Rosetta Code

Permutations/Rank of a permutation: Difference between revisions

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Permutations/Rank of a permutation (view source)

Revision as of 17:20, 14 March 2020

18 bytes added ,  4 years ago
Rename Perl 6 -> Raku, alphabetize, minor clean-up
m (→‎{{header|Phix}}: corrected output)
(Rename Perl 6 -> Raku, alphabetize, minor clean-up)
Line 252:
6844249986266452118: [18, 20, 11, 19, 10, 12, 8, 9, 3, 13, 7, 15, 0, 1, 6, 5, 14, 17, 4, 16, 2] = 6844249986266452118
12804085840772788456: [8, 4, 14, 2, 5, 12, 19, 0, 9, 17, 11, 7, 16, 1, 20, 6, 10, 15, 18, 3, 13] = 12804085840772788456</pre>
 
=={{header|FreeBASIC}}==
===Up to 20 objects===
Line 1,081 ⟶ 1,082:
{118,52,6,67,24,8,105,3,55,29,99,111,14,21,0,48,45,80,131,63,76,16,68,25,125,72,47,98,126,75,28,30,85,143,129,90,32,54,119,117,116,88,115,73,123,11,7,78,141,87,114,91,96,37,106,46,31,133,100,20,17,27,42,36,134,138,120,9,66,74,112,33,77,101,104,12,64,121,40,58,43,136,61,135,132,79,81,49,69,19,82,4,53,1,38,84,108,56,70,86,10,89,107,44,15,35,26,5,110,137,62,140,92,113,103,142,97,51,93,65,128,18,95,50,102,23,2,57,13,34,71,130,83,94,39,60,59,109,122,41,127,22,124,139}
{100,48,125,13,85,95,54,128,111,79,10,103,83,52,143,78,16,114,133,105,43,53,104,37,12,5,17,26,68,61,73,141,34,14,138,140,59,21,77,99,29,117,108,62,39,41,45,91,116,25,131,31,118,94,90,46,49,98,51,137,7,101,44,56,50,87,110,120,142,27,135,18,58,113,69,75,42,107,130,86,80,127,123,15,3,1,122,47,134,106,119,92,136,20,55,74,36,65,67,72,81,0,23,96,32,88,126,97,19,64,4,102,76,66,35,132,139,60,129,6,30,124,57,70,71,82,22,112,24,9,115,63,8,33,89,93,84,38,28,11,109,121,2,40}</pre>
 
=={{header|PARI/GP}}==
The functions are built into GP already: <code>numtoperm</code> and <code>permtonum</code>
Line 1,142 ⟶ 1,144:
6089 14383 3397 31577
61539 80497 47550 53322
</pre>
 
=={{header|Perl 6}}==
It is similar to Haskell, but separate something like [https://en.wikipedia.org/wiki/Inversion_(discrete_mathematics) inversion vector].
It is easy generate random inversion vector without BigInt.
 
<lang perl6>use v6;
 
sub rank2inv ( $rank, $n = * ) {
$rank.polymod( 1 ..^ $n );
}
 
sub inv2rank ( @inv ) {
[+] @inv Z* [\*] 1, 1, * + 1 ... *
}
 
sub inv2perm ( @inv, @items is copy = ^@inv.elems ) {
my @perm;
for @inv.reverse -> $i {
@perm.append: @items.splice: $i, 1;
}
@perm;
}
 
sub perm2inv ( @perm ) { #not in linear time
(
{ @perm[++$ .. *].grep( * < $^cur ).elems } for @perm;
).reverse;
}
for ^6 {
my @row.push: $^rank;
for ( *.&rank2inv(3) , &inv2perm, &perm2inv, &inv2rank ) -> &code {
@row.push: code( @row[*-1] );
}
say @row;
}
 
my $perms = 4; #100;
my $n = 12; #144;
 
say 'Via BigInt rank';
for ( ( ^([*] 1 .. $n) ).pick($perms) ) {
say $^rank.&rank2inv($n).&inv2perm;
};
 
say 'Via inversion vectors';
for ( { my $i=0; inv2perm (^++$i).roll xx $n } ... * ).unique( with => &[eqv] ).[^$perms] {
.say;
};
 
