Re: Permutations

> (Please note that running time increasing
> dramatically as n increases, making the code only
> practical for n <= 4.)
> 
> #!/usr/bin/perl -l
> sub f {$_[0]<2?$_[0]:$_[0]*f($_[0]-1)}
> sub g {
>    $_[2]=$_[0]**$_[1];
>    $_[2]-=(f($_[0])/(f($_[0]-$_)*f($_)))*g($_,$_[1])for 1..$_[0]-1;
>    $_[2]
> }
> print g(f($ARGV[0]),$ARGV[1])/f($ARGV[0])**$ARGV[1]

Your version repeatedly calculates g(i,x) for 1<=i<n!. How about this
version, which avoids this:

#!/usr/bin/perl -l
use bignum;
sub f {$_[0]<2?$_[0]:$_[0]*f($_[0]-1)}
sub g {
    #$_[2]=new Math::BigFloat($_[0])**$_[1];
    $_[2]=($_[0]+0.1-0.1)**$_[1];
      $_[2]-=(f($_[0])/(f($_[0]-$_)*f($_)))*$g[$_]for 1..$_[0]-1;
        $_[2]
}
$g[$_]=g($_,$ARGV[1])for 1..f($ARGV[0]);
print $g[f($ARGV[0])]/f($ARGV[0])**$ARGV[1]

Also note I used bignum, because you want that when you're dealing with
numbers this size.

Still takes a while, but I think it's a shorter while.

- Roie