Binary search problem once you see it clearly.
Start by clarifying requirements: are ranges static or dynamic? Should overlapping ranges be handled? Then propose a solution using sorting and binary search for efficient queries, or an interval tree if dynamic updates are needed. Discuss trade-offs between preprocessing time and query time, and consider edge cases like gaps and overlapping ranges.
Pro tip: Mention that if ranges are static, you can preprocess them into a sorted list of non-overlapping intervals and use binary search for O(log n) queries; if dynamic, an interval tree or segment tree is more appropriate. This shows you consider both algorithmic efficiency and practical constraints.
Ask about the nature of the ranges: Are they static or will they be updated frequently? Can they overlap? What should be returned if the integer falls in multiple ranges or none? This determines the optimal data structure.
For static ranges, sort and merge overlapping intervals, then use binary search. For dynamic ranges, consider an interval tree or segment tree. Explain the trade-offs in time and space complexity.
Define the class with a constructor that preprocesses the ranges (e.g., sorting and merging) and a query method that returns the range containing the integer. Include handling for edge cases like no matching range.
State the time complexity for preprocessing and querying, and the space complexity. For binary search approach: O(n log n) preprocessing, O(log n) query, O(n) space.
Walk through examples like [1,3] and [50,100] with queries 2, 75, and 10 to demonstrate correctness and edge case handling.
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