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DiscreteMathToolkit
Set of extensions for Kotlin that provides Discrete Math functionalities as an Kotlin extension functions.
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Permutations
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
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
Powerset
Powerset of any set S is the set of all subsets of S, including the empty set and S itself.
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.
(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.
3.factorial() // 6L
10.factorial() // 3628800L
20.factorial() // 2432902008176640000L
More examples here.
Numbers divisible and non-divisible by
(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
(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
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:
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:
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:
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:
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.