Cycles of a permutation: Difference between revisions
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→{{header|Raku}}: Add a Raku example
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10 STOREDAILYPUNCH
</pre>
=={{header|Raku}}==
<syntaxhighlight lang="raku" line>
# one-line
sub infix:<➜> ($start, $end) {$start.fc.comb(/\w/).antipairs.hash{ $end.fc.comb(/\w/) } »+» 1}
# cycle
sub infix:<➰> ($start, $end) {
my @one-line = flat ($end ➜ $start);
my @index = flat 1..+@one-line;
my ($index, @cycles) = 0;
for @index {
my $this = $_ - 1;
while @one-line[$this] {
my $next = @one-line[$this];
@cycles[$index].push: @index[$this];
@one-line[$this] = Nil;
$this = $next - 1;
}
++$index;
}
@cycles.grep: *.elems > 1
}
# order of a cycle
sub order (@cycles) { [lcm] @cycles }
# signature of a cycle
sub signature (@cycles) {
(@cycles.elems %% 2 and all @@cycles».elems %% 2) ?? 1 !! -1
}
# apply a one-line transform
sub apply-o ($string, @oneline) { $string.comb[@oneline].join }
# apply a cyclical transform
sub apply-c ($string, @cycle) {
my @string = flat '', $string.comb;
@cycle.map: { @string[|$_].=rotate(-1) }
@string.join
}
# Alf & Bettys letter arrangements
my %arrangment =
:Mon<HANDYCOILSERUPT>,
:Tue<SPOILUNDERYACHT>,
:Wed<DRAINSTYLEPOUCH>,
:Thu<DITCHSYRUPALONE>,
:Fri<SOAPYTHIRDUNCLE>,
:Sat<SHINEPARTYCLOUD>,
:Sun<RADIOLUNCHTYPES>;
# some convenience variables
my @days = <Sun Mon Tue Wed Thu Fri Sat Sun>;
my @o = @days.rotor(2 => -1).map: { (%arrangment{.[0]} ➜ %arrangment{.[1]}) »-» 1 }
my @c = @days.rotor(2 => -1).map: { (%arrangment{.[0]} ➰ %arrangment{.[1]}) }
my $today;
# The task
say qq:to/ALF&BETTY/;
On Thursdays Alf and Betty should rearrange
their letters using these cycles: {gist %arrangment<Wed> ➰ %arrangment<Thu>}
So that {%arrangment<Wed>} becomes {%arrangment<Wed>.&apply-o: (%arrangment<Wed> ➜ %arrangment<Thu>) »-» 1}
or they could use the one-line notation: {gist %arrangment<Wed> ➜ %arrangment<Thu>}
To revert to the Wednesday arrangement they
should use these cycles: {gist %arrangment<Thu> ➰ %arrangment<Wed>}
or with the one-line notation: {gist %arrangment<Thu> ➜ %arrangment<Wed>}
So that {%arrangment<Thu>} becomes {%arrangment<Thu>.&apply-o: (%arrangment<Thu> ➜ %arrangment<Wed>) »-» 1}
Starting with the Sunday arrangement and applying each of the daily
permutations consecutively, the arrangements will be:
{$today = %arrangment<Sun>}
{join "\n", @days[1..*].map: { sprintf "%s: %s", $_, $today = $today.&apply-o: @o[$++] } }
To go from Wednesday to Friday in a single step they should use these cycles:
{gist %arrangment<Wed> ➰ %arrangment<Fri>}
So that {%arrangment<Wed>} becomes {%arrangment<Fri>}
These are the signatures of the permutations:
Mon Tue Wed Thu Fri Sat Sun
{@c.map(&signature)».fmt("%2d").join: ' '}
These are the orders of the permutations:
Mon Tue Wed Thu Fri Sat Sun
{@c.map(&order)».fmt("%2d").join: ' '}
Applying the Friday cycle to a string 10 times:
{$today = 'STOREDAILYPUNCH'}
{join "\n", (1..10).map: {sprintf "%2d %s", $_, $today = $today.&apply-c: @c[4]} }
ALF&BETTY
say 'and one last transform:';
say 'STOREDAILYPUNCH'.&apply-c: [[<1 6 12 2 3 4 13 15 9 11 5 14 8 10 7>],];</syntaxhighlight>
{{out}}
<pre>On Thursdays Alf and Betty should rearrange
their letters using these cycles: ([2 8 7 3 11 10 15 5 14 4] [9 12 13])
So that DRAINSTYLEPOUCH becomes DITCHSYRUPALONE
or they could use the one-line notation: (1 4 7 14 15 6 8 2 13 11 3 9 12 5 10)
To revert to the Wednesday arrangement they
should use these cycles: ([2 4 14 5 15 10 11 3 7 8] [9 13 12])
or with the one-line notation: (1 8 11 2 14 6 3 7 12 15 10 13 9 4 5)
So that DITCHSYRUPALONE becomes DRAINSTYLEPOUCH
Starting with the Sunday arrangement and applying each of the daily
permutations consecutively, the arrangements will be:
RADIOLUNCHTYPES
Mon: HANDYCOILSERUPT
Tue: SPOILUNDERYACHT
Wed: DRAINSTYLEPOUCH
Thu: DITCHSYRUPALONE
Fri: SOAPYTHIRDUNCLE
Sat: SHINEPARTYCLOUD
Sun: RADIOLUNCHTYPES
To go from Wednesday to Friday in a single step they should use these cycles:
([1 10 15 7 6] [2 9 14 13 11 4 8 5 12])
So that DRAINSTYLEPOUCH becomes SOAPYTHIRDUNCLE
These are the signatures of the permutations:
Mon Tue Wed Thu Fri Sat Sun
-1 -1 1 1 -1 1 -1
These are the orders of the permutations:
Mon Tue Wed Thu Fri Sat Sun
18 30 12 30 10 33 40
Applying the Friday cycle to a string 10 times:
STOREDAILYPUNCH
1 DNPYAOETISLCRUH
2 ORLSEPANTDIUYCH
3 PYIDALERNOTCSUH
4 LSTOEIAYRPNUDCH
5 IDNPATESYLRCOUH
6 TORLENADSIYUPCH
7 NPYIAREODTSCLUH
8 RLSTEYAPONDUICH
9 YIDNASELPROCTUH
10 STOREDAILYPUNCH
and one last transform:
AUTOPSYCHILDREN
</pre>
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