Refund Allocation: Distribute Partial Refunds Across Orders Fairly

Question

## Problem

A customer is owed a total refund of `R` dollars across multiple orders. Each order has an `order_id` and `amount_paid`. Distribute the refund proportionally (each order gets `amount_paid / total_paid * R`), rounded down to the nearest cent. Apply any rounding remainder to the order with the largest fractional part.

Return a list of `{order_id, refund_amount}` dicts.

```python
def allocate_refund(orders: list[dict], R: float) -> list[dict]:
    # orders: [{"order_id": str, "amount_paid": float}]
    pass
```

**Example:**
```
orders = [{order_id:"A", amount_paid:100},
          {order_id:"B", amount_paid:150},
          {order_id:"C", amount_paid:250}]
R = 10.00

Proportions: A=2.00, B=3.00, C=5.00 -> exact, no rounding needed.
Output: [{"order_id":"A","refund_amount":2.00}, ...]

If R = 10.01:
A gets 2.002 -> $2.00, B gets 3.003 -> $3.00, C gets 5.005 -> $5.00, remainder $0.01 -> C (largest fraction)
```

## Follow-ups

1. Why should you use integer arithmetic (cents) instead of floats for financial calculations?
2. What if two orders have identical fractional parts — how do you break the tie deterministically?
3. How would you handle partial refunds where a single order's refund cannot exceed what was paid?
4. How would you write an audit log proving the allocation was fair?

Refund Allocation: Distribute Partial Refunds Across Orders Fairly

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