and how to update best_start and best_end when a new maximum is found.
Trace the algorithm on a small array (e.g., [-2,1,-3,4,-1,2,1,-5,4]) to show how indices are updated and verify the result.
Mention handling of all-negative arrays, single-element arrays, and confirm time and space complexity remain O(n) and O(1).
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Knew this was O(n log n) and could sketch the idea: split the array, recurse on both halves, then compute the max crossing subarray in linear time.
Start by restating the problem and clarifying assumptions, then outline the divide-and-conquer strategy step by step, including recurrence relation and complexity analysis. Finally, compare it to the linear solution in terms of time/space complexity, constant factors, and practical trade-offs, concluding with when each approach is preferable.
Pro tip: Demonstrate awareness of real-world constraints: mention that while divide-and-conquer may have better asymptotic complexity, the linear solution often wins in practice due to lower constant factors and cache efficiency. Also, relate the discussion to LinkedIn's scale and need for efficient algorithms.
Restate the problem in your own words and ask clarifying questions about input size, constraints, and expected output. This ensures you and the interviewer are aligned before diving into solutions.
Describe how to break the problem into smaller subproblems, solve them recursively, and combine results. Include the recurrence relation and derive time/space complexity using the Master Theorem or substitution.
Outline the linear approach, highlighting its single pass or iterative nature. Derive its time and space complexity, noting any auxiliary data structures used.
Compare the two approaches on time complexity, space complexity, constant factors, and implementation complexity. Discuss scenarios where one outperforms the other, such as small vs. large inputs or memory constraints.
Summarize which approach you would choose for the given context and why, considering factors like input size, performance requirements, and code maintainability.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.