Start by clarifying the data model and edge cases (e.g., target user not found, no friends, duplicate purchases). Then outline an algorithm using sets: collect the target user's purchased products, gather all products purchased by their friends, and return the set difference. Finally, analyze time and space complexity, and discuss potential optimizations or trade-offs.
Pro tip: Explicitly state your assumptions about the input format and constraints (e.g., number of users, products, friendships) before diving into the solution—this shows you think about scalability and real-world data, which Amazon values.
Ask questions to confirm the data structure (e.g., how users, friends, and purchases are represented) and handle edge cases like missing target user, no friends, or empty purchase lists.
Propose using sets: build a set of the target user's purchased products, then iterate through each friend to collect their purchased products into another set. The result is the set difference (friends' products minus target's products).
Trace the algorithm with a small concrete example to verify correctness and demonstrate your thought process.
State time complexity: O(F * P) where F is number of friends and P is average purchases per friend, or O(total purchases among friends) if using hash sets for O(1) lookups. Space complexity: O(P_target + P_friends) for the sets.
Mention potential improvements like early termination if the target user has no friends, or using a single pass with a hash map if the data is large. Discuss trade-offs between time and space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Reachability in a directed graph, basically BFS or DFS from url1.
Start by clarifying the problem: we need to build an in-memory graph from navigation events (source and destination URLs) and determine reachability from url1 to url2. Then, outline the graph representation (adjacency list) and the traversal algorithm (BFS or DFS), followed by complexity analysis in terms of distinct URLs (V) and edges (E).
Pro tip: Mention that BFS is preferred for reachability because it finds the shortest path in terms of hops and can early-exit when the target is found, which is efficient for large graphs. Also, discuss handling of duplicate edges and self-loops to avoid unnecessary work.
Confirm that the graph is directed (since navigation has a source and destination) and that we need a boolean reachability check. Ask about constraints like graph size, memory limits, and whether the graph is static or dynamic.
Use an adjacency list (hash map from URL to list of neighboring URLs) to efficiently store the graph. This handles sparse graphs well and allows O(1) average lookup for neighbors.
Choose BFS or DFS to traverse from url1. BFS is often better for reachability due to early exit and shortest path guarantee. Use a visited set to avoid cycles and redundant work.
Time complexity: O(V + E) for traversal, where V is distinct URLs and E is edges. Space complexity: O(V + E) for the graph and O(V) for visited set and queue/stack.
Handle cases like url1 == url2, url1 or url2 not in graph, disconnected components, and duplicate edges. Mention possible optimizations like bidirectional BFS for large graphs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.