Subscription Tracking: Manage User Subscriptions and Compute Monthly Billing

Question

## Round 1 - Coding

## Problem

Implement a subscription tracking system. Users subscribe to plans with monthly prices. Mid-cycle plan changes are prorated. Compute the total bill for a user at the end of each month.

```python
class SubscriptionTracker:
    def subscribe(self, user_id: str, plan: str,
                  price_per_month: float, start_day: int) -> None:
        ...
    def change_plan(self, user_id: str, new_plan: str,
                    new_price: float, change_day: int) -> None:
        ...
    def cancel(self, user_id: str, cancel_day: int) -> None:
        ...
    def monthly_bill(self, user_id: str, days_in_month: int) -> float:
        ...
```

## Example

```
tracker = SubscriptionTracker()
tracker.subscribe("u1", "basic", 30.0, start_day=1)
tracker.monthly_bill("u1", days_in_month=30)  -> 30.0

tracker.subscribe("u2", "basic", 30.0, start_day=1)
tracker.change_plan("u2", "pro", 60.0, change_day=16)
# Day 1-15: basic @ 30/30 * 15 = 15.00
# Day 16-30: pro @ 60/30 * 15 = 30.00
tracker.monthly_bill("u2", days_in_month=30)  -> 45.0
```

## Follow-ups

1. How do you handle a user who cancels mid-month — do they get a refund or not?
2. How would you support annual subscriptions with monthly billing breakdowns?
3. What data structure tracks multiple plan changes within a single month?
4. How do you generate an invoice line-item breakdown instead of just the total?

Subscription Tracking: Manage User Subscriptions and Compute Monthly Billing

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