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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 ...
Recursion that contains only a single self-reference is known as single recursion, while recursion that contains multiple self-references is known as multiple recursion. Standard examples of single recursion include list traversal, such as in a linear search, or computing the factorial function, while standard examples of multiple recursion ...
In computer science, hybrid algorithms are very common in optimized real-world implementations of recursive algorithms, particularly implementations of divide-and-conquer or decrease-and-conquer algorithms, where the size of the data decreases as one moves deeper in the recursion. In this case, one algorithm is used for the overall approach (on ...
A total recursive function is a partial recursive function that is defined for every input. Every primitive recursive function is total recursive, but not all total recursive functions are primitive recursive. The Ackermann function A(m,n) is a well-known example of a total recursive function (in fact, provable total), that is not primitive ...
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 ...
The basic form of the Bron–Kerbosch algorithm is a recursive backtracking algorithm that searches for all maximal cliques in a given graph G.More generally, given three disjoint sets of vertices R, P, and X, it finds the maximal cliques that include all of the vertices in R, some of the vertices in P, and none of the vertices in X.
The μ-recursive functions (or general recursive functions) are partial functions that take finite tuples of natural numbers and return a single natural number.They are the smallest class of partial functions that includes the initial functions and is closed under composition, primitive recursion, and the minimization operator μ.
In computer science, corecursion is a type of operation that is dual to recursion.Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case.