Social Network Relationship Analysis with SQL

This challenge asks you to simulate graph database queries using standard SQL. Social networks are inherently graph-structured, with users as nodes and relationships (friendships, follows, etc.) as edges. You'll be given a relational database schema representing a simplified social network and tasked with writing SQL queries to answer common graph-related questions.

Problem Description

You are provided with a relational database schema representing a social network. The schema consists of two tables: Users and Relationships. Your goal is to write SQL queries to retrieve information about the network, mimicking the functionality of a graph database.

Tables:

• Users:
  • user_id (INTEGER, PRIMARY KEY): Unique identifier for each user.
  • name (VARCHAR): User's name.
• Relationships:
  • source_user_id (INTEGER, FOREIGN KEY referencing Users.user_id): The user initiating the relationship.
  • target_user_id (INTEGER, FOREIGN KEY referencing Users.user_id): The user being targeted by the relationship.
  • relationship_type (VARCHAR): The type of relationship (e.g., 'friend', 'follows', 'blocked').

What needs to be achieved:

You need to write SQL queries to answer the following questions, which are analogous to graph database traversals:

1. Find all friends of a given user: Given a user_id, return the names of all users who are friends of that user.
2. Find all users who follow a given user: Given a user_id, return the names of all users who follow that user.
3. Find the mutual friends of two users: Given two user_ids, return the names of all users who are friends with both of them.
4. Find the shortest path (in terms of relationship hops) between two users: Given two user_ids, return a list of user_ids representing the shortest path between them. If no path exists, return an empty list. Assume only 'friend' relationships are used for path finding.
5. Find users who are 'friends' with a user who is 'friends' with another user: Given two user_ids (user1 and user2), find all users who are friends with a user who is also friends with both user1 and user2.

Key Requirements:

• Queries must be valid SQL and executable against a standard relational database (e.g., PostgreSQL, MySQL, SQLite).
• Queries should be efficient and avoid unnecessary joins or subqueries where possible.
• The queries should accurately reflect the graph relationships defined in the schema.

Expected Behavior:

• Queries should return the correct results based on the provided input data.
• Queries should handle edge cases gracefully (e.g., user not found, no relationships, no path between users).
• The shortest path query should return the shortest path, not just any path.

Edge Cases to Consider:

• Users with no friends or followers.
• Users who are friends with themselves (self-loops).
• Cycles in the graph (e.g., A is friends with B, B is friends with C, C is friends with A).
• No path exists between two users.
• Duplicate relationships (e.g., two entries with the same source and target user IDs).

Examples

Example 1:

Input: user_id = 1
Query: Find all friends of user 1.
Output: [name1, name2]
Explanation: User 1 has 'friend' relationships with users with IDs name1 and name2.

Example 2:

Input: user_id = 3
Query: Find all users who follow user 3.
Output: [name3, name4]
Explanation: Users with IDs name3 and name4 have 'follows' relationships with user 3.

Example 3:

Input: user_id1 = 1, user_id2 = 2
Query: Find the mutual friends of users 1 and 2.
Output: [name5]
Explanation: User 5 is a friend of both user 1 and user 2.

Example 4:

Input: user_id1 = 1, user_id2 = 4
Query: Find the shortest path between users 1 and 4.
Output: [1, 3, 4]
Explanation: The shortest path from user 1 to user 4 is 1 -> 3 -> 4 (assuming user 3 is a friend of both 1 and 4).

Example 5:

Input: user_id1 = 1, user_id2 = 5
Query: Find users who are 'friends' with a user who is 'friends' with both user1 and user2.
Output: [name6]
Explanation: User 3 is friends with both user 1 and user 2. User 6 is friends with user 3.

Constraints

• user_id will always be a positive integer.
• relationship_type will be one of: 'friend', 'follows', 'blocked'.
• The database will contain at least 10 users and 20 relationships.
• The shortest path will be no longer than 10 hops.
• Queries should execute within 5 seconds on a moderately sized dataset (up to 1000 users and 5000 relationships).

Notes

• You are not required to create the database schema or populate it with data. Assume the schema exists and is populated.
• Focus on writing efficient and correct SQL queries.
• Consider using Common Table Expressions (CTEs) to improve query readability and modularity, especially for the shortest path query.
• The shortest path query is the most challenging and may require a recursive approach or iterative search. There are multiple valid approaches.
• For the shortest path, assume that the relationship type 'friend' is the only type that can be used to traverse the graph. Other relationship types are ignored.