Start by clarifying the data model and constraints (directed graph, average degree d, top K). Then outline a two-phase algorithm: first gather all depth-2 candidates from U's followees, count how many distinct followees follow each candidate, filter out U and existing followees, then sort by count descending and lexicographically for ties, and return top K. Finally, analyze time and space complexity in terms of d and the number of followees.
Pro tip: Mention that you can optimize by using a min-heap of size K to avoid sorting all candidates, and that early filtering (e.g., skipping U and already-followed users during traversal) reduces unnecessary work.
Confirm that the graph is directed, that followees are users U directly follows, and that the output should be top K users sorted by frequency then lexicographically. Ask about constraints like average degree, maximum degree, and whether K is small relative to total users.
Use a hash map to count how many of U's followees follow each candidate. Iterate over U's followees, then over each followee's followees, incrementing counts and skipping U and anyone U already follows. Then sort candidates by count descending and username ascending, and take top K.
If K is much smaller than the number of candidates, maintain a min-heap of size K to track the top K without sorting all candidates. For ties, use a custom comparator that considers count and lexicographic order.
Time: O(d^2) to traverse depth-2 (each of d followees has d followees on average), plus O(C log C) for sorting where C is number of candidates (≤ d^2), or O(C log K) with heap. Space: O(C) for the hash map and heap.
Handle cases where U has no followees, all candidates are already followed, or ties are frequent. For large-scale systems, mention distributed processing or approximate algorithms (e.g., using MapReduce) and caching.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.