Order Book: Design a High-Performance Limit Order Book With Real-Time BBO Updates

Question

## Problem

Implement a limit order book that maintains bids and asks sorted by price-time priority. Support: add order, cancel order, and market order execution. After every operation, report the best bid and best offer (BBO). All operations must be O(log n) or better.

```python
class LimitOrderBook:
    def add_limit(self, order_id: str, side: str, price: float, qty: int) -> dict: ...
    def cancel(self, order_id: str) -> bool: ...
    def execute_market(self, side: str, qty: int) -> list[dict]: ...
    def bbo(self) -> dict:  # {best_bid: float, best_ask: float}
```

**Example:**
```
add_limit("L1", "buy",  99.5, 100)  -> bbo: {best_bid: 99.5, best_ask: None}
add_limit("L2", "sell",100.0,  50)  -> bbo: {best_bid: 99.5, best_ask: 100.0}
execute_market("buy", 50)           -> [{fill: L2, price:100.0, qty:50}]
bbo()                                -> {best_bid: 99.5, best_ask: None}
```

## Follow-ups

1. What data structure gives you O(log n) add/cancel and O(1) best-price? Describe the two-level structure.
2. How do you handle multiple orders at the same price level (price queue vs. sorted set)?
3. At 1M order operations/sec, what are the bottlenecks in a single-threaded Python implementation?
4. How would you persist the order book state so it survives a crash mid-session?

Order Book: Design a High-Performance Limit Order Book With Real-Time BBO Updates

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