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The empty multiset is the unique multiset with an empty support (underlying set), and thus a cardinality 0. The usual operations of sets may be extended to multisets by using the multiplicity function, in a similar way to using the indicator function for subsets.
It provides the unordered_multiset class for the unsorted multiset, as a kind of unordered associative container, which implements this multiset using a hash table. 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 ...
Using the iterator created earlier, the find() function searches for an element with the given key. If it finds the key, the program prints the element's value. If it doesn't find it, an iterator to the end of the map is returned and it outputs that the key could not be found. Finally all the elements in the tree are erased using clear().
The following containers are defined in the current revision of the C++ standard: unordered_set, unordered_map, unordered_multiset, unordered_multimap. Each of these containers differ only on constraints placed on their elements.
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 mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root.
where is the multiset for which () =, and μ(S) = 1 if S is a set (i.e. a multiset without double elements) of even cardinality. μ(S) = −1 if S is a set (i.e. a multiset without double elements) of odd cardinality. μ(S) = 0 if S is a proper multiset (i.e. S has double elements).
The 3-partition problem is a strongly NP-complete problem in computer science.The problem is to decide whether a given multiset of integers can be partitioned into triplets that all have the same sum.