150 lines
7.0 KiB
Factor
150 lines
7.0 KiB
Factor
USING: help.markup help.syntax kernel math math.order sequences ;
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IN: math.combinatorics
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HELP: factorial
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{ $values { "n" "a non-negative integer" } { "n!" integer } }
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{ $description "Outputs the product of all positive integers less than or equal to " { $snippet "n" } "." }
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{ $examples
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{ $example "USING: math.combinatorics prettyprint ;"
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"4 factorial ." "24" }
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} ;
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HELP: nPk
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{ $values { "n" "a non-negative integer" } { "k" "a non-negative integer" } { "nPk" integer } }
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{ $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" } "." }
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{ $examples
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{ $example "USING: math.combinatorics prettyprint ;"
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"10 4 nPk ." "5040" }
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} ;
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HELP: nCk
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{ $values { "n" "a non-negative integer" } { "k" "a non-negative integer" } { "nCk" integer } }
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{ $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\"." }
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{ $examples
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{ $example "USING: math.combinatorics prettyprint ;"
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"10 4 nCk ." "210" }
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} ;
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HELP: permutation
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{ $values { "n" "a non-negative integer" } { "seq" sequence } { "seq'" sequence } }
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{ $description "Outputs the " { $snippet "nth" } " lexicographical permutation of " { $snippet "seq" } "." }
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{ $notes "Permutations are 0-based and a bounds error will be thrown if " { $snippet "n" } " is larger than " { $snippet "seq length factorial 1 -" } "." }
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{ $examples
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{ $example "USING: math.combinatorics prettyprint ;"
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"1 { 0 1 2 } permutation ." "{ 0 2 1 }" }
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{ $example "USING: math.combinatorics prettyprint ;"
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"5 { \"apple\" \"banana\" \"orange\" } permutation ." "{ \"orange\" \"banana\" \"apple\" }" }
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} ;
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HELP: <permutations>
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{ $values { "seq" sequence } { "permutations" sequence } }
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{ $description "An efficient sequence containing the lexicographical permutations of " { $snippet "seq" } "." } ;
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HELP: <k-permutations>
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{ $values { "seq" sequence } { "k" integer } { "permutations" sequence } }
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{ $description "An efficient sequence containing the " { $snippet "k" } " lexicographical permutations of " { $snippet "seq" } "." } ;
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HELP: all-permutations
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{ $values { "seq" sequence } { "seq'" sequence } }
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{ $description "Outputs a sequence containing all permutations of " { $snippet "seq" } " in lexicographical order." }
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{ $examples
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{ $example "USING: math.combinatorics prettyprint ;"
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"{ 0 1 2 } all-permutations ." "{ { 0 1 2 } { 0 2 1 } { 1 0 2 } { 1 2 0 } { 2 0 1 } { 2 1 0 } }" }
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} ;
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HELP: each-permutation
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{ $values { "seq" sequence } { "quot" { $quotation ( ... elt -- ... ) } } }
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{ $description "Applies the quotation to each permutation of " { $snippet "seq" } " in order." } ;
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HELP: inverse-permutation
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{ $values { "seq" sequence } { "permutation" sequence } }
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{ $description "Outputs a sequence of indices representing the lexicographical permutation of " { $snippet "seq" } "." }
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{ $notes "All items in " { $snippet "seq" } " must be comparable by " { $link <=> } "." }
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{ $examples
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{ $example "USING: math.combinatorics prettyprint ;"
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"\"dcba\" inverse-permutation ." "{ 3 2 1 0 }" }
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{ $example "USING: math.combinatorics prettyprint ;"
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"{ 12 56 34 78 } inverse-permutation ." "{ 0 2 1 3 }" }
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} ;
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HELP: combination
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{ $values { "m" "a non-negative integer" } { "seq" sequence } { "k" "a non-negative integer" } { "seq'" sequence } }
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{ $description "Outputs the " { $snippet "mth" } " lexicographical combination of " { $snippet "seq" } " choosing " { $snippet "k" } " elements." }
