Implement a simplified trading simulation in **three parts**. ## Part 1 — Process market data / exchange interaction (order book) Design a minimal limit-order-book simulator for a **single symbol**. ### Events Each event is one of: - `NEW orderId side price qty` - `side` is `B` (buy) or `S` (sell) - Add a limit order. - `CANCEL orderId` - Remove the remaining quantity of that order (if it exists). ### Matching rules When a new order arrives, immediately match it against resting orders on the opposite side using: 1. **Price priority**: best price first (highest buy, lowest sell). 2. **Time priority**: FIFO among orders at the same price. A match produces one or more trades. A trade is: - `tradePrice` = resting order’s price - `tradeQty` = min(incomingRemaining, restingRemaining) ### Output For every input event, output the list of trades generated by that event (may be empty). --- ## Part 2 — Execute for one client with participation rate A single client submits a parent order: - `clientId`, `side`, total target quantity `Q`, and participation rate `p` (0 < p <= 1). You also receive a time-ordered stream of **market prints** (executed market volume): - `PRINT t marketQty` At each print, you may execute some quantity for the client, but must satisfy at all times: \[ executedSoFar \le \lfloor p \cdot marketVolumeSoFar \rfloor \] Where `marketVolumeSoFar` is the cumulative sum of `marketQty` from prints up to time `t`. ### Output For each print, output how many shares you execute for the client at that time (0 if none), until the client reaches `Q` or prints end. --- ## Part 3 — Multiple clients and fairness Now there are multiple simultaneous clients, each with `(Q_i, p_i)`. At each `PRINT`, compute executions for all clients such that: 1. For every client `i`: `executed_i <= floor(p_i * marketVolumeSoFar)`. 2. No client executes more than its remaining quantity. 3. Total executed at a print does not exceed that print’s `marketQty`. 4. If there isn’t enough available volume to satisfy everyone’s allowed amount, allocate **fairly** by prioritizing the client(s) with the smallest \[ \frac{executed_i}{Q_i} \] ties broken by smaller `clientId`. ### Task Implement the simulator for all three parts. ### Notes - You may assume all inputs are validly formatted. - You should state and handle edge cases like canceling unknown orders, or `p_i * marketVolumeSoFar` allowing more than remaining.