Friends With No Mutual Friends - Problem

Given a Friends table that represents friendship relationships, find all pairs of users who are friends with each other but have no mutual friends.

The Friends table contains pairs of user IDs where each row indicates that user_id1 and user_id2 are friends with each other. The friendship relationship is bidirectional.

Return the result table ordered by user_id1, user_id2 in ascending order.

Table Schema

Friends
Column Name Type Description
user_id1 PK int First user in the friendship pair
user_id2 PK int Second user in the friendship pair
Primary Key: (user_id1, user_id2)
Note: Each row represents a bidirectional friendship between user_id1 and user_id2

Input & Output

Example 1 — Mixed Friendship Network
Input Table:
user_id1 user_id2
1 2
1 3
2 3
4 5
Output:
user_id1 user_id2
4 5
💡 Note:

Users 1, 2, and 3 form a triangle where each pair has a mutual friend: (1,2) share friend 3, (1,3) share friend 2, and (2,3) share friend 1. Only users 4 and 5 are friends with no mutual connections.
Example 2 — All Isolated Pairs
Input Table:
user_id1 user_id2
1 2
3 4
5 6
Output:
user_id1 user_id2
1 2
3 4
5 6
💡 Note:

All friendship pairs are isolated - none of them share mutual friends, so all pairs are returned in the result.
Example 3 — No Valid Pairs
Input Table:
user_id1 user_id2
1 2
1 3
2 3
1 4
2 4
3 4
Output:
user_id1 user_id2
💡 Note:

This forms a complete graph where every pair of users has mutual friends. For example, (1,2) share friends 3 and 4, so no pairs qualify as having no mutual friends.

Constraints

  • 1 ≤ user_id1, user_id2 ≤ 10^6
  • user_id1 ≠ user_id2
  • All friendship relationships are bidirectional

Visualization

Tap to expand
Friends With No Mutual Friends INPUT user_id1 user_id2 1 2 1 3 2 3 4 5 Graph View: 1 2 3 4 5 ALGORITHM STEPS 1 Create Bidirectional Union Friends table with swapped columns 2 Find Mutual Friends Self-join to find pairs sharing common friend 3 Filter Direct Friends Keep only pairs that are actual friends 4 Exclude With Mutuals LEFT JOIN and filter WHERE mutual IS NULL SELECT DISTINCT f.user_id1, f.user_id2 FROM Friends f LEFT JOIN mutuals m WHERE m.mutual IS NULL FINAL RESULT Pair Analysis: (1,2): Mutual = 3 EXCLUDED (1,3): Mutual = 2 EXCLUDED (2,3): Mutual = 1 EXCLUDED (4,5): No Mutual! INCLUDED - OK Output: user_id1 user_id2 4 5 Key Insight: Two friends have no mutual friends when their sets of friends (excluding each other) have no intersection. Use self-join on bidirectional friendship table to find common connections, then exclude pairs with any mutual. LEFT JOIN with NULL check efficiently identifies pairs where no mutual friend exists in the joined result. TutorialsPoint - Friends With No Mutual Friends | Optimal Solution

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