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In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product. [1]
Recursion (computer science) Tree created using the Logo programming language and relying heavily on recursion. Each branch can be seen as a smaller version of a tree. Recursive drawing of a Sierpiński Triangle through turtle graphics. In computer science, recursion is a method of solving a computational problem where the solution depends on ...
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 ...
In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator), [1]: p.26 is a higher-order function (i.e. a function which takes a function as argument) that returns some fixed point (a value that is mapped to itself) of its argument function, if one exists. Formally, if is a fixed-point combinator and the ...
Double factorial. The fifteen different chord diagrams on six points, or equivalently the fifteen different perfect matchings on a six-vertex complete graph. These are counted by the double factorial 15 = (6 − 1)‼. In mathematics, the double factorial of a number n, denoted by n‼, is the product of all the positive integers up to n that ...
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 ...
Primitive recursive function. In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all "for" loops (that is, an upper bound of the number of iterations of every loop is fixed before entering the loop). Primitive recursive functions form a strict ...
Now, to perform our recursive call to the factorial function, we would simply call (Y G) n, where n is the number we are calculating the factorial of. Given n = 4, for example, this gives: (Y G) 4 G (Y G) 4 (λr.λn.(1, if n = 0; else n × (r (n−1)))) (Y G) 4 (λn.(1, if n = 0; else n × ((Y G) (n−1)))) 4