Let's delve deeper into designing a limit order book for a trading system. Imagine you're building the core matching engine for a high-frequency trading platform. The order book is the heart of this engine, responsible for efficiently matching buy and sell orders based on price and time priority. This problem focuses specifically on the in-memory representation and core matching logic of a single order book for a single trading instrument (e.g., AAPL stock).

A limit order book essentially maintains a sorted list of buy (bid) and sell (ask) orders at various price levels. When a new order arrives, the system must first attempt to match it against existing orders in the book at compatible prices. If a match is found, trades are executed. Any remaining quantity from the incoming order is then added to the order book as a new limit order at the specified price.

The crucial aspect of this design is ensuring efficiency for frequent order placements and cancellations, while maintaining data integrity and thread safety, given that multiple threads will be accessing and modifying the order book concurrently. We need to consider how to represent orders, price levels, and the overall order book structure, along with appropriate data structures and algorithms to optimize matching performance. This isn't just about storing data; it's about creating a robust, scalable, and correct system for processing financial transactions.

Requirements