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 you can order the elements in the set, you can look into using Mergesort on the sets. The only modification needed is to check for duplicates during the merge phase. If one is found, just discard the duplicate. Since mergesort is O(n*log(n)), this will offer imrpoved speed when compared to the naive O(n^2) algorithm.

However, to really be effective, you should maintain a sorted set and keep it sorted, so that you can skip the sort phase and go straight to the merge phase.