https://github.com/clojure/math.combinatorics
Efficient, functional algorithms for generating lazy sequences for common combinatorial functions
https://github.com/clojure/math.combinatorics
Last synced: 7 months ago
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Efficient, functional algorithms for generating lazy sequences for common combinatorial functions
- Host: GitHub
- URL: https://github.com/clojure/math.combinatorics
- Owner: clojure
- License: epl-1.0
- Created: 2011-07-29T15:26:54.000Z (over 14 years ago)
- Default Branch: master
- Last Pushed: 2024-07-15T17:55:02.000Z (over 1 year ago)
- Last Synced: 2025-04-11T15:57:04.406Z (8 months ago)
- Language: Clojure
- Homepage:
- Size: 190 KB
- Stars: 354
- Watchers: 36
- Forks: 31
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
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README
clojure.math.combinatorics
========================================
Formerly clojure.contrib.combinatorics.
Efficient, functional algorithms for generating lazy
sequences for common combinatorial functions.
Releases and Dependency Information
========================================
Latest stable release: 0.3.0
* [All Released Versions](https://search.maven.org/#search%7Cgav%7C1%7Cg%3A%22org.clojure%22%20AND%20a%3A%22math.combinatorics%22)
* [Development Snapshot Versions](https://oss.sonatype.org/index.html#nexus-search;gav~org.clojure~math.combinatorics~~~)
[CLI/`deps.edn`](https://clojure.org/reference/deps_and_cli) dependency information:
```clojure
org.clojure/math.combinatorics {:mvn/version "0.3.0"}
```
[Leiningen](https://github.com/technomancy/leiningen) dependency information:
```clojure
[org.clojure/math.combinatorics "0.3.0"]
```
[Maven](https://maven.apache.org/) dependency information:
```xml
org.clojure
math.combinatorics
0.3.0
```
*Note: If you are using Clojure 1.2 - 1.6, you will need math.combinatorics version 0.1.3.*
Example Usage
========================================
The following functions take sequential collections
(such as lists and vectors) as inputs. If you want
to call a function on a set, you must explicitly
call `seq` on the set first.
All functions return lazy sequences.
```clojure
(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]))
```
Refer to docstrings in the `clojure.math.combinatorics` namespace for
additional documentation.
[API Documentation](https://clojure.github.io/math.combinatorics/)
Developer Information
========================================
* [GitHub project](https://github.com/clojure/math.combinatorics)
* [Bug Tracker](https://clojure.atlassian.net/browse/MCOMB)
* [Continuous Integration](https://github.com/clojure/math.combinatorics/actions/workflows/test.yml)
Changelog
========================================
* Release 0.3.0 on 2024-02-19
* Update parent pom
* Release 0.2.0 on 2023-03-18
* MCOMB-11 - Fix incorrect results, overflow in partitions-M
* Release 0.1.6 on 2019-07-24
* Improved laziness characteristics of many functions
* Added `permuted-combinations`
* Release 0.1.5 on 2019-04-07
* Removed deprecated annotation on lex-permutations, which was causing problems for clojurescript users.
* Release 0.1.4 on 2017-01-06
* Support for clojurescript (tested with 1.9.293)
* Dropped support for Clojure 1.2 - 1.6
* Release 0.1.3 on 2016-06-02
* Changed boxing to use Long/valueOf.
* Release 0.1.2 on 2016-05-18
* Added explicit boxing to eliminate auto-boxing warnings.
No change in functionality or performance from previous release.
* Release 0.1.1 on 2015-03-20
* Backwards compatibility with 1.2.0 and 1.2.1
* Release 0.1.0 on 2015-03-17
* combinations and subsets now have special handling for duplicate items
* Added count-permutations, count-combinations, count-subsets,
nth-permutation, nth-combination, nth-subset
drop-permutations, permutation-index
* Release 0.0.9 on 2015-03-16
* Exclude "update" function from core for compatibility with 1.7.
* Release 0.0.8 on 2014-07-20
* Minor improvement of helper function used by permutations.
* Release 0.0.7 on 2013-11-13
* Unchunk range in `subsets` to minimize memory usage.
* Release 0.0.6 on 2013-10-31
* Removed use of mapv for backwards compat with older versions of Clojure.
* Release 0.0.5 on 2013-10-31
* Added partitions function
* Release 0.0.4 on 2013-03-26
* Moved comment after ns declaration
* Release 0.0.3 on 2012-07-06
* Fixed bug with (selections [false] 3) returning nil
* Fixed test syntax for Clojure 1.4.0/1.5.0
* Release 0.0.2 on 2011-10-24
* Deprecated lex-permutations (permutations is now intelligent)
* Release 0.0.1 on 2011-09-29
* Initial release.
* Source-compatible with clojure.contrib.math, except for the name change.
License
========================================
Distributed under the Eclipse Public License, the same as Clojure.