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12.58 util.combinations - Combination library

Module: util.combinations

This module implements several useful procedures of combinations, permutations and related operations.

Most procedures in the module have two variants: a procedure without star (e.g. permutations) treats all elements in the given set distinct, while a procedure with star (e.g. permutations*) considers duplication. The procedures with star take optional eq argument that is used to test equality, which defaults to eqv?.

Function: permutations set
Function: permutations* set :optional eq

Returns a list of all permutations of a list set.

(permutations '(a b c))
  ⇒ ((a b c) (a c b) (b a c) (b c a) (c a b) (c b a))

(permutations '(a a b))
  ⇒ ((a a b) (a b a) (a a b) (a b a) (b a a) (b a a))

(permutations* '(a a b))
  ⇒ ((a a b) (a b a) (b a a))

The number of possible permutations explodes if set has more than several elements. Use with care. If you want to process each permutation at a time, consider permutations-for-each below.

Function: permutations-for-each proc set
Function: permutations*-for-each proc set :optional eq

For each permutation of a list set, calls proc. Returns an undefined value.

Function: combinations set n
Function: combinations* set n :optional eq

Returns a list of all possible combinations of n elements out of a list set.

(combinations '(a b c) 2)
  ⇒ ((a b) (a c) (b c))

(combinations '(a a b) 2)
  ⇒ ((a a) (a b) (a b))

(combinations* '(a a b) 2)
  ⇒ ((a a) (a b))

Watch out the explosion of combinations when set is large.

Function: combinations-for-each proc set n
Function: combinations*-for-each proc set n :optional eq

Calls proc for each combination of n elements out of set. Returns an undefined value.

Function: power-set set
Function: power-set* set :optional eq

Returns power set (all subsets) of a list set.

(power-set '(a b c))
  ⇒ (() (a) (b) (c) (a b) (a c) (b c) (a b c))

(power-set* '(a a b)
  ⇒ (() (a) (b) (a a) (a b) (a a b))
Function: power-set-for-each proc set
Function: power-set*-for-each proc set :optional eq

Calls proc for each subset of set.

Function: power-set-binary set

Returns power set of set, like power-set, but in different order. Power-set-binary traverses subset space in depth-first order, while power-set in breadth-first order.

(power-set-binary '(a b c))
  ⇒ (() (c) (b) (b c) (a) (a c) (a b) (a b c))
Function: cartesian-product list-of-sets
Function: cartesian-product-right list-of-sets

Returns a cartesian product of sets in list-of-sets. Cartesian-product construct the result in left fixed order (the rightmost element varies first), while cartesian-product-right in right fixed order (the leftmost element varies first).

(cartesian-product '((a b c) (0 1)))
  ⇒ ((a 0) (a 1) (b 0) (b 1) (c 0) (c 1))

(cartesian-product-right '((a b c) (0 1)))
  ⇒ ((a 0) (b 0) (c 0) (a 1) (b 1) (c 1))

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