# clojure/math.combinatorics

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# clojure.math.combinatorics

Efficient, functional algorithms for generating lazy sequences for common combinatorial functions.

## Usage

• (combinations items n) - A lazy sequence of all the unique ways of taking n different elements from items.

Example: (combinations [1 2 3] 2) -> ((1 2) (1 3) (2 3))

• (subsets items) - A lazy sequence of all the subsets of items (but generalized to all sequences, not just sets).

Example: (subsets [1 2 3]) -> (() (1) (2) (3) (1 2) (1 3) (2 3) (1 2 3))

• (cartesian-product & seqs) - Takes any number of sequences as arguments, and returns a lazy sequence of all the ways to take one item from each seq.

Example: (cartesian-product [1 2] [3 4]) -> ((1 3) (1 4) (2 3) (2 4))

(cartesian-product seq1 seq2 seq3 ...) behaves like but is faster than a nested for loop, such as:

• (selections items n) - A lazy sequence of all the ways to take n (possibly the same) items from the sequence of items.

Example: (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))

• (permutations items) - A lazy sequence of all the permutations of items.

Example: (permutations [1 2 3]) -> ((1 2 3) (1 3 2) (2 1 3) (2 3 1) (3 1 2) (3 2 1))