#!/usr/bin/perl

use constant pi => 3.14159265358979;

sub volume_var {
    my ($r, $n) = @_;
    my $denom;
    if ($n % 2) {
        $denom = sqrt(pi) * factorial(2 * (int($n / 2)) + 2) /
            factorial(int($n / 2) + 1) / (4 ** (int($n / 2) + 1));
    } else {
        $denom = factorial($n / 2);
    }
    return ($r ** $n) * (pi ** ($n / 2)) / $denom;
}

sub volume_novar {
    my ($r, $n) = @_;
    if ($n % 2) {
        return ($r ** $n) * (pi ** ($n / 2)) /
        (sqrt(pi) * factorial(2 * (int($n / 2)) + 2) /
         factorial(int($n / 2) + 1) / (4 ** (int($n / 2) + 1)));
    } else {
        return ($r ** $n) * (pi ** ($n / 2)) / factorial($n / 2);
    }
}


# factorial($n) computes the factorial of $n,
#   using an iterative algorithm.
sub factorial {
    my ($n) = shift;
    my ($result, $i) = (1, 2);
    for ( ; $i <= $n; $i++) {
        $result *= $i;
    }
    return $result;
}