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One example is tree traversal as in depth-first search; though both recursive and iterative methods are used, [17] they contrast with list traversal and linear search in a list, which is a singly recursive and thus naturally iterative method. Other examples include divide-and-conquer algorithms such as Quicksort, and functions such as the ...
In some languages, such as BASIC, a callable has different syntax (i.e. keyword) for a callable that returns a value vs. one that does not. In other languages, the syntax is the same regardless. In some of these languages an extra keyword is used to declare no return value; for example void in C, C++ and C#. In some languages, such as Python ...
A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent (base case), or; One's parent's ancestor (recursive step). The Fibonacci sequence is another classic example of recursion: Fib(0) = 0 as ...
This definition is elegant and easy to work with abstractly (such as when proving theorems about properties of trees), as it expresses a tree in simple terms: a list of one type, and a pair of two types. This mutually recursive definition can be converted to a singly recursive definition by inlining the definition of a forest:
An example of a primitive recursive programming language is one that contains basic arithmetic operators (e.g. + and −, or ADD and SUBTRACT), conditionals and comparison (IF-THEN, EQUALS, LESS-THAN), and bounded loops, such as the basic for loop, where there is a known or calculable upper bound to all loops (FOR i FROM 1 TO n, with neither i ...
Mutual recursion is very common in functional programming, and is often used for programs written in LISP, Scheme, ML, and similar programming languages. For example, Abelson and Sussman describe how a meta-circular evaluator can be used to implement LISP with an eval-apply cycle. [7] In languages such as Prolog, mutual recursion is almost ...
If the target of a tail is the same subroutine, the subroutine is said to be tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end recursion) is particularly useful, and is often easy to optimize in implementations. Tail calls can be implemented without adding a new stack frame to the call stack.
For example, the Java language does not allow client code that accesses the private data of a class to compile. [12] In the C++ language, private methods are visible, but not accessible in the interface; however, they may be made invisible by explicitly declaring fully abstract classes that represent the interfaces of the class. [13]