Price Change: Detect Significant Price Changes and Compute Running Price Statistics

Question

## Problem

You receive a stream of `(symbol, price, timestamp)` ticks. Implement a `PriceChangeDetector` that: (1) tracks the running VWAP (volume-weighted average price) per symbol, (2) fires an alert if a new price deviates more than X% from the VWAP, and (3) returns the percentage change from the previous tick.

```python
class PriceChangeDetector:
    def __init__(self, alert_threshold_pct: float): ...

def tick(self, symbol: str, price: float, volume: int, timestamp: int) -> dict:
        """
        Returns {
          "pct_change_from_prev": float,
          "vwap": float,
          "alert": bool
        }
        """
```

**Example:**
```
d = PriceChangeDetector(alert_threshold_pct=5.0)
d.tick("AAPL", 150.0, 1000, 1)  -> {pct_change: None, vwap: 150.0, alert: False}
d.tick("AAPL", 160.0, 500,  2)  -> {pct_change: 6.67, vwap: 153.3, alert: True}
```

## Follow-ups

1. How do you compute VWAP incrementally without storing all historical ticks?
2. If you want a rolling VWAP over only the last N minutes, how does the calculation change?
3. How would you handle the case where the same symbol arrives from multiple exchanges simultaneously?
4. Design a simple alerting pipeline: how do alerts flow from detection to a trader's dashboard?

Price Change: Detect Significant Price Changes and Compute Running Price Statistics

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