BFS from all initially infected nodes at once, basically a multi-source BFS.
Model the problem as a multi-source BFS on the contact graph, where the initial infected set are sources at day 0. Compute the shortest path from any source to each node; the answer is the maximum distance, or -1 if any node is unreachable.
Pro tip: Clarify edge cases upfront: empty graph, no initial infected, and disconnected components. Also mention that if the graph is large, BFS is optimal O(V+E) and can be parallelized or optimized with bitsets if needed.
Confirm that infection spreads to all neighbors each day, and that we need the minimum days until all are infected. Ask about graph representation (adjacency list/matrix) and constraints.
Initialize a queue with all initially infected nodes at distance 0. Perform BFS, tracking the distance (day) each node gets infected.
After BFS, if any node remains unvisited, return -1. Otherwise, the answer is the maximum distance assigned to any node.
State time complexity O(V+E) and space O(V). Discuss edge cases: no initial infected (return -1 unless n=0), graph with isolated nodes, and all nodes initially infected (return 0).
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Straightforward extension of the BFS, just skip immune nodes.
Model the spread as a BFS over days, where each day newly infected people are those susceptible with at least one infected neighbor. Track infected, immune, and susceptible sets, and stop when no new infections occur; the day count is the number of BFS layers. After termination, report susceptible nodes never infected.
Pro tip: Clarify that immune individuals are removed from the graph entirely for transmission purposes, and explicitly handle the edge case where patient zero is immune (then 0 days).
Confirm the graph representation (adjacency list/matrix), initial infected set, and immune set. State that immune nodes cannot be infected or transmit.
Use a queue for BFS, a set for infected, a set for immune, and a set for susceptible (all nodes not initially infected or immune).
For each day, process all currently infected nodes, collect susceptible neighbors, and mark them as newly infected. Increment day count only if new infections occur.
Stop when no new infections occur. Return the number of days (BFS layers). The remaining susceptible nodes are those never infected.
Discuss time O(V+E) and space O(V). Handle edge cases: no initial infected, all immune, disconnected graph, and patient zero immune.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Model the system as a state machine where each person's status (susceptible, infected, immune) evolves daily. Simulate day by day, tracking the number of infected and the day each infected person will recover, until no infected remain and no new infections can occur (i.e., all infected have recovered and the susceptible population cannot be infected because there are no infected).
Pro tip: Clarify the infection model upfront (e.g., whether infection spreads to all susceptible or probabilistically) and discuss how you would handle large populations efficiently, perhaps using counts rather than individual tracking.
Ask clarifying questions about the infection and recovery rules: How does infection spread? Is recovery exactly after a fixed number of days? Are there any births or deaths?
Define the state variables (e.g., number of susceptible, infected, immune) and the daily transition rules, including how infected become immune after the fixed recovery period.
Choose an efficient simulation approach: either track each individual's infection day or use a queue to schedule recoveries. Update counts each day.
The system is stable when there are no infected individuals and no new infections can occur. Since infection requires infected individuals, this means the day after the last infected recovers, provided no new infections occurred that day.
Simulate until the condition is met, then return the day number. Ensure you handle edge cases like initial population with no infected.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
By this point I was running low on time and mostly talked through it rather than coded it.
Model the system as a state machine with Susceptible, Infected, Recovered, and Dead states, using a day-by-day simulation. Track transitions based on fixed recovery/death durations, and stop when the state counts no longer change. Return the stabilization day and final counts.
Pro tip: Clarify whether the fixed number of days is from infection or from symptom onset, and whether deaths occur simultaneously with recoveries. This shows attention to detail and prevents off-by-one errors.
Identify the states (S, I, R, D) and the rules for moving between them, including the fixed duration for recovery or death.
Decide between a day-by-day simulation or a more efficient event-driven approach, considering constraints like population size and time to stabilize.
For each day, update each infected individual based on their infection day: if days since infection equals the fixed duration, they either recover or die (with some probability).
Continue simulation until no new infections occur and all infected have transitioned, i.e., the counts of each state remain unchanged from one day to the next.