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{ $notes "Combinations are 0-based and a bounds error will be thrown if " { $snippet "m" } " is larger than " { $snippet "seq length k nCk" } "." }
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{ $examples
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{ $example "USING: math.combinatorics sequences prettyprint ;"
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"6 7 iota 4 combination ." "{ 0 1 3 6 }" }
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{ $example "USING: math.combinatorics prettyprint ;"
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"0 { \"a\" \"b\" \"c\" \"d\" } 2 combination ." "{ \"a\" \"b\" }" }
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} ;
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HELP: <combinations>
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{ $values { "seq" sequence } { "k" "a non-negative integer" } { "combinations" sequence } }
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{ $description "An efficient sequence containing the combinations of " { $snippet "seq" } " choosing " { $snippet "k" } " elements." } ;
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HELP: all-combinations
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{ $values { "seq" sequence } { "k" "a non-negative integer" } { "seq'" sequence } }
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{ $description "Outputs a sequence containing all combinations of " { $snippet "seq" } " choosing " { $snippet "k" } " elements, in lexicographical order." }
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{ $examples
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{ $example "USING: math.combinatorics prettyprint ;"
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"{ \"a\" \"b\" \"c\" \"d\" } 2 all-combinations ."
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"""{
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{ "a" "b" }
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{ "a" "c" }
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{ "a" "d" }
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{ "b" "c" }
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{ "b" "d" }
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{ "c" "d" }
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}""" } } ;
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HELP: each-combination
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{ $values { "seq" sequence } { "k" "a non-negative integer" } { "quot" { $quotation ( ... elt -- ... ) } } }
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{ $description "Applies the quotation to each combination of " { $snippet "seq" } " choosing " { $snippet "k" } " elements, in order." } ;
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IN: math.combinatorics.private
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HELP: factoradic
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{ $values { "n" integer } { "factoradic" sequence } }
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{ $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." }
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{ $examples { $example "USING: math.combinatorics.private prettyprint ;" "859 factoradic ." "{ 1 1 0 3 0 1 0 }" } } ;
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HELP: >permutation
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{ $values { "factoradic" sequence } { "permutation" sequence } }
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{ $description "Converts an integer represented in factoradic form into its corresponding unique permutation (0-based)." }
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{ $notes "For clarification, the following two statements are equivalent:" { $code "10 factoradic >permutation" "{ 1 2 0 0 } >permutation" } }
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{ $examples { $example "USING: math.combinatorics.private prettyprint ;" "{ 0 0 0 0 } >permutation ." "{ 0 1 2 3 }" } } ;
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HELP: next-permutation
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{ $values { "seq" sequence } }
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{ $description "Rearranges the elements in " { $snippet "seq" } " into the lexicographically next greater permutation of elements." }
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{ $notes "Performs an in-place modification of " { $snippet "seq" } "." }
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{ $examples { $example "USING: math.combinatorics prettyprint ;" "\"ABC\" next-permutation ." "\"ACB\"" } } ;
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HELP: all-subsets
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{ $values { "seq" sequence } { "subsets" sequence } }
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{ $description
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"Returns all the subsets of a sequence."
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}
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{ $examples
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{ $example
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"USING: math.combinatorics prettyprint ;"
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"{ 1 2 3 } all-subsets ."
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"{ { } { 1 } { 2 } { 3 } { 1 2 } { 1 3 } { 2 3 } { 1 2 3 } }"
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}
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} ;
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HELP: selections
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{ $values { "seq" sequence } { "n" integer } { "selections" sequence } }
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{ $description
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"Returns all the ways to take n (possibly the same) items from the "
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"sequence of items."
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}
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{ $examples
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{ $example
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"USING: math.combinatorics prettyprint ;"
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"{ 1 2 } 2 selections ."
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"{ { 1 1 } { 1 2 } { 2 1 } { 2 2 } }"
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}
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} ;
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