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A class hierarchy in an object-oriented language can be thought of as a tree, with different types of object inheriting from their parents. If different classes need to be combined, such as in a comparison (like A < B) then the number of possible combinations which may occur explodes. If each type of comparison needs to be programmed then this ...
A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
MaxSNP is then defined as the class of all problems with an L-reduction (linear reduction, not log-space reduction) to problems in MaxSNP 0. [2] For example, MAX-3SAT is a problem in MaxSNP 0 : given an instance of 3-CNF-SAT (the boolean satisfiability problem with the formula in conjunctive normal form and at most 3 literals per clause), find ...
In computational complexity theory, co-NP is a complexity class.A decision problem X is a member of co-NP if and only if its complement X is in the complexity class NP.The class can be defined as follows: a decision problem is in co-NP if and only if for every no-instance we have a polynomial-length "certificate" and there is a polynomial-time algorithm that can be used to verify any purported ...
A solution to Kirkman's schoolgirl problem with vertices denoting girls and colours denoting days of the week [1] Kirkman's schoolgirl problem is a problem in combinatorics proposed by Thomas Penyngton Kirkman in 1850 as Query VI in The Lady's and Gentleman's Diary (pg.48). The problem states:
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.
Thus, such problems have a complexity that is at least linear, that is, using big omega notation, a complexity (). The solution of some problems, typically in computer algebra and computational algebraic geometry, may be very large. In such a case, the complexity is lower bounded by the maximal size of the output, since the output must be written.