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A demo for Union-Find when using Kruskal's algorithm to find minimum spanning tree. Disjoint-set data structures model the partitioning of a set, for example to keep track of the connected components of an undirected graph. This model can then be used to determine whether two vertices belong to the same component, or whether adding an edge ...
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For example, the union of three sets A, B, and C contains all elements of A, all elements of B, and all elements of C, and nothing else. Thus, x is an element of A ∪ B ∪ C if and only if x is in at least one of A, B, and C. A finite union is the union of a finite number of sets; the phrase does not imply that the union set is a finite set ...
A union containing another union is treated as the set of all its constituent possibilities, and if the context requires it a union is automatically coerced into the wider union. A union can explicitly contain no value, which can be distinguished at runtime. An example is:
Venn diagram showing the union of sets A and B as everything not in white. In combinatorics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as
A universe set is an absorbing element of binary union . The empty set ∅ {\displaystyle \varnothing } is an absorbing element of binary intersection ∩ {\displaystyle \cap } and binary Cartesian product × , {\displaystyle \times ,} and it is also a left absorbing element of set subtraction ∖ : {\displaystyle \,\setminus :}
Untagged unions depend on program logic to correctly identify the currently active field, which may result in strange behavior and hard-to-find bugs if that logic fails. The primary advantage of a tagged union over a simple record containing a field for each type is that it saves storage by overlapping storage for all the types. Some ...
The set of allowable primitives is limited by each software package. Some software packages allow CSG on curved objects while other packages do not. An object is constructed from primitives by means of allowable operations , which are typically Boolean operations on sets : union , intersection and difference , as well as geometric ...