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Disjoint sets - Wikipedia, the free encyclopedia
In mathematics and computer science, two sets are said to be disjoint if they have no element in common. For example, {1, 2, 3} and {4, 5, 6} are disjoint sets. Formally, two sets A and B are ...
en.wikipedia.org/wiki/Disjoint_sets |
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Disjoint-set data structure - Wikipedia, the free encyclopedia
Given a set of elements, it is often useful to break them up or partition them into a number of separate, nonoverlapping sets. A disjoint-set data structure is a data structure that keeps track of s...
en.wikipedia.org/wiki/Disjoint-set_data_structure |
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are disjoint if A_i intersection A_j=emptyset for i!=j . For example, {A,B,C} and {D,E} are disjoint, but {A,B,C} and {C,D,E} are not. Disjoint sets are ...
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This is class that provides disjoint sets operations with union by rank and path compression. A disjoint-sets data structure maintains a collection S = {S1, S2, ..., Sk} of disjoint sets. Each set is identified by a representative which is some member of of the set.
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for K=3: A={3, 4, 5} and B={8, 9, 10} are the least disjoint sets of consecutive numbers that share the same set P={2, 3, 5} of prime divisors. ... Ërdos conjectures that there are only finite examples of these couples of sets. See: B35, p. 90, R. K. Guy.
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sets, logic, proofs ... Disjoint Sets; Non-Overlapping Sets ... Two or more sets which have no elements in common. For example, the sets A = {a,b,c} and B = {d,e,f} are disjoint.
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Below are implementations in C++ and C# of the Disjoint Sets data structure (also known as the Union-Find data structure). The implementation is fairly simple (about 200 lines with comments).
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