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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, analogously to the mathematical definition of factorial. Recursion in computer programming is exemplified when a function is defined in terms of simpler, often smaller versions of ...
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 include tree traversal, such as in a depth-first search.
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, addition and division, the factorial and exponential function, and the function which returns the nth prime are all primitive recursive. [1] In fact, for showing that a computable function is primitive recursive, it suffices to show that its time complexity is bounded above by a primitive recursive function of the input size. [ 2 ]
The factorial function is a common feature in scientific calculators. [73] ... In the recursive calls to the algorithm, ...
The factorial function provides a good example of how a fixed-point combinator may be used to define recursive functions. The standard recursive definition of the factorial function in mathematics can be written as
A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs. For example, the factorial function n! is defined by the rules ! = (+)! = (+)!.
This is the recursion, and executes the function again until the base case is reached. Using the product function from the Prelude, a number of small functions analogous to C's standard library, and using the Haskell syntax for arithmetic sequences, the factorial function can be expressed in Haskell as follows: