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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.
English: Printable pdf version of C Programming Wikibook. This file was created with MediaWiki to LaTeX . The LaTeX source code is attached to the PDF file (see imprint).
In some cases a multiset in this counting sense may be generalized to allow negative values, as in Python. C++'s Standard Template Library implements both sorted and unsorted multisets. It provides the multiset class for the sorted multiset, as a kind of associative container, which implements this multiset using a self-balancing binary search ...
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 ...
In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class. A collection F {\displaystyle F} of subsets of a given set S {\displaystyle S} is called a family of subsets of S {\displaystyle S} , or a family of sets over S ...
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]
Let C i (for i between 1 and k) be the sum of subset i in a given partition. Instead of minimizing the objective function max(C i), one can minimize the objective function max(f(C i)), where f is any fixed function. Similarly, one can minimize the objective function sum(f(C i)), or maximize min(f(C i)), or maximize sum(f(C i)).
Equal-cardinality partition is a variant in which both parts should have an equal number of items, in addition to having an equal sum. This variant is NP-hard too. [5]: SP12 Proof. Given a standard Partition instance with some n numbers, construct an Equal-Cardinality-Partition instance by adding n zeros. Clearly, the new instance has an equal ...