The matching logic itself is not that bad once you commit to a structure.
Start by clarifying requirements and assumptions (e.g., order types, price-time priority, output format). Then outline the core data structures: a price-sorted structure for bids and asks, and a FIFO queue per price level. Walk through the matching logic for NEW and CANCEL events, emphasizing efficiency and correctness.
Pro tip: Discuss the trade-offs between different data structures (e.g., heap vs. balanced BST vs. sorted list) and how they affect performance for high-frequency trading scenarios. Mention that you would use a doubly linked list for the FIFO queue to allow O(1) cancellation.
Ask about order types (limit only?), event types (NEW, CANCEL), matching rules (price-time priority), and output format (list of trades per event). Confirm assumptions like no partial fills or self-trade prevention unless specified.
Propose using two sorted structures (e.g., balanced BST or heap) for bids and asks, each mapping price levels to a FIFO queue of orders. Use a hash map for O(1) order lookup by ID to support cancellations.
For a NEW order, match against the opposite side while prices cross, consuming orders from the best price level in time priority. For CANCEL, remove the order from its price level and clean up empty levels.
Consider edge cases like cancelling non-existent orders, empty book, and orders that don't match. Ensure each event outputs the list of trades generated (price, quantity, buy/sell order IDs).
Discuss time complexity: O(log P) for insertion/removal from price levels (P = number of price levels), O(1) for order lookup and queue operations. Mention potential optimizations like using a skip list or array for price levels if price range is bounded.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The floor function tripped me up more than I expected.
Clarify the problem constraints and edge cases, then propose a greedy algorithm that tracks cumulative market volume and cumulative executed shares, ensuring the participation constraint is never violated. Discuss trade-offs between simplicity and optimality, and consider potential improvements like smoothing or predictive adjustments.
Pro tip: Emphasize the importance of maintaining the invariant that executed shares never exceed floor(p * cumulative market volume) at any point, and discuss how to handle fractional shares and rounding consistently.
Restate the problem: given a stream of market prints (each with a volume), output the number of shares to execute at each print such that cumulative executed shares ≤ floor(p * cumulative market volume) at all times. Clarify if p is a fixed participation rate, if there are any other constraints (e.g., minimum execution), and how to handle rounding.
Maintain cumulative market volume (CMV) and cumulative executed shares (CES). At each print with volume V, compute the maximum allowed cumulative execution: maxCES = floor(p * (CMV + V)). The number of shares to execute at this print is max(0, maxCES - CES). Update CES and CMV accordingly.
Prove that the greedy algorithm never violates the constraint: after each step, CES ≤ floor(p * CMV). Discuss edge cases: p=0 (execute nothing), p=1 (execute full volume), very small p causing zero execution for many prints, and handling of fractional shares (e.g., using integer arithmetic to avoid floating-point errors).
Mention that the greedy approach is simple and optimal for maximizing execution while respecting the constraint. However, in practice, one might want to smooth execution over time or use predictive models to avoid being too aggressive early on. Discuss the impact of latency and the difference between theoretical and practical implementations.
Talk about data structures: just a few variables to track cumulative volumes. Use integer arithmetic to avoid floating-point precision issues (e.g., represent p as a fraction). Ensure the algorithm is O(1) per print and can handle high-frequency streams.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the problem constraints and requirements, then propose a data structure that efficiently tracks each client's ratio and supports fair allocation. Describe the algorithm for processing each print, including how to update ratios and break ties, and discuss trade-offs and potential optimizations.
Pro tip: Emphasize the importance of fairness and determinism in financial systems, and mention how your solution ensures both while being efficient. Also, proactively discuss edge cases like zero targets or no available volume.
Ask questions to confirm assumptions: What is the definition of 'fair'? How are clients represented? What is the expected scale (number of clients, prints per second)? Are there constraints on latency or memory?
Propose a priority queue (min-heap) keyed by the ratio of executed quantity to total target quantity, with client ID as a tiebreaker. Alternatively, consider a balanced BST or a custom heap that supports efficient updates.
For each print, repeatedly extract the client with the smallest ratio, allocate a unit of volume (or the remaining volume) to them, update their executed quantity and ratio, and reinsert them into the heap. Continue until the print volume is exhausted or all clients have reached their targets.
Analyze time complexity per print: O(k log n) where k is the number of allocations and n is the number of clients. Discuss potential optimizations, such as batch processing or lazy updates, and trade-offs between fairness and performance.
Consider edge cases: zero target quantities, clients with no remaining capacity, print volume larger than total remaining target, and ties in ratios. Describe how to test the solution for correctness and fairness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.