# Van Eck by'eck

This is a solution to challenge #1 from the 14th Perl Weekly Challenge.

Write a script to generate Van Eck’s sequence starts with 0.

I thought it would be fun to try and solve this using the ... sequence operator. This first solution is very naive; it retains all generated values internally and uses grep to find previous occurrences.

my $van-eck := 0, ->$a {
state @items.push($a); my ($m, $n) = @items.grep($a, :k).tail(2);
$n.defined ??$n - $m !! 0 } ... *; say$van-eck[^30].join(', ');
say "Took " ~ (now - ENTER now) ~ " seconds";

say $van-eck[5000..^5030].join(', '); say "Took " ~ (now - ENTER now) ~ " seconds";  0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, 5, 3, 0, 3, 2, 9, 0, 4, 9, 3, 6, 14 Took 0.01310128 seconds 0, 5, 33, 776, 0, 4, 28, 447, 0, 4, 4, 1, 20, 60, 185, 340, 350, 1473, 0, 10, 35, 411, 910, 0, 5, 23, 232, 2110, 0, 5 Took 15.4696878 seconds  It is fine for a short sequence, but performance drops quite dramatically. A better solution is to retain the last seen index of each generated value, which vastly reduces the computation cost. my$van-eck := 0, -> $a { state$index++;
state %last-seen; LEAVE %last-seen{$a} =$index;
%last-seen{$a}:exists ??$index - %last-seen{$a} !! 0 } ... *; say$van-eck[^30].join(', ');
say "Took " ~ (now - ENTER now) ~ " seconds";

say \$van-eck[5000..^5030].join(', ');
say "Took " ~ (now - ENTER now) ~ " seconds";

0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, 5, 3, 0, 3, 2, 9, 0, 4, 9, 3, 6, 14
Took 0.0081188 seconds
0, 5, 33, 776, 0, 4, 28, 447, 0, 4, 4, 1, 20, 60, 185, 340, 350, 1473, 0, 10, 35, 411, 910, 0, 5, 23, 232, 2110, 0, 5
Took 0.1163919 seconds


I didn't expect sequences to be this much fun ;-)