Continuous Limit Order Book Matching Engine

Design and implement a continuous double-auction in-memory Limit Order Book (LOB) matching engine conforming to production exchange specifications.

Price-Time Priority (FIFO):

• Limit orders with the best prices (highest bid, lowest ask) have highest priority.
• Orders at the same price level are executed in the exact chronological sequence of their arrival.

Your Task

Implement the LimitOrderBook class:

1. add_limit_order(order_id: int, side: str, price: float, volume: int) -> list[dict]:
   • Side is 'buy' or 'sell'. Matches against existing opposite resting liquidity.
   • Generates trade fills: [{'maker_id': int, 'taker_id': int, 'price': float, 'volume': int}, ...].
   • Any unfilled remaining volume rests in the book.
2. add_market_order(order_id: int, side: str, volume: int) -> list[dict]:
   • Sweeps available opposite liquidity until filled or book exhausted. Any unfilled volume is dropped.
3. cancel_order(order_id: int) -> bool:
   • Removes resting limit order in $\mathcal{O}(1)$ or $\mathcal{O}(\log P)$ time. Returns True if found, False otherwise.
4. get_bbo() -> tuple[tuple[float, int] | None, tuple[float, int] | None]:
   • Returns ((best_bid_price, best_bid_volume), (best_ask_price, best_ask_volume)) or None for empty side.
5. get_depth(levels: int = 5) -> dict[str, list[tuple[float, int]]]: Returns top $K$ price levels with cumulative volume: {'bids': [...], 'asks': [...]}.

Constraints

• $order\_id$ is a unique positive integer.
• $price > 0.0$, $volume > 0$.
• All operations must maintain consistent state and pass execution verification.