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Classic cycle detection in a directed graph.
Model the problem as a directed graph where each course is a node and each prerequisite pair is a directed edge, then apply cycle detection using either DFS with coloring (white/gray/black states) or Kahn's algorithm (topological sort via BFS with in-degree tracking). If a cycle exists, it's impossible to complete all courses; otherwise it is possible. Clearly articulate the time and space complexity of your chosen approach before coding.
Pro tip: Mention both DFS-based and BFS-based (Kahn's algorithm) approaches upfront, then explain your preference — interviewers at companies like Snowflake appreciate candidates who demonstrate awareness of trade-offs, such as BFS being more intuitive for iterative environments and DFS being elegant recursively but risking stack overflow on very large graphs.
Restate the problem as cycle detection in a directed graph, where nodes are courses and directed edges represent prerequisites. Confirm edge cases such as n=0, no prerequisites, or duplicate pairs.
Select either DFS with 3-color node states (unvisited/visiting/visited) or BFS topological sort using in-degree counts (Kahn's algorithm). Briefly justify your choice by comparing their trade-offs in readability, iterative vs. recursive style, and suitability for large inputs.
Construct an adjacency list from the prerequisite pairs and, if using Kahn's algorithm, compute the in-degree for each node. Walk through a small example to validate your graph construction.
For DFS, traverse each unvisited node and flag a cycle if you revisit a 'visiting' (gray) node. For BFS, process nodes with in-degree zero, decrement neighbors' in-degrees, and check if all n nodes were processed at the end.
State that both approaches run in O(V + E) time and O(V + E) space, where V = n courses and E = number of prerequisite pairs. Discuss edge cases like disconnected graph components, self-loops, and isolated nodes.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is just the longest path in a DAG, or equivalently the number of levels in the topological order.
Model the problem as finding the longest path in a DAG (Directed Acyclic Graph), since the minimum number of semesters equals the length of the critical path through the prerequisite chain. Use topological sort (BFS/Kahn's algorithm) and track the earliest semester each course can be taken by propagating the maximum depth level from prerequisites. The answer is simply the maximum level assigned to any course.
Pro tip: Explicitly mention that this is equivalent to finding the 'critical path' — a concept from project scheduling — which signals systems-level thinking and impresses interviewers at data-infrastructure companies like Snowflake where pipeline scheduling is a real-world concern.
Recognize that since you can take unlimited courses per semester, the bottleneck is purely the longest prerequisite chain. The minimum semesters equals the length of the longest path in the prerequisite DAG.
Construct an adjacency list representing course dependencies and compute the in-degree (number of prerequisites) for each course node. This sets up Kahn's BFS-based topological sort.
Initialize a queue with all courses that have zero in-degree (no prerequisites) and assign them to semester 1. Process the queue level by level — each level represents one semester — decrementing in-degrees and enqueuing newly unblocked courses.
Maintain a 'semester' array where semester[i] = max(semester[prerequisite]) + 1 for each course, ensuring each course is scheduled only after all its prerequisites are completed. The answer is the maximum value in this array.
State time complexity O(V + E) and space O(V + E). Discuss edge cases: a single chain of n courses requires n semesters, while completely independent courses require only 1 semester.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This one tripped me up more than I expected.
Simulate the rate limiter by iterating through the sorted timestamps and applying two independent drop conditions: a per-timestamp counter check and a sliding window count check using a deque or two-pointer approach. Track dropped requests separately so they don't pollute the sliding window of processed requests. Clearly separate the two rule evaluations to keep the logic clean and testable.
Pro tip: Emphasize that dropped requests must NOT be counted toward the sliding window total — only successfully processed requests count. This subtle distinction is easy to miss and is likely an intentional trap in the problem; catching it signals strong attention to spec details, which is critical in systems like Snowflake's data pipelines.
Restate both drop conditions clearly: (1) more than 3 requests share the exact same timestamp, and (2) accepting a request would cause more than 20 processed requests within any 10-second window [t-9, t]. Ask whether 'same timestamp' resets after 3 drops or continues dropping all extras.
Use a deque (or queue) to maintain the sliding window of processed request timestamps, enabling O(1) eviction of timestamps outside the 10-second window. Use a counter or dictionary to track how many requests have been seen at the current timestamp for the per-timestamp rule.
For each incoming timestamp, first check the per-timestamp count — if this is the 4th or more request at this timestamp, mark it dropped. Otherwise, evict stale entries from the deque (those with timestamp < current - 9), then check if the deque size is already 20; if so, drop the request.
Only append the timestamp to the sliding window deque and increment the per-timestamp counter when a request is accepted, not dropped. This ensures dropped requests don't inflate the window count or the timestamp frequency count.
Walk through at least two examples: one where the per-timestamp rule triggers (e.g., four requests at t=5) and one where the sliding window rule triggers (e.g., 21 requests spread across 10 seconds). Also test the boundary condition where the window is exactly 10 seconds wide (e.g., timestamps 1 and 10 should be in the same window).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.