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The Kleene star is defined for any monoid, not just strings. More precisely, let ( M , ⋅) be a monoid, and S ⊆ M . Then S * is the smallest submonoid of M containing S ; that is, S * contains the neutral element of M , the set S , and is such that if x , y ∈ S * , then x ⋅ y ∈ S * .
The regular octagonal star is very popular as a symbol of rowing clubs in the Cologne Lowland, as seen on the club flag of the Cologne Rowing Association. The geometry can be adjusted so 3 edges cross at a single point, like the Auseklis symbol An 8-point compass rose can be seen as an octagonal star, with 4 primary points, and 4 secondary points.
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.
Along with exploring the capabilities and pitfalls of object-oriented programming, it describes 23 common programming problems and patterns for solving them. The book describes the following patterns: Creational patterns (5): Factory method pattern, Abstract factory pattern, Singleton pattern, Builder pattern, Prototype pattern
In graph theory, a star S k is the complete bipartite graph K 1,k : a tree with one internal node and k leaves (but no internal nodes and k + 1 leaves when k ≤ 1). Alternatively, some authors define S k to be the tree of order k with maximum diameter 2; in which case a star of k > 2 has k − 1 leaves. A star with 3 edges is called a claw.
The decorator pattern is a design pattern used in statically-typed object-oriented programming languages to allow functionality to be added to objects at run time; Python decorators add functionality to functions and methods at definition time, and thus are a higher-level construct than decorator-pattern classes.
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The indirection pattern supports low coupling and reuses potential between two elements by assigning the responsibility of mediation between them to an intermediate object. An example of this is the introduction of a controller component for mediation between data (model) and its representation (view) in the model-view-controller pattern.