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Add docs for combination words

db4
Aaron Schaefer 2009-05-06 21:27:04 -04:00
parent 78037d8d05
commit b84a3158fa
1 changed files with 63 additions and 7 deletions
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basis/math/combinatorics/combinatorics-docs.factor
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@ -1,37 +1,93 @@
USING: help.markup help.syntax kernel math math.order sequences ;
USING: help.markup help.syntax kernel math math.order multiline sequences ;
IN: math.combinatorics
HELP: factorial
{ $values { "n" "a non-negative integer" } { "n!" integer } }
{ $description "Outputs the product of all positive integers less than or equal to " { $snippet "n" } "." }
{ $examples { $example "USING: math.combinatorics prettyprint ;" "4 factorial ." "24" } } ;
{ $examples
{ $example "USING: math.combinatorics prettyprint ;"
"4 factorial ." "24" }
} ;
HELP: nPk
{ $values { "n" "a non-negative integer" } { "k" "a non-negative integer" } { "nPk" integer } }
{ $description "Outputs the total number of unique permutations of size " { $snippet "k" } " (order does matter) that can be taken from a set of size " { $snippet "n" } "." }
{ $examples { $example "USING: math.combinatorics prettyprint ;" "10 4 nPk ." "5040" } } ;
{ $examples
{ $example "USING: math.combinatorics prettyprint ;"
"10 4 nPk ." "5040" }
} ;
HELP: nCk
{ $values { "n" "a non-negative integer" } { "k" "a non-negative integer" } { "nCk" integer } }
{ $description "Outputs the total number of unique combinations of size " { $snippet "k" } " (order does not matter) that can be taken from a set of size " { $snippet "n" } ". Commonly written as \"n choose k\"." }
{ $examples { $example "USING: math.combinatorics prettyprint ;" "10 4 nCk ." "210" } } ;
{ $examples
{ $example "USING: math.combinatorics prettyprint ;"
"10 4 nCk ." "210" }
} ;
HELP: permutation
{ $values { "n" "a non-negative integer" } { "seq" sequence } { "seq" sequence } }
{ $description "Outputs the " { $snippet "nth" } " lexicographical permutation of " { $snippet "seq" } "." }
{ $notes "Permutations are 0-based and a bounds error will be thrown if " { $snippet "n" } " is larger than " { $snippet "seq length factorial 1-" } "." }
{ $examples { $example "USING: math.combinatorics prettyprint ;" "1 3 permutation ." "{ 0 2 1 }" } { $example "USING: math.combinatorics prettyprint ;" "5 { \"apple\" \"banana\" \"orange\" } permutation ." "{ \"orange\" \"banana\" \"apple\" }" } } ;
{ $examples
{ $example "USING: math.combinatorics prettyprint ;"
"1 3 permutation ." "{ 0 2 1 }" }
{ $example "USING: math.combinatorics prettyprint ;"
"5 { \"apple\" \"banana\" \"orange\" } permutation ." "{ \"orange\" \"banana\" \"apple\" }" }
} ;
HELP: all-permutations
{ $values { "seq" sequence } { "seq" sequence } }
{ $description "Outputs a sequence containing all permutations of " { $snippet "seq" } " in lexicographical order." }
{ $examples { $example "USING: math.combinatorics prettyprint ;" "3 all-permutations ." "{ { 0 1 2 } { 0 2 1 } { 1 0 2 } { 1 2 0 } { 2 0 1 } { 2 1 0 } }" } } ;
{ $examples
{ $example "USING: math.combinatorics prettyprint ;"
"3 all-permutations ." "{ { 0 1 2 } { 0 2 1 } { 1 0 2 } { 1 2 0 } { 2 0 1 } { 2 1 0 } }" }
} ;
HELP: each-permutation
{ $values { "seq" sequence } { "quot" { $quotation "( seq -- )" } } }
{ $description "Applies the quotation to each permuation of " { $snippet "seq" } " in order." } ;
HELP: inverse-permutation
{ $values { "seq" sequence } { "permutation" sequence } }
{ $description "Outputs a sequence of indices representing the lexicographical permutation of " { $snippet "seq" } "." }
{ $notes "All items in " { $snippet "seq" } " must be comparable by " { $link <=> } "." }
{ $examples { $example "USING: math.combinatorics prettyprint ;" "\"dcba\" inverse-permutation ." "{ 3 2 1 0 }" } { $example "USING: math.combinatorics prettyprint ;" "{ 12 56 34 78 } inverse-permutation ." "{ 0 2 1 3 }" } } ;
{ $examples
{ $example "USING: math.combinatorics prettyprint ;"
"\"dcba\" inverse-permutation ." "{ 3 2 1 0 }" }
{ $example "USING: math.combinatorics prettyprint ;"
"{ 12 56 34 78 } inverse-permutation ." "{ 0 2 1 3 }" }
} ;
HELP: combination
{ $values { "m" "a non-negative integer" } { "seq" sequence } { "k" "a non-negative integer" } { "seq" sequence } }
{ $description "Outputs the " { $snippet "mth" } " lexicographical combination of " { $snippet "seq" } " choosing " { $snippet "k" } " elements." }
{ $notes "Combinations are 0-based and a bounds error will be thrown if " { $snippet "m" } " is larger than " { $snippet "seq length k nCk" } "." }
{ $examples
{ $example "USING: math.combinatorics prettyprint ;"
"6 7 iota 4 combination ." "{ 0 1 3 6 }" }
{ $example "USING: math.combinatorics prettyprint ;"
"0 { \"a\" \"b\" \"c\" \"d\" } 2 combination ." "{ \"a\" \"b\" }" }
} ;
HELP: all-combinations
{ $values { "seq" sequence } { "k" "a non-negative integer" } { "seq" sequence } }
{ $description "Outputs a sequence containing all combinations of " { $snippet "seq" } " choosing " { $snippet "k" } " elements, in lexicographical order." }
{ $examples
{ $example "USING: math.combinatorics prettyprint ;"
"{ \"a\" \"b\" \"c\" \"d\" } 2 all-combinations ."
<" {
{ "a" "b" }
{ "a" "c" }
{ "a" "d" }
{ "b" "c" }
{ "b" "d" }
{ "c" "d" }
}"> } } ;
HELP: each-combination
{ $values { "seq" sequence } { "k" "a non-negative integer" } { "quot" { $quotation "( seq -- )" } } }
{ $description "Applies the quotation to each combination of " { $snippet "seq" } " choosing " { $snippet "k" } " elements, in order." } ;
IN: math.combinatorics.private