# Paste: more combinatorics

Author: mrjbq7 factor Wed, 14 Jul 2010 15:55:42
Plain Text |
```USING: arrays combinators kernel make math math.combinatorics
math.ranges sequences sequences.deep ;

IN: combinatorics

: all-subsets ( seq -- subsets )
dup length [0,b] [
[ dupd all-combinations [ , ] each ] each
] { } make nip ;

: (selections) ( seq n -- selections )
dupd [ dup 1 > ] [
swap pick cartesian-product [
[ [ dup length 1 > [ flatten ] when , ] each ] each
] { } make swap 1 -
] while drop nip ;

: selections ( seq n -- selections )
{
{ 0 [ drop { } ] }
{ 1 [ 1array ] }
[ (selections) ]
} case ;```

## Annotation: some tests

Author: mrjbq7 factor Wed, 14 Jul 2010 15:56:00
Plain Text |
```[ { { } } ] [ { } all-subsets ] unit-test

[ { { } { 1 } { 2 } { 3 } { 1 2 } { 1 3 } { 2 3 } { 1 2 3 } } ]
[ { 1 2 3 } all-subsets ] unit-test

[ { } ] [ { 1 2 } 0 selections ] unit-test

[ { { 1 2 } } ] [ { 1 2 } 1 selections ] unit-test

[ { { 1 1 } { 1 2 } { 2 1 } { 2 2 } } ]
[ { 1 2 } 2 selections ] unit-test

[ { { 1 1 1 } { 1 1 2 } { 1 2 1 } { 1 2 2 }
{ 2 1 1 } { 2 1 2 } { 2 2 1 } { 2 2 2 } } ]
[ { 1 2 } 3 selections ] unit-test```

## Annotation: some docs

Author: mrjbq7 factor Wed, 14 Jul 2010 16:05:48
Plain Text |
```HELP: all-subsets
{ \$values { "seq" sequence } { "subsets" sequence } }
{ \$description
"Returns all the subsets of a sequence."
}
{ \$examples
{ \$example
"USING: combinatorics ;"
"{ 1 2 3 } all-subsets"
"{ { } { 1 } { 2 } { 3 } { 1 2 } { 1 3 } { 2 3 } { 1 2 3 } }"
}
} ;

HELP: selections
{ \$values { "seq" sequence } { "n" integer } { "selections" sequence } }
{ \$description
"Returns all the ways to take n (possibly the same) items from the "
"sequence of items."
}
{ \$examples
{ \$example
"USING: combinatorics ;"
"{ 1 2 } 2 selections"
"{ { 1 1 } { 1 2 } { 2 1 } { 2 2 } }"
}
} ;```