Algorithm for merging sets that share at least 2 elements

Question

Given a list of sets:

• S_1 : [ 1, 2, 3, 4 ]
• S_2 : [ 3, 4, 5, 6, 7 ]
• S_3 : [ 8, 9, 10, 11 ]
• S_4 : [ 1, 8, 12, 13 ]
• S_5 : [ 6, 7,

Answer 1

If your elements are numerical in nature, or can be naturally ordered (ie. you can assign a value such as 1, 2, 42 etc...), I would suggest using a radix sort on the merged sets, and make a second pass to pick up on the unique elements.

This algorithm should be of O(n), and you can optimize the radix sort quite a bit using bitwise shift operators and bit masks. I have done something similar for a project I was working on, and it works like a charm.