Compute factorial of positive integer

3 
 $ fac() { (echo 1; seq $1) | paste -s -d\* | bc; }

May 21, 2014, 10:55 p.m. — jeroenjanssens

Explanation

This one-liner defines a shell function named fac that computes the factorial of a positive integer. Once this function has been defined (you can put it in your .bashrc), you can use it as follows:

$ fac 10
3628800

Let's break the function down. Assume that we want to compute the factorial of 4. First, it echo's 1, so that the factorial of 0 works correctly (because seq 0 outputs nothing). Then, seq is used to generate a list of numbers: 

$ (echo 1; seq 4)
1
1
2
3
4

Then, it uses paste to put these numbers on one line, with * (multiplication) as the seperator:

$ (echo 1; seq 4) | paste -s -d\*
1*1*2*3*4

Finally, it passes this "equation" to bc, which evalutes it:

$ (echo 1; seq 4) | paste -s -d\* | bc
24

The actual function uses $1 so that we can compute the factorial of any positive integer using fac.

Alternative one-liners

0

Recursively compute factorial of positive integer using only built-ins 

 $ bang() ( IFS=\*; let N=$1-1 k="$*" && bang $N $k || echo ${2-1} )

Nov. 25, 2019, 8:06 a.m. — CK

Explanation

A recursive function that leverages the arithmetic expansions evaluated by the let command, and the significance of the field separator when arguments are expanded using "$*".

  • IFS=\* concatenates the arguments "$*" using a * symbol, which let interprets as a multiplication operator;

  • let N=$1-1 k="$*" assigns arithmetic values to variables N and k. N will have a value one less than the first argument; k will be the product of all the arguments;

  • && performs the command immediately to its right iff the expression immediately to its left evaluates to true;

  • bang $N $k calls itself with the first argument being one less than it was, and the second argument being the cumulative product of the arguments thus far across all iterations;

  • || performs the command immediately to its right iff the command immediately to its left wasn't performed;

  • echo ${2-1} prints the second argument, which—if there is one—will be the factorial, otherwise it prints 1.

Limitations

If a positive integer is not the one and only argument passed to it when invoked by the user, the result will be nonsense or an error will be thrown.