The Factorial Function

The factorial function is a mathematical function that takes a non-negative integer n and returns the product of all positive integers less than or equal to n. The factorial function is denoted by n!.

This is a reference page for the factorial function, written in C and Python.

Background

The first 10 factorials are:

Where $n!=n\times(n-1)\times(n-2)\times\cdots\times2\times1$ and $n! = n\times(n-1)!$.

The Wikipedia page has a more detailed explanation of the factorial function.

Code

Psuedocode

This is the psuedocode for the factorial function:

FUNCTION factorial(n)
    IF n = 0
        RETURN 1
    ELSE
        RETURN n * factorial(n-1)
    END IF
END FUNCTION

Factorial in C

This is a sample factorial function that gets the user’s input and returns the factorial of the input, written in C.

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#include <stdio.h>

int main();
int factorial(int n);

int main(){
    int n;
    printf("Enter a number: ");
    scanf("%d", &n);
    int fac = factorial(n);
    printf("\nThe factorial of %d is %d.", n, fac);
}

int factorial(int n){
    if(n == 0 || n == 1){
        return 1;
    }
    else{
        return(n* factorial(n-1));
    }
    //return (n == 0) ? 1 : (n * factorial(n-1));
}

{: file="Factorial.c” }

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Enter a number: 9

The factorial of 9 is 362880.

{: file="Factorial.c Input and Output” }

The recursive factorial function could be simplified to a single line of code:

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return (n == 0) ? 1 : (n * factorial(n-1));

{: file="Factorial With Ternary Operator” }

This returns 1 if n is 0, otherwise it recursively returns n multiplied by the factorial of n-1.

I really like the use and elegance of Ternary Operators in C.

Factorial in Python

This is the same factorial function written in Python.

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def factorial(x):
    if (x == 0):
        return (1)

    else:
        return (x * factorial(x - 1))

#    return (1 if x == 0 else x * factorial(x - 1))

num = int(input("Please Enter a number: "))
print("Factorial: ",str(factorial(num)))

{: file="Factorial.py” }

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Please Enter a number: 9
Factorial:  362880

{: file="Factorial.py Input and Output” }

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def factorial(x):
    return (1 if x == 0 else x * factorial(x - 1))

{: file="Factorial.py” }

Similar to the C Version, the Python version could be simplified to a single line of code.