Search for a Range (First and Last Position)
Given a sorted array of integers `nums` and a target value, find the starting and ending position of the target. Your algorithm's runtime complexity should be $O(\log n)$. Use two Binary Searches.
Why Interviewers Ask This
Spotify evaluates candidates on algorithmic precision and edge-case handling. This question tests if you can optimize a linear scan to logarithmic time using binary search variants. It specifically assesses your ability to maintain sorted array invariants while finding boundary conditions, a skill critical for their large-scale data processing pipelines.
How to Answer This Question
1. Clarify constraints: Confirm the array is sorted and handle empty inputs immediately. 2. Define strategy: State clearly that you will use two separate binary searches—one to find the first occurrence and another for the last. 3. Implement lower bound logic: Write code that moves the right pointer when the target is found or greater, ensuring you capture the leftmost index. 4. Implement upper bound logic: Create a mirrored function that moves the left pointer when the target is found or smaller to locate the rightmost index. 5. Validate edge cases: Explicitly check if the target exists before returning ranges to avoid returning incorrect indices like -1 for both. 6. Analyze complexity: Conclude by explaining why this approach meets the O(log n) requirement compared to a naive O(n) scan.
Key Points to Cover
- Explicitly state the O(log n) constraint and how two binary searches satisfy it
- Demonstrate clear separation between finding the lower and upper bounds
- Handle the case where the target does not exist in the array correctly
- Explain the specific pointer movement logic (left vs right) for each search variant
- Reference Spotify's focus on efficiency when dealing with large sorted datasets
Sample Answer
To solve the Search for a Range problem efficiently within Spotify's performance standards, I would avoid a simple linear scan which takes O(n). Instead, I will leverage the sorted nature of the input to perform two dist…
Common Mistakes to Avoid
- Using a single binary search and assuming it finds all occurrences, leading to O(n) worst-case scenarios
- Failing to check if the target actually exists before calculating the range boundaries
- Incorrectly updating pointers during the binary search, causing infinite loops or missing the boundary
- Ignoring edge cases such as arrays with only one element or targets outside the array range
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