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The cardinality or "size" of a multiset is the sum of the multiplicities of all its elements. For example, in the multiset {a, a, b, b, b, c} the multiplicities of the members a, b, and c are respectively 2, 3, and 1, and therefore the cardinality of this multiset is 6.
In object-oriented programming, a class defines the shared aspects of objects created from the class. The capabilities of a class differ between programming languages , but generally the shared aspects consist of state ( variables ) and behavior ( methods ) that are each either associated with a particular object or with all objects of that class.
The unsorted multiset is standard as of C++11; previously SGI's STL provides the hash_multiset class, which was copied and eventually standardized. For Java, third-party libraries provide multiset functionality: Apache Commons Collections provides the Bag and SortedBag interfaces, with implementing classes like HashBag and TreeBag.
Class (set theory) – Collection of sets in mathematics that can be defined based on a property of its members; Combinatorial design – Symmetric arrangement of finite sets; δ-ring – Ring closed under countable intersections; Field of sets – Algebraic concept in measure theory, also referred to as an algebra of sets
In the object-oriented application programming paradigm, which is related to database structure design, UML class diagrams may be used for object modeling. In that case, object relationships are modeled using UML associations, and multiplicity is used on those associations to denote cardinality. Here are some examples: [5]
HyperLogLog is an algorithm for the count-distinct problem, approximating the number of distinct elements in a multiset. [1] Calculating the exact cardinality of the distinct elements of a multiset requires an amount of memory proportional to the cardinality, which is impractical for very large data sets. Probabilistic cardinality estimators ...
Modern object-oriented languages, such as C++ and Java, support a form of abstract data types. When a class is used as a type, it is an abstract type that refers to a hidden representation. In this model, an ADT is typically implemented as a class, and each instance of the ADT is usually an object of that class.
The input to the problem is a multiset S of numbers (usually integers), whose sum is k*T. The associated decision problem is to decide whether S can be partitioned into k subsets such that the sum of each subset is exactly T. There is also an optimization problem: find a partition of S into k subsets, such that the k sums are "as near as ...