146 lines
6.7 KiB
Factor
146 lines
6.7 KiB
Factor
USING: help.markup help.syntax kernel math math.order 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" }
|
|
} ;
|
|
|
|
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" }
|
|
} ;
|
|
|
|
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" }
|
|
} ;
|
|
|
|
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 { 0 1 2 } permutation ." "{ 0 2 1 }" }
|
|
{ $example "USING: math.combinatorics prettyprint ;"
|
|
"5 { \"apple\" \"banana\" \"orange\" } permutation ." "{ \"orange\" \"banana\" \"apple\" }" }
|
|
} ;
|
|
|
|
HELP: <permutations>
|
|
{ $values { "seq" sequence } { "permutations" sequence } }
|
|
{ $description "An efficient sequence containing the lexicographical permutations of " { $snippet "seq" } "." } ;
|
|
|
|
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 ;"
|
|
"{ 0 1 2 } 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 permutation 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 }" }
|
|
} ;
|
|
|
|
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 sequences 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: <combinations>
|
|
{ $values { "seq" sequence } { "k" "a non-negative integer" } { "combinations" sequence } }
|
|
{ $description "An efficient sequence containing the combinations of " { $snippet "seq" } " choosing " { $snippet "k" } " elements." } ;
|
|
|
|
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
|
|
|
|
HELP: factoradic
|
|
{ $values { "n" integer } { "factoradic" sequence } }
|
|
{ $description "Converts a positive integer " { $snippet "n" } " to factoradic form. The factoradic of an integer is its representation based on a mixed radix numerical system that corresponds to the values of " { $snippet "n" } " factorial." }
|
|
{ $examples { $example "USING: math.combinatorics.private prettyprint ;" "859 factoradic ." "{ 1 1 0 3 0 1 0 }" } } ;
|
|
|
|
HELP: >permutation
|
|
{ $values { "factoradic" sequence } { "permutation" sequence } }
|
|
{ $description "Converts an integer represented in factoradic form into its corresponding unique permutation (0-based)." }
|
|
{ $notes "For clarification, the following two statements are equivalent:" { $code "10 factoradic >permutation" "{ 1 2 0 0 } >permutation" } }
|
|
{ $examples { $example "USING: math.combinatorics.private prettyprint ;" "{ 0 0 0 0 } >permutation ." "{ 0 1 2 3 }" } } ;
|
|
|
|
HELP: next-permutation
|
|
{ $values { "seq" sequence } }
|
|
{ $description "Rearranges the elements in " { $snippet "seq" } " into the lexicographically next greater permutation of elements." }
|
|
{ $notes "Performs an in-place modification of " { $snippet "seq" } "." }
|
|
{ $examples { $example "USING: math.combinatorics prettyprint ;" "\"ABC\" next-permutation ." "\"ACB\"" } } ;
|
|
|
|
HELP: all-subsets
|
|
{ $values { "seq" sequence } { "subsets" sequence } }
|
|
{ $description
|
|
"Returns all the subsets of a sequence."
|
|
}
|
|
{ $examples
|
|
{ $example
|
|
"USING: math.combinatorics prettyprint ;"
|
|
"{ 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: math.combinatorics prettyprint ;"
|
|
"{ 1 2 } 2 selections ."
|
|
"{ { 1 1 } { 1 2 } { 2 1 } { 2 2 } }"
|
|
}
|
|
} ;
|