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Example implementation of expression templates : An example implementation of expression templates looks like the following. A base class VecExpression represents any vector-valued expression. It is templated on the actual expression type E to be implemented, per the curiously recurring template pattern.
In object-oriented programming, the singleton pattern is a software design pattern that restricts the instantiation of a class to a singular instance. It is one of the well-known "Gang of Four" design patterns , which describe how to solve recurring problems in object-oriented software. [ 1 ]
The cross product operation is an example of a vector rank function because it operates on vectors, not scalars. Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing ...
In object-oriented programming, the iterator pattern is a design pattern in which an iterator is used to traverse a container and access the container's elements. The iterator pattern decouples algorithms from containers; in some cases, algorithms are necessarily container-specific and thus cannot be decoupled.
For example, a container defined as std::vector<Shape*> does not work because Shape is not a class, but a template needing specialization. A container defined as std::vector<Shape<Circle>*> can only store Circles, not Squares. This is because each of the classes derived from the CRTP base class Shape is a unique type.
As another, more significant, example of compile-time loop unrolling, template metaprogramming can be used to create length-n vector classes (where n is known at compile time). The benefit over a more traditional length-n vector is that the loops can be unrolled, resulting in very optimized code. As an example, consider the addition operator.
A line graph has an articulation point if and only if the underlying graph has a bridge for which neither endpoint has degree one. [2] For a graph G with n vertices and m edges, the number of vertices of the line graph L(G) is m, and the number of edges of L(G) is half the sum of the squares of the degrees of the vertices in G, minus m. [6]
Bresenham's line algorithm is a line drawing algorithm that determines the points of an n-dimensional raster that should be selected in order to form a close approximation to a straight line between two points.