say 'Via Perl 6 method pick';
for ( { [(^$n).pick(*)] } ... * ).unique( with => &[eqv] ).head($perms) {
.say
};
</lang>
{{out}}
<pre>
[0 (0 0 0) [0 1 2] (0 0 0) 0]
[1 (0 1 0) [0 2 1] (0 1 0) 1]
[2 (0 0 1) [1 0 2] (0 0 1) 2]
[3 (0 1 1) [1 2 0] (0 1 1) 3]
[4 (0 0 2) [2 0 1] (0 0 2) 4]
[5 (0 1 2) [2 1 0] (0 1 2) 5]
Via BigInt rank
[4 3 1 8 6 2 0 7 9 11 5 10]
[0 8 11 4 9 3 7 5 2 6 10 1]
[5 7 9 11 10 6 4 1 2 3 0 8]
[9 11 8 6 3 5 7 2 4 0 1 10]
Via inversion vectors
[9 0 3 1 8 2 4 5 11 7 10 6]
[7 3 1 10 0 6 4 11 2 9 8 5]
[9 8 5 11 1 10 0 7 4 6 2 3]
[10 8 6 5 4 9 0 2 11 7 1 3]
Via Perl 6 method pick
[11 0 7 10 9 4 1 8 6 5 2 3]
[4 5 8 3 2 1 7 9 11 0 10 6]
[11 7 9 4 0 8 10 1 5 2 6 3]
[11 10 0 3 4 6 7 9 8 5 1 2]
</pre>
 
Line 1,506 ⟶ 1,429:
(22 (3 2 0 1) 22)
(23 (3 2 1 0) 23))
</pre>
 
=={{header|Raku}}==
(formerly Perl 6)
It is similar to Haskell, but separate something like [https://en.wikipedia.org/wiki/Inversion_(discrete_mathematics) inversion vector].
It is easy generate random inversion vector without BigInt.
 
<lang perl6>use v6;
 
sub rank2inv ( $rank, $n = * ) {
$rank.polymod( 1 ..^ $n );
}
 
sub inv2rank ( @inv ) {
[+] @inv Z* [\*] 1, 1, * + 1 ... *
}
 
sub inv2perm ( @inv, @items is copy = ^@inv.elems ) {
my @perm;
for @inv.reverse -> $i {
@perm.append: @items.splice: $i, 1;
}
@perm;
}
 
sub perm2inv ( @perm ) { #not in linear time
(
{ @perm[++$ .. *].grep( * < $^cur ).elems } for @perm;
).reverse;
}
for ^6 {
my @row.push: $^rank;
for ( *.&rank2inv(3) , &inv2perm, &perm2inv, &inv2rank ) -> &code {
@row.push: code( @row[*-1] );
}
say @row;
}
 
my $perms = 4; #100;
my $n = 12; #144;
 
say 'Via BigInt rank';
for ( ( ^([*] 1 .. $n) ).pick($perms) ) {
say $^rank.&rank2inv($n).&inv2perm;
};
 
say 'Via inversion vectors';
for ( { my $i=0; inv2perm (^++$i).roll xx $n } ... * ).unique( with => &[eqv] ).[^$perms] {
.say;
};
 
say 'Via Perl 6 method pick';
for ( { [(^$n).pick(*)] } ... * ).unique( with => &[eqv] ).head($perms) {
.say
};
</lang>
{{out}}
<pre>
[0 (0 0 0) [0 1 2] (0 0 0) 0]
[1 (0 1 0) [0 2 1] (0 1 0) 1]
[2 (0 0 1) [1 0 2] (0 0 1) 2]
[3 (0 1 1) [1 2 0] (0 1 1) 3]
[4 (0 0 2) [2 0 1] (0 0 2) 4]
[5 (0 1 2) [2 1 0] (0 1 2) 5]
Via BigInt rank
[4 3 1 8 6 2 0 7 9 11 5 10]
[0 8 11 4 9 3 7 5 2 6 10 1]
[5 7 9 11 10 6 4 1 2 3 0 8]
[9 11 8 6 3 5 7 2 4 0 1 10]
Via inversion vectors
[9 0 3 1 8 2 4 5 11 7 10 6]
[7 3 1 10 0 6 4 11 2 9 8 5]
[9 8 5 11 1 10 0 7 4 6 2 3]
[10 8 6 5 4 9 0 2 11 7 1 3]
Via Perl 6 method pick
[11 0 7 10 9 4 1 8 6 5 2 3]
[4 5 8 3 2 1 7 9 11 0 10 6]
[11 7 9 4 0 8 10 1 5 2 6 3]
[11 10 0 3 4 6 7 9 8 5 1 2]
</pre>
 
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