The add/remove/lookup by name part is basically just a hash map and I got through that fine.
Start by clarifying the requirements and constraints, such as whether names are unique and if multiple numbers per name are allowed. Then propose a dual-index design using two hash maps: one mapping name to number(s) and another mapping number to a set of names. Walk through each operation, explaining how the maps are updated and analyze the time complexity, noting that all operations are O(1) on average.
Pro tip: Mention that the number-to-names index is crucial for the reverse lookup, and discuss how to handle updates (e.g., when a name's number changes) to maintain consistency between the two maps.
Ask whether a name can have multiple numbers, whether a number can be associated with multiple names, and if names are unique. This determines the data structures needed.
Suggest using two hash maps: nameToNumbers (name -> set of numbers) and numberToNames (number -> set of names). Explain that sets handle multiple associations and enable efficient add/remove.
For each operation (add, remove, lookup by name, find names by number), describe how to update both maps. For add: insert into both maps; for remove: delete from both maps and clean up empty sets.
State that all operations are O(1) average time due to hash map lookups, with O(k) for iterating over sets where k is the number of associated entries. Mention worst-case O(n) for hash collisions but assume average case.
Compare with alternatives like a single map or a trie, and discuss how to handle updates (e.g., changing a number) and potential memory overhead. Mention scalability considerations for large datasets.
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