excellent.pl

use Time::HiRes qw(time);

sub perl1 {
    my $k = $_[0];
    foreach my $n (10**($k-1) .. 10**($k)-1) {
        my $front = $n * (10**$k + $n);
        my $root = int(sqrt($front));

        foreach my $t ($root-2 .. $root+2) {
            my $back = $t * ($t - 1);
            last if length($t) > $k;
            last if $back > $front;
            if ($back == $front) {
                print STDERR "$n$t\n";
                last;
            }
        }
    }
}

sub perl2 {
    my $k = $_[0];
    foreach my $a (10**($k-1) .. 10**($k)-1) {
        my $front = $a * (10**$k + $a);
        my $root = int($front**0.5);

        foreach my $b ($root-1 .. $root+1) {
            my $back = $b * ($b - 1);
            last if $back > $front;
            next if log($b)/log(10) > $k;
            if ($front == $back) {
                print STDERR "$a$b\n"
            }
        }
    }
}

my $digits = $ARGV[0] // 2;
die "Number of digits must be even and non-zero! You said [$digits]\n"
    unless $digits > 0 and $digits % 2 == 0 and int($digits) eq $digits;

my $k = $digits/2;

for (1 .. 10) {
    my $start = time();
    perl1($k);
    my $end = time();
    print "perl1,$digits,", $end-$start, "\n";

    my $start = time();
    perl2($k);
    my $end = time();
    print "perl2,$digits,", $end-$start, "\n";
}