Railway circuit: Difference between revisions
added Raku programming solution
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(0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1)
(0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1)</pre>
=={{header|Raku}}==
{{trans|Julia}}
<lang raku>#!/usr/bin/env raku
# 20200406 Raku programming solution
class 𝒫 { has ($.x, $.y) } # Point
multi infix:<⊞>(𝒫 \p, 𝒫 \q) { 𝒫.bless: x => p.x + q.x , y => p.y + q.y }
multi infix:<≈>(𝒫 \p, 𝒫 \q) { my $*TOLERANCE = .0001; p.x ≅ q.x and p.y ≅ q.y }
constant twelvesteps = (1..12).map: { 𝒫.new: x =>sin(π*$_/6), y=>cos(π*$_/6) };
constant foursteps = (1..4).map: { 𝒫.new: x =>sin(π*$_/2), y=>cos(π*$_/2) };
sub digits($n!, $base!, $pad=0) {
my @output = $n.base($base).comb.reverse;
if ($pad > my $size = +@output) { @output.append: 0 xx ($pad - $size) }
return @output
} # rough port of https://docs.julialang.org/en/v1/base/numbers/#Base.digits
sub addsymmetries(%infound, \turns) {
sub circularsymmetries(@c is copy) { (0..^+@c).map: {rotate @c, $_} }
my @allsym = |(circularsymmetries turns), |(circularsymmetries turns.map: {-$_});
%infound{$_.Str} = 1 for @allsym;
return @allsym.max
}
sub isclosedpath(@turns is copy, \straight, \start= 𝒫.bless: x => 0, y => 0) {
return False unless ( @turns.sum % (straight ?? 4 !! 12) ) == 0;
my ($angl, $point) = (0, start);
for @turns -> $turn {
$angl += $turn;
$point ⊞= straight ?? foursteps[$angl % 4] !! twelvesteps[$angl % 12];
}
return $point ≈ start;
}
sub allvalidcircuits(\N, \doPrint=False, \straight=False) {
my ( @found, %infound );
say "\nFor N of ",N," and ", straight ?? "straight" !! "curved", " track: ";
for (straight ?? (0..^3**N) !! (0..^2**N)) -> \i {
my @turns = straight ??
digits(i,3,N).map: { $_ == 0 ?? 0 !! ($_ == 1 ?? -1 !! 1) } !!
digits(i,2,N).map: { $_ == 0 ?? -1 !! 1 } ;
if isclosedpath(@turns, straight) && !(%infound{@turns.Str}:exists) {
my \canon = addsymmetries(%infound, @turns);
say canon if doPrint;
@found.push: canon.Str;
}
}
say "There are ", +@found, " unique valid circuits.";
return @found
}
allvalidcircuits($_, $_ < 28) for 12, 16, 20; # 12, 16 … 36
allvalidcircuits($_, $_ < 12, True) for 4, 6, 8; # 4, 6 … 16;</lang>
{{out}}
<pre>For N of 12 and curved track:
[1 1 1 1 1 1 1 1 1 1 1 1]
There are 1 unique valid circuits.
For N of 16 and curved track:
[1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 -1]
There are 1 unique valid circuits.
For N of 20 and curved track:
[1 1 1 1 1 1 1 1 -1 -1 1 1 1 1 1 1 1 1 -1 -1]
[1 1 1 1 1 1 1 -1 1 1 -1 1 1 1 1 1 1 1 -1 -1]
[1 1 1 1 1 1 1 -1 1 -1 1 1 1 1 1 1 1 -1 1 -1]
[1 1 1 1 1 1 -1 1 1 -1 1 1 1 1 1 1 -1 1 1 -1]
[1 1 1 1 1 -1 1 1 1 -1 1 1 1 1 1 -1 1 1 1 -1]
[1 1 1 1 -1 1 1 1 1 -1 1 1 1 1 -1 1 1 1 1 -1]
There are 6 unique valid circuits.
For N of 4 and straight track:
[1 1 1 1]
There are 1 unique valid circuits.
For N of 6 and straight track:
[1 1 0 1 1 0]
There are 1 unique valid circuits.
For N of 8 and straight track:
[1 1 0 0 1 1 0 0]
[1 0 1 0 1 0 1 0]
[1 1 0 1 0 1 1 -1]
[1 1 1 0 -1 -1 -1 0]
[1 1 1 1 1 1 1 1]
[1 1 1 1 -1 -1 -1 -1]
[1 1 1 -1 1 1 1 -1]
There are 7 unique valid circuits.</pre>
=={{header|Swift}}==
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