DiscreteMathToolkit

Set of extensions for Kotlin that provides Discrete Math functionalities as an Kotlin extension functions.

To stay current with news about library

Permutations

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setOf(1, 2, 3).permutations() // {[1, 2, 3], [2, 1, 3], [3, 2, 1], [1, 3, 2], [2, 3, 1], [3, 1, 2]}
setOf(1, 2, 3).permutationsNumber() // 6
listOf(1, 2, 2).permutations() // {[1, 2, 2], [2, 1, 2], [2, 2, 1]}
listOf(1, 2, 2).permutationsNumber() // 3

More examples here

Combinations

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setOf(1, 2, 3, 4).combinations(3) // { {1, 2, 3}, {1, 2, 4}, {1, 4, 3}, {4, 2, 3} }
setOf(1, 2, 3, 4).combinationNumber(3) // 4

setOf(1, 2, 3, 4).combinationsWithRepetitions(2) // [{1=2}, {1=1, 2=1}, {1=1, 3=1}, {1=1, 4=1}, {2=2}, {2=1, 3=1}, {2=1, 4=1}, {3=2}, {3=1, 4=1}, {4=2}]
setOf(1, 2, 3, 4).combinationsWithRepetitionsNumber(2) // 10

More examples here and here

Powerset

Powerset of any set S is the set of all subsets of S, including the empty set and S itself.

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setOf(1, 2, 3).powerset() // { {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3} }
setOf(1, 2, 3).powersetSize() // 8

Product

Product is the result of multiplying.

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(3..4).product() // 12
listOf(10, 10, 10).product() // 1000

More examples here.

Factorial

Factorian of n (n!) is a product of all positive integers less than or equal to n.

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3.factorial() // 6L
10.factorial() // 3628800L
20.factorial() // 2432902008176640000L

More examples here.

Numbers divisible and non-divisible by

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(1..1000).countNonDivisiveBy(2) // 500
(1..1000).countNonDivisiveBy(3) // 777
(1..1000).countNonDivisiveBy(2, 6, 13) // 462
(1..1000).countNonDivisiveBy(3, 7, 11) // 520

(1..1000).countDivisiveBy(2) // 500
(1..1000).countDivisiveBy(3) // 333
(1..1000).countDivisiveBy(2, 6, 13) // 538
(1..1000).countDivisiveBy(3, 7, 11) // 480

More examples here.

Splits of sets and numbers

In Descrete Math there are two functions used to count number of splits:
S(n, k) - Stirling function - number of splits of n different elements to k groups
P(n, k) - number of splits of n identical elements to k groups

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(1..n).toSet().splitsNumber(1) // 1
(1..n).toSet().splitsNumber(n) // 1
setOf(1, 2, 3).splitsNumber(2) // 3
setOf(1, 2, 3, 4).splitsNumber(2) // 7
setOf(1, 2, 3, 4, 5).splitsNumber(3) // 25
setOf(1, 2, 3, 4, 5, 6, 7).splitsNumber(4) // 350
setOf(1, 2, 3).splits(2) // { { {1, 2}, {3} },{ {1, 3}, {2} },{ {3, 2}, {1} } }

More examples here

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n.splitsNumber(1) // 1
n.splitsNumber(n) // 1
7.splitsNumber(4) // 3
11.splitsNumber(4) // 11
9.splitsNumber(5) // 5
13.splitsNumber(8) // 7

More examples here

Iterable multiplication

Multiplication of iterables returns iterable with pairs of each possible connections of elements from first and iterable:

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listOf(1, 2) * listOf("A", "B") // returns List<Pair<Int, String>>
// [(1, "A"), (1, "B"), (2, "A"), (2, "B")] 
listOf('a', 'b') * listOf(1, 2) * listOf("A", "B") // returns List<Triple<Char, Int, String>>
// [
//    ('a', 1, "A"), ('a', 1, "B"), 
//    ('a', 2, "A"), ('a', 2, "B"), 
//    ('b', 1, "A"), ('b', 1, "B"), 
//    ('b', b, "A"), ('b', 2, "B")
// ] 

More examples here.

Cartesian product of lists

Similar to iterable multiplication but produces sequence of lists:

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listOf('A', 'B', 'C', D).cartesianProduct(listOf('x', 'y')) // returns List<List<Char>>
// [
//     ['A', 'x'],
//     ['A', 'y'],
//     ['B', 'x'],
//     ['B', 'y'],
//     ['C', 'x'],
//     ['C', 'y'],
//     ['D', 'x'],
//     ['D', 'y']
// ]
listOf(0, 1).cartesianProduct(repeat = 2) // returns List<List<Int>>
// [
//     [0, 0],
//     [0, 1],
//     [1, 0],
//     [1, 1]
// ]
listOf(1, 2).cartesianProduct(listOf("ABC")) // returns List<List<Any>>
// [
//     [1, "ABC"],
//     [2, "ABC"]
// ]

More examples here.

Java support

Library is fully supporting usage from Java. All functions can be used as static function of DiscreteMath. For example:

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DiscreteMath.permutationsNumber(set)
DiscreteMath.permutationsNumber(list)
DiscreteMath.factorial(10) // 3628800L

Returned list and sets are Java standard lists and sets. More examples of Java usage here.

Install

Gradle:

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compile "com.marcinmoskala:DiscreteMathToolkit:1.0.3"

Maven:

<dependency>
  <groupId>com.marcinmoskala</groupId>
  <artifactId>DiscreteMathToolkit</artifactId>
  <version>1.0.3</version>
</dependency>

Jar to download together with sources and javadoc can be found on Maven Central.

License

Copyright 2017 Marcin Moskała

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

   http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.