Smallest Range Covering Elements from K Lists
You have $k$ lists of sorted integers. Find the smallest range that includes at least one number from each of the $k$ lists. Use a Min-Heap.
Why Interviewers Ask This
Spotify engineers ask this to evaluate your ability to manage dynamic state across multiple data streams efficiently. It tests if you can move beyond brute-force solutions to optimize time complexity using a Min-Heap. They specifically look for your understanding of how to balance range minimization with the constraint of covering every list simultaneously.
How to Answer This Question
1. Clarify constraints: Confirm if lists are sorted and the value range, as Spotify values precise problem scoping before coding. 2. Define the strategy: Propose using a Min-Heap to track the current minimum element from each of the k lists while maintaining a running maximum. 3. Initialize: Explain pushing the first element of every list into the heap and tracking the initial max value. 4. Iterate: Describe the loop where you extract the min, update the smallest range if the current window is better, then insert the next element from that same list's source. 5. Terminate: State that the process stops when any list is exhausted, ensuring no valid range exists beyond that point. 6. Analyze: Conclude by calculating O(N log K) time complexity, where N is total elements, demonstrating optimization awareness.
Key Points to Cover
- Explicitly mention using a Min-Heap to efficiently retrieve the smallest element among k lists
- Demonstrate understanding that the range is defined by the current minimum and the running maximum
- Explain the termination condition clearly: stopping when any list is fully traversed
- Correctly derive the time complexity as O(N log K) rather than O(N*K)
- Show step-by-step logic for updating the heap and range bounds during iteration
Sample Answer
To solve the Smallest Range Covering Elements from K Lists problem, I would first verify that the input lists are indeed sorted, which allows us to leverage their order for efficiency. My approach involves a sliding wind…
Common Mistakes to Avoid
- Attempting a brute-force solution that checks every possible combination, leading to TLE (Time Limit Exceeded)
- Failing to maintain a separate variable for the current maximum value inside the heap, causing incorrect range calculations
- Not handling edge cases where lists might be empty or contain duplicate values correctly
- Confusing the heap operations and removing elements without properly inserting the next element from the same source list
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