Compute top-K branches by openings

Given a stream of account-opening events (branch_id, user_id, timestamp), design algorithms and data structures to compute the top-K branches by number of openings for (a) all time and (b) a sliding window of the last T minutes. Support event ingestion in near real time, queries at any time, and updates in O(log K) or better. Address late or out-of-order events, memory usage, and trade-offs between exact and approximate methods (e.g., heaps + hash maps vs. sketches). Extend your design to a distributed environment and analyze time and space complexity.

What a Strong Answer Covers

• A clear algorithm with the right data structures and enough pseudocode or code-level detail to implement it.
• A correctness argument that explains why the algorithm covers all required cases.
• Time and space complexity, plus at least one alternative approach when relevant.
• Focused tests for normal cases, edge cases, and failure modes.

Follow-up Questions

• How would the approach change if the input were streaming or too large for memory?
• What invariants would you assert in production code?
• Which tests would catch off-by-one, duplicate, or tie-breaking bugs?

Solution

Solution Alignment

The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests.

Problem Restatement

Given a stream of account-opening events (branch_id, user_id, timestamp), design algorithms and data structures to compute the top-K branches by number of openings for (a) all time and (b) a sliding window of the last T minutes. Support event ingestion in near real time, queries at any time, and updates in O(log K) or better. Address late or out-of-order events, memory usage, and trade-offs between exact and approximate methods (e.g., heaps + hash maps vs. sketches). Extend your design to a distributed environment and analyze time and space complexity.

Recommended Approach

For one-time top-K, use a size-K min-heap or quickselect plus sorting the selected K. For streaming windows, maintain counts in a hash map plus a heap with lazy deletion or bucketed frequency structures when updates must be near O(1). Define deterministic tie-breaking.

Correctness

The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call.

Complexity

One-time heap: O(n log k) time and O(k) space. Quickselect: expected O(n) plus O(k log k) to order output. Streaming complexity depends on window eviction and tie-breaking.

Edge Cases and Tests

k = 0, k > n, duplicate values, ties, negative values, stale heap entries, and deterministic output ordering.