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A related example is the multiset of solutions of an algebraic equation. A quadratic equation, for example, has two solutions. However, in some cases they are both the same number. Thus the multiset of solutions of the equation could be {3, 5}, or it could be {4, 4}. In the latter case it has a solution of multiplicity 2.
The multiple subset sum problem is an optimization problem in computer science and operations research. It is a generalization of the subset sum problem . The input to the problem is a multiset S {\displaystyle S} of n integers and a positive integer m representing the number of subsets.
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle T} , and the question is to decide whether any subset of the integers sum to precisely T {\displaystyle T} . [ 1 ]
In number theory and computer science, the partition problem, or number partitioning, [1] is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S 1 and S 2 such that the sum of the numbers in S 1 equals the sum of the numbers in S 2.
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.
Conversely, in every solution of S u, since the target sum is 7 T and each element is in ( T /4, 7 T /2), there must be exactly 3 elements per set, so it corresponds to a solution of S r. The ABC-partition problem (also called numerical 3-d matching ) is a variant in which, instead of a set S with 3 m integers, there are three sets A , B , C ...
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
[1]: sec.5 The problem is parametrized by a positive integer k, and called k-way number partitioning. [2] 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.