Friends Purchases - Find Items Bought by Friends but Not by User

Question

## Problem

Given:
- A dict `purchases: {user_id -> set of item_ids}` that a user has bought
- A list `friends: list[str]` of the current user's friend IDs
- The current `user_id`

Return all items that at least one friend has purchased but the current user has not, sorted by item_id.

```python
def friend_recommendations(
    purchases: dict[str, set[str]],
    friends: list[str],
    user_id: str
) -> list[str]:
```

## Example

```
purchases = {
  "alice": {"book", "pen"},
  "bob":   {"pen", "lamp"},
  "carol": {"book", "lamp", "cup"},
}
friend_recommendations(purchases, ["bob","carol"], "alice")
-> ["cup", "lamp"]  (alice already has "book" and "pen")
```

## Follow-ups

1. How would you rank the results by "number of friends who bought this item" descending?
2. Write this as a SQL query given tables `purchases(user_id, item_id)` and `friends(user_id, friend_id)`.
3. The purchases dict has 10M users. How do you avoid loading it all into memory for a single recommendation query?
4. How does this change if friendship is directional (follows, not mutual friends)?

Friends Purchases - Find Items Bought by Friends but Not by User

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