org.clojure/math.combinatorics {:mvn/version "0.2.0"}

[org.clojure/math.combinatorics "0.2.0"]

(ns example.core
  (:require [clojure.math.combinatorics :as combo]))

; PERMUTATIONS
; all the unique arrangements of items
=> (combo/permutations [1 2 3])
([1 2 3] [1 3 2] [2 1 3] [2 3 1] [3 1 2] [3 2 1])

; Note that permutations intelligently handles duplicate items
=> (combo/permutations [1 1 2])
([1 1 2] [1 2 1] [2 1 1])

; These functions are more efficient than calling count, nth, drop
; on the underlying sequence
=> (combo/count-permutations [1 2 3])
6
=> (combo/count-permutations [1 1 2])
3
=> (combo/nth-permutation [1 2 3] 3)
[2 3 1]
=> (combo/nth-permutation [1 1 2 2] 5)
[2 2 1 1]
=> (combo/drop-permutations [1 2 3] 3)
([2 3 1] [3 1 2] [3 2 1])

; For a sortable collection of items, you can find out where it is
; in the lexicographic sequence of permutations
=> (combo/permutation-index [\a \b \a \c \a \b])
16
=> (combo/nth-permutation [\a \a \a \b \b \c] 16)
[\a \b \a \c \a \b]


; COMBINATIONS
; all the unique ways of taking t different elements from items
(combo/combinations [1 2 3] 2)
;;=> ((1 2) (1 3) (2 3))

; Note that combinations intelligently handles duplicate items
; treating the input list as a representation of a 'multiset'
 => (combo/combinations [1 1 1 2 2] 3)
((1 1 1) (1 1 2) (1 2 2))

; These functions are more efficient than calling count and nth
; on the underlying sequence
=> (combo/count-combinations [1 1 1 2 2] 3)
3
=> (combo/nth-combination [1 2 3 4 5] 2 5)
[2 4]

; Permuting all the combinations
=> (combo/permuted-combinations [1 2 3] 2)
([1 2] [2 1] [1 3] [3 1] [2 3] [3 2])
=> (combo/permuted-combinations [1 2 2] 2)
([1 2] [2 1] [2 2])))


; SUBSETS
; all the subsets of items
=> (combo/subsets [1 2 3])
(() (1) (2) (3) (1 2) (1 3) (2 3) (1 2 3))

; Note that subsets intelligently handles duplicate items
; treating the input list as a representation of a 'multiset'
=> (combo/subsets [1 1 2])
(() (1) (2) (1 1) (1 2) (1 1 2))

; These functions are more efficient than calling count and nth
; on the underlying sequence
=> (combo/count-subsets [1 1 2])
6
=> (combo/nth-subset [1 1 2] 3)
[1 1]

; CARTESIAN PRODUCT
; all the ways to take one item from each passed-in sequence
=> (combo/cartesian-product [1 2] [3 4])
((1 3) (1 4) (2 3) (2 4))

; SELECTIONS
; all the ways to take n (possibly the same) items from the sequence of items
=> (combo/selections [1 2] 3)
((1 1 1) (1 1 2) (1 2 1) (1 2 2) (2 1 1) (2 1 2) (2 2 1) (2 2 2))

; PARTITIONS
; all the partitions of items.
=> (combo/partitions [1 2 3])
(([1 2 3])
 ([1 2] [3])
 ([1 3] [2])
 ([1] [2 3])
 ([1] [2] [3]))

 ; Note that partitions intelligently handles duplicate items
=> (combo/partitions [1 1 2])
(([1 1 2])
 ([1 1] [2])
 ([1 2] [1])
 ([1] [1] [2]))

 ; You can also specify a min and max number of partitions
(combo/partitions [1 1 2 2] :min 2 :max 3)
(([1 1 2] [2])
 ([1 1] [2 2])
 ([1 1] [2] [2])
 ([1 2 2] [1])
 ([1 2] [1 2])
 ([1 2] [1] [2])
 ([1] [1] [2 2]))