Set consolidation

FCC link

Given two sets of items then if any item is common to any set then the result of applying consolidation to those sets is a set of sets whose contents is:

• The two input sets if no common item exists between the two input sets of items.
• The single set that is the union of the two input sets if they share a common item.

Given N sets of items where N > 2 then the result is the same as repeatedly replacing all combinations of two sets by their consolidation until no further consolidation between set pairs is possible. If N < 2 then consolidation has no strict meaning and the input can be returned.

Here are some examples:

Example 1:

Given the two sets {A,B} and {C,D} then there is no common element between the sets and the result is the same as the input.

Example 2:

Given the two sets {A,B} and {B,D} then there is a common element B between the sets and the result is the single set {B,D,A}. (Note that order of items in a set is immaterial: {A,B,D} is the same as {B,D,A} and {D,A,B}, etc).

Example 3:

Given the three sets {A,B} and {C,D} and {D,B} then there is no common element between the sets {A,B} and {C,D} but the sets {A,B} and {D,B} do share a common element that consolidates to produce the result {B,D,A}. On examining this result with the remaining set, {C,D}, they share a common element and so consolidate to the final output of the single set {A,B,C,D}

Example 4:

The consolidation of the five sets:

{H,I,K}, {A,B}, {C,D}, {D,B}, and {F,G,H}

Is the two sets:

{A, C, B, D}, and {G, F, I, H, K}