multichoose



multiset combinations of k out of n (n multichoose k)

Overview

This library implements an efficient loopless multiset combination generation algorithm which is (approximately) described in "Loopless algorithms for generating permutations, combinations, and other combinatorial configurations." G Ehrlich - Journal of the ACM (JACM), 1973. (Algorithm 7.)

The method generates all multisets that would be generated from taking k elements from a multiset of n. Repeated multisets are possible if the input set contains repeated elements. The number of multiset combinations equals the multinomial coefficient (n multichoose k).

Usage

$3

Install via

`` bash
npm install -g multichoose
`

` js
var multichoose = require('multichoose')
multichoose(2, [1,2,3], console.log)
// [ 1, 1 ]
// [ 1, 2 ]
// [ 1, 3 ]
// [ 2, 2 ]
// [ 2, 3 ]
// [ 3, 3 ]
`

` bash
% multichoose 3 A B C
A A A
A A B
A A C
A B B
A B C
A C C
B B B
B B C
B C C
C C C
`

$3

Include is a C++ library/program which contains a generic function to generate multisets for vectors of any type of object. You can test out the program using strings input from the command line by typing:

` bash
% make
`

Running the bare executable prints usage information:

` bash
% ./multichoose
usage:
./multichoose ... ~ n multichoose k
`

Example usage:

` bash
% ./multichoose 2 a t g c
a a
a t
a g
a c
t t
t g
t c
g g
g c
c c
`

This example lists all the possible unordered genotypes at a given genetic loci of which there are two copies (e.g. chromosomes). In this case k` (=2) could be understood as the expected ploidy of the given locus.

(Note that this is not currently built as the default binary for the npm module, which uses cli.js.)

$3

A python library implementation is also included for those who like to indent their code consistently.

multiset permutations

TODO: These will be factored into a separate module.