Search results
Results from the WOW.Com Content Network
A classic example of recursion is computing the factorial, which is defined recursively by 0! := 1 and n! := n × (n - 1)!.. To recursively compute its result on a given input, a recursive function calls (a copy of) itself with a different ("smaller" in some way) input and uses the result of this call to construct its result.
For example, in the factorial function, properly the base case is 0! = 1, while immediately returning 1 for 1! is a short circuit, and may miss 0; this can be mitigated by a wrapper function. The box shows C code to shortcut factorial cases 0 and 1.
As an example, the function argument in the recursive expression for the factorial function below will always decrease by 1; by the well-ordering property of natural numbers, the argument will eventually reach 1 and the recursion will terminate. function factorial (argument as natural number) if argument = 0 or argument = 1 return 1 otherwise ...
function factorial (n is a non-negative integer) if n is 0 then return 1 [by the convention that 0! = 1] else if n is in lookup-table then return lookup-table-value-for-n else let x = factorial(n – 1) times n [recursively invoke factorial with the parameter 1 less than n] store x in lookup-table in the n th slot [remember the result of n! for ...
The factorial function is a common feature in scientific calculators. [73] It is also included in scientific programming libraries such as the Python mathematical functions module [74] and the Boost C++ library. [75]
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.
The Y combinator allows recursion to be defined as a set of rewrite rules, [21] without requiring native recursion support in the language. [22] In programming languages that support anonymous functions, fixed-point combinators allow the definition and use of anonymous recursive functions, i.e. without having to bind such functions to identifiers.
A classic example of recursion is the definition of the factorial function, given here in Python code: def factorial ( n ): if n > 0 : return n * factorial ( n - 1 ) else : return 1 The function calls itself recursively on a smaller version of the input (n - 1) and multiplies the result of the recursive call by n , until reaching the base case ...