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The leaves of the tree are the base cases of the recursion, the subproblems (of size less than k) that do not recurse. The above example would have a child nodes at each non-leaf node. Each node does an amount of work that corresponds to the size of the subproblem n passed to that instance of the recursive call and given by (). The total amount ...
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 ...
Many well-known recursive algorithms generate an entirely new piece of data from the given data and recur on it. HtDP (How to Design Programs) refers to this kind as generative recursion. Examples of generative recursion include: gcd, quicksort, binary search, mergesort, Newton's method, fractals, and adaptive integration.
Any mutual recursion between two procedures can be converted to direct recursion by inlining the code of one procedure into the other. [9] If there is only one site where one procedure calls the other, this is straightforward, though if there are several it can involve code duplication.
A quine's output is exactly the same as its source code. A quine is a computer program that takes no input and produces a copy of its own source code as its only output. The standard terms for these programs in the computability theory and computer science literature are "self-replicating programs", "self-reproducing programs", and "self-copying programs".
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
Another example is a similar singly linked type in Java: class List < E > { E value ; List < E > next ; } This indicates that non-empty list of type E contains a data member of type E, and a reference to another List object for the rest of the list (or a null reference to indicate that this is the end of the list).