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If, for example, there are two balls and three bins, then the number of ways of placing the balls is (+) = =. The table shows the six possible ways of distributing the two balls, the strings of stars and bars that represent them (with stars indicating balls and bars separating bins from one another), and the subsets that correspond to the strings.
An example of the printf function. printf is a C standard library function that formats text and writes it to standard output.. The name, printf is short for print formatted where print refers to output to a printer although the functions are not limited to printer output.
The curiously recurring template pattern (CRTP) is an idiom, originally in C++, in which a class X derives from a class template instantiation using X itself as a template argument. [1] More generally it is known as F-bound polymorphism , and it is a form of F -bounded quantification .
A similar problem exists in other languages, for example Java. Ranges have been proposed as a safer, more flexible alternative to iterators. [11] Certain iteration patterns such as callback enumeration APIs cannot be made to fit the STL model without the use of coroutines, [12] which were outside the C++ standard until C++20.
A basic example of string searching is when the pattern and the searched text are arrays of elements of an alphabet Σ. Σ may be a human language alphabet, for example, the letters A through Z and other applications may use a binary alphabet (Σ = {0,1}) or a DNA alphabet (Σ = {A,C,G,T}) in bioinformatics .
Example of Kleene star applied to the empty set: ∅ * = {ε}. Example of Kleene plus applied to the empty set: ∅ + = ∅ ∅ * = { } = ∅, where concatenation is an associative and noncommutative product. Example of Kleene plus and Kleene star applied to the singleton set containing the empty string:
The C++ examples in this section demonstrate the principle of using composition and interfaces to achieve code reuse and polymorphism. Due to the C++ language not having a dedicated keyword to declare interfaces, the following C++ example uses inheritance from a pure abstract base class .
C++: Used in Standard Template Library and the C++ Standard Library to support generic container classes [9] [10] and in the Boost TypeTraits library. [11] Curl: Abstract classes as mixins permit method implementations and thus constitute traits by another name. [citation needed] Fortress [12] Groovy: Since version 2.3 [13]