project-euler / project-euler / 155 /


use strict;
use warnings;

use Math::BigRat;

=begin explation.

An electric circuit uses exclusively identical capacitors of the same value C.
The capacitors can be connected in series or in parallel to form sub-units, which can then be connected in series or in parallel with other capacitors or other sub-units to form larger sub-units, and so on up to a final circuit.

Using this simple procedure and up to n identical capacitors, we can make circuits having a range of different total capacitances. For example, using up to n=3 capacitors of 60 F each, we can obtain the following 7 distinct total capacitance values:

If we denote by D(n) the number of distinct total capacitance values we can obtain when using up to n equal-valued capacitors and the simple procedure described above, we have: D(1)=1, D(2)=3, D(3)=7 ...

Find D(18).

Reminder : When connecting capacitors C1, C2 etc in parallel, the total capacitance is CT = C1 + C2 +...,
whereas when connecting them in series, the overall capacitance is given by:


my @c;

$c[1] = ['1/1'];

for my $d (2 .. 18)
    my %h;
    for my $first (1 .. int($d/2))
        my $second = $d-$first;
        for my $f_key (@{$c[$first]})
            my $f = Math::BigRat->new($f_key);
            for my $s_key (@{$c[$second]})
                my $s = Math::BigRat->new($s_key);
                for my $t ($f+$s, (1/(1/$f+1/$s)))
    $c[$d] = [keys(%h)];
    print "Reached Depth $d : Got " . scalar(@{$c[$d]}). "\n";