This one tripped me up more than it should have.
Model the problem as scheduling: each plane has a deadline equal to the number of seconds until it lands (altitude / descent rate, rounded up). To maximize the number of planes shot, sort planes by deadline and greedily shoot the one with the earliest deadline each second, skipping any that have already landed. This is equivalent to the classic 'maximum number of tasks completed before deadlines' problem, solvable with a min-heap or sorting.
Pro tip: Clarify edge cases upfront: planes with zero or negative initial altitude, zero descent rate, and whether shooting happens before or after descent. Also, mention that if a plane's deadline is less than or equal to the current second, it cannot be shot and the game ends if it lands.
Restate the problem: each second, you can shoot one plane before all planes descend. If any plane's altitude becomes ≤0 after descent, the game ends. You want to maximize the number of planes shot before that happens.
For each plane, calculate the number of seconds it can survive: deadline = ceil(altitude / descent_rate). If descent_rate is 0, the plane never lands (infinite deadline). If altitude ≤0 initially, it has already landed.
Sort the planes in ascending order of their deadlines. This helps in prioritizing planes that will land sooner.
Iterate through seconds, and at each second, among available planes (those not yet shot and with deadline > current second), shoot the one with the smallest deadline. Use a min-heap to efficiently select the next plane to shoot.
Continue until no more planes can be shot without causing a landing. The count of shot planes is the answer. If a plane's deadline is ≤ current second and it hasn't been shot, the game ends.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Pretty clean once you sort per user and scan through.
First, clarify the input format and edge cases, then propose sorting events by userId and timestamp. Use a hash map to track the last timestamp per user and count sessions when the gap exceeds the timeout. Analyze time and space complexity, and discuss potential optimizations for large-scale data.
Pro tip: Mention that if events are already sorted or can be processed in a streaming fashion, you can avoid sorting and use a single pass with O(n) time. Also, highlight the importance of handling users with no events and the timeout boundary condition (>= vs >).
Ask about input size, whether events are sorted, and the exact timeout condition (inclusive or exclusive). Confirm that sessions are per-user and that a new session starts when the gap exceeds the timeout.
Sort events by userId and timestamp, then iterate while tracking the last timestamp per user. Alternatively, use a hash map to store the last event time for each user and process events in any order if sorting is not required.
For each event, if the user is new or the time difference from the last event exceeds the timeout, increment the session count and update the last timestamp. Otherwise, just update the last timestamp.
State that sorting takes O(n log n) time and O(n) space, while the counting pass is O(n). If events are already sorted or can be streamed, the overall time can be O(n). Mention memory considerations for large user bases.
Walk through a small example, including cases with multiple users, gaps exactly equal to the timeout, and users with a single event. Verify the session count matches expectations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.