Classic graph problem but you need to check two things: no cycles and the graph is fully connected.
Clarify the definition of a valid tree: a connected acyclic graph with exactly n-1 edges for n nodes. Then propose using Union-Find (Disjoint Set Union) to detect cycles while ensuring all nodes are connected, or BFS/DFS to check connectivity and edge count.
Pro tip: Mention edge cases upfront: empty graph, single node, self-loops, and parallel edges. Also, note that if the number of edges is not exactly n-1, it's immediately invalid, which can save time.
Confirm that a valid tree must be connected, acyclic, and have exactly n-1 edges for n nodes. Ask about input format: are nodes labeled 0 to n-1? Can there be duplicate edges or self-loops?
If the number of edges is not exactly n-1, return false immediately. This is a necessary condition for a tree.
Use Union-Find to detect cycles while building the graph, or use BFS/DFS to check connectivity and cycle presence. Union-Find is often more efficient for cycle detection.
Code the solution, handling edge cases like empty input, single node, and disconnected components. Walk through a small example to verify correctness.
State time and space complexity. For Union-Find with path compression and union by rank, it's nearly O(E) time and O(N) space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use a stack to simulate collisions: iterate through asteroids, and for each right-moving asteroid push it onto the stack; for a left-moving asteroid, resolve collisions with the top of the stack until it either survives or is destroyed. Finally, the stack contains the surviving asteroids in order.
Pro tip: Clarify the collision rules upfront (e.g., equal sizes both explode, larger survives) and mention edge cases like all asteroids moving in the same direction or no collisions. This shows attention to detail and prevents misunderstandings.
Confirm the collision rules: when two asteroids meet, the smaller one explodes; if equal, both explode; asteroids moving in the same direction never collide. Also clarify input format and expected output.
Recognize that a stack is ideal because collisions only happen between the most recent right-moving asteroid and a new left-moving asteroid, following a last-in-first-out order.
Iterate through the array: if the asteroid moves right, push it onto the stack; if it moves left, repeatedly compare it with the top of the stack (if the top moves right) and resolve collisions until the left-moving asteroid is destroyed or the stack is empty or the top moves left.
After processing all asteroids, the stack contains the survivors in order. Consider edge cases like no collisions, all moving left, or all moving right, and ensure the solution handles them correctly.
State that the time complexity is O(n) because each asteroid is pushed and popped at most once, and space complexity is O(n) for the stack. Walk through a few examples to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying functional and non-functional requirements, then design the high-level architecture covering core entities like movies, theaters, shows, and seats. Dive into critical components such as seat locking, booking flow, and payment integration, while discussing trade-offs around consistency, scalability, and concurrency.
Pro tip: Emphasize how you handle race conditions during seat selection—this is the crux of the problem and demonstrates your ability to design for real-world concurrency. Also, relate your design to Zepto's scale and low-latency requirements to show contextual awareness.
Ask questions to define scope: user flows (search, select, book, pay), scale (users, shows, seats), and constraints (consistency, latency, availability).
Outline core services (movie, theater, show, booking, payment) and data models. Sketch API endpoints and data flow from search to booking confirmation.
Focus on seat locking and booking concurrency: discuss optimistic vs pessimistic locking, distributed locks, and idempotency. Explain payment integration and failure handling.
Address scaling reads/writes, caching strategies, database choices (SQL vs NoSQL), and trade-offs between consistency and availability (e.g., CAP theorem).
Summarize key decisions, mention monitoring, and suggest potential improvements like recommendation systems or dynamic pricing.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.