Output the day when stabilization occurs and the final counts of susceptible, infected, recovered, and dead individuals.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The snapshot part is what makes this interesting.
Start by clarifying requirements and constraints, then propose a design that separates the mutable follow graph from immutable snapshots. Use a versioned approach where each follow/unfollow operation creates a new version, and snapshots reference a specific version. Implement getFriends to query the appropriate version based on the snapshot.
Pro tip: Mention that snapshots can be implemented efficiently using persistent data structures or copy-on-write to avoid full copies, and discuss trade-offs between memory and performance. Also, consider concurrency and thread-safety if the system is multi-threaded.
Ask about expected scale (number of users, operations per second), consistency requirements, and whether snapshots need to be persisted or can be in-memory. Clarify if follow relationships are directed (like Twitter) or undirected (like Facebook).
Propose a data model: e.g., a map from user ID to a set of followee IDs for the current state, and a version number or timestamp. For snapshots, consider storing a reference to a persistent data structure or a copy of the graph at that version.
For follow/unfollow, update the current graph and increment the version. For snapshot, capture the current version (or create a persistent copy). For getFriends, retrieve the friend list from the snapshot's version.
Discuss optimizations: using persistent data structures (e.g., immutable maps) to share structure between versions, or copy-on-write for snapshots. Compare with naive full copy. Mention time/space complexity for each operation.
Address edge cases: following/unfollowing non-existent users, self-follow, duplicate follows. If concurrent access is possible, discuss locking or lock-free approaches to ensure snapshot consistency.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the data model and constraints first, then propose an efficient algorithm that traverses the snapshot's friend graph to find two-hop candidates, counts mutual connections, and ranks them. Discuss trade-offs between precomputation and on-the-fly computation, and outline how to handle ties and scalability.
Pro tip: Mention that you would exclude the user themselves and existing direct friends from recommendations, and consider using a min-heap to efficiently select top k when the candidate set is large.
Ask about the snapshot's data structure (e.g., adjacency list), whether the graph is directed or undirected, and what 'mutual intermediate followers' means precisely. Confirm that recommendations should exclude the user and their direct friends, and discuss tie-breaking rules.
Propose a two-hop traversal: for each direct friend of the user, iterate through their friends (excluding the user and direct friends) and count occurrences. Use a hash map to tally mutual connections, then sort or use a heap to get top k.
State time and space complexity (e.g., O(d * f) where d is degree, f is average friend count). Discuss optimizations like early termination, caching, or precomputing mutual friend counts if the operation is frequent.
Address cases like no candidates, fewer than k candidates, ties, and large graphs. Mention distributed processing or approximate algorithms if the graph is massive.
Outline test cases: small graphs, disconnected users, users with many friends, and performance tests. Suggest verifying correctness against a brute-force implementation.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the data model and snapshot semantics, then design the diffFriends operation to compute set differences between the follow lists from two snapshots. Discuss API design, efficiency, and edge cases, and consider trade-offs between different implementations.
Pro tip: Demonstrate awareness of real-world constraints like large follow lists and snapshot storage by proposing an efficient algorithm and discussing how to handle scale. Mention that you would validate assumptions with the interviewer before diving into code.
Ask questions to understand the snapshot format, whether snapshots are immutable, and how the follow list is represented (e.g., set, sorted list). Confirm the expected output format and any performance requirements.
Propose a function signature, such as diffFriends(userId, snapshot1, snapshot2) returning added and removed lists. Choose appropriate data structures (e.g., hash sets) for efficient lookups.
Outline the steps: retrieve follow lists from both snapshots, compute set difference for added (snapshot2 - snapshot1) and removed (snapshot1 - snapshot2). Discuss time and space complexity.
Consider cases like missing snapshots, empty follow lists, and large datasets. Discuss optimizations like streaming or parallel processing if needed.
Compare approaches: in-memory vs. database-level diff, using sorted lists vs. hash sets, and trade-offs between precomputation and on-demand calculation.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.