This project contains realisations of common-used math functions and classical algorithms, written in Scala's pure-functional style.

Some of them are a new sight at Scala's standard library, some are persistent data structures, some are completely new functions.

The main purpose of this library is to spread ideas of a functional programming in Scala and to challenge yourself by creating classical imperative algorithms in a new way.

Would be great, if you contribute, in case that presented algorithms are not as effective as they can be, and you know how to fix this, or if you have ideas, that can be added in the future.

1. Quick sort sortingAlgorithms/QuickSort

2. Bogosort sortingAlgorithms/unseriousAlgorithms/Bogosort

3. Sleep sort sortingAlgorithms/unseriousAlgorithms/SleepSort

4. Bubble sort sortingAlgorithms/BubbleSort

5. Merge sort sortingAlgorithms/MergeSort

6. Insertion sort sortingAlgorithms/InsertionSort

7. Selection sort sortingAlgorithms.SelectionSort

8. Heap sort sortingAlgorithms.HeapSort

1. LinkedList dataStructures.LinkedList

2. Queue dataStructures.Queue

3. Stack dataStructures.Stack

4. Set dataStructures.Set

5. Binary tree dataStructures.BinaryTree

6. Heap dataStructures.Heap

7. Red-Black Tree dataStructures.RedBlackTree

1. Polymorphic lambda calculus lambdaCalculus/PolymorphicLambdaCalculus

2. Pure Lambda Calculus PureLambdaCalculus.scala lambdaCalculus/PureLambdaCalculus

integerOperations.IntegerProperties

1. .isOdd

2. .isEven

3. .isSquared

4. .sumOfDigits

5. .compositionOfDigits

6. .numOfDigits

7. .divisors

8. .nthGreatestDivisor(n)

9. .numOfDivisors

10. .sumOfDivisors

11. .isPrime, works with O(sqrt(n)) speed

12. .isPrimeFermat(). works with O(log(n)) speed

13. .sqr

14. .powN()

15. .gcdWith(secondInt)

16. .isPrimeFermatStrict (does not fail on Carmichael numbers, works slowly)

17. .isPrimeFermatFast (does not fail on Carmichael numbers, works fast, only with Ints)

18. .lcmWith(secondInt)

19. Factorial (!)

20. Double factorial (!!)

21. Convolution of a number (127 -> 1+2+7 -> 10 -> 1+0 -> 1)

integerOperations.IntegerMath

1. .isFreeOfSquares

2. .isCarmichael

3. .isLuc_Carmichael

4. .isFibonacci

5. .nthCatalan

6. .binaryPower(), works with O(log(n)) speed

7. .isZuckerman

8. .isHarshad

9. .gcdExtendedWith()

integerOperations.IntegerGenerators

1. Arithmetic regression

2. Arithmetic progression

3. Squares until N

4. Divisors of N

5. Binary divisors of N

6. Divisors, multiple by N

7. Prime divisors

8. Carmichael numbers

9. Luc-Carmichael numbers

10. Fibonacci numbers

11. Random ints

12. Catalan numbers

integerOperations.IntegerGeneratorsMath

1. Fermat numbers

2. Eratosthenes primes sieve O(log(log(n)))

charOperations.CharProperties

1. .isVowel

2. .isConsonant

doubleOperations.DoubleProperties

1. .inverse

2. .sqrDouble

3. .abs

4. .toDegrees

5. .incDouble

listOperations

1. get(List[A], index)

2. isPalindrome(List[A])

3. isPalindrome([A])

4. Counter for the number of sign changes in a list of integers

5. Counter for the number of letter changes from vowel to consonant in a list of integers

6. .isSorted

7. binary search in a list

8. linear search in a list

9. permutations(List[A], len)

combinatorics

1. permutationsCount

2. accomodations

3. combinations

4. accomodations with repeats

5. combinations with repeats

1. RLE cryptographyOperations.encoders.RLE_Encoder

2. Huffman cryptographyOperations.encoders.HuffmanEncoder

3. Gray cryptographyOperations.encoders.GrayEncoder

4. Morse cryptographyOperations.encoders.MorseEncoder

1. RLE functionalAlgorithms.decoders.RLE_Decoder

2. Huffman functionalAlgorithms.decoders.HuffmanDecoder

3. Gray functionalAlgorithms.decoders.GrayDecoder

4. Morse functionalAlgorithms.decoders.MorseDecoder

1. Rational numbers additionalArithmetics.Rational

2. Complex numbers complexOperations.Complex

asynchronous.UsefulFuture

1. .bypassOnComplete()

2. .ifFailure()

3. .result

4. .completeAndThen()

5. .completeAndThenComplete()

asynchronous.UsefulOption

1. .getOrZero

2. .getOrZeroL

3. .getOrThrow

4. .getOrEmpty

5. .getOrMax

MathConstants

1. Pi

2. Tau

3. E

4. Pythagoras constant

5. Theodorus constant

6. Gamma

7. Phi

8. Plastic number

time.Time

1. Conversions of hours, seconds and minutes.

1. Operations with double

0. Martin Odersky's "Functional Programming in Scala Specialization "https://www.coursera.org/specializations/scala" (English)

1. Chris Okasaki's "Purely Functional Data Structures" (English)

2. Richard Bird's "Pearls of Functional Algorithm Design" (English)

3. Denis Shevchenko's "About Haskell in a human way": https://www.ohaskell.guide (Russian)

4. Louis Botterill's mostly software and techy Blog: http:https://louisbotterill.blogspot.ru (English)

5. Alvin Alexander's scala blog: https://alvinalexander.com (English)

6. Richard G.E. Pinch "The Carmichael numbers up to 10^18" https://arxiv.org/pdf/math/0604376v1.pdf (English)

7. Site about algorithms http:https://e-maxx.ru (Russian/English)

8. "Rosetta code" website about algorithms: https://rosettacode.org/wiki/Rosetta_Code (English)

9. Vladimir Kostykov's Scala algorithms library: https://github.com/vkostyukov/scalacaster (English)

10. Raul Rojas's "A Tutorial Introduction to the Lambda Calculus": http:https://www.inf.fu-berlin.de/lehre/WS03/alpi/lambda.pdf (English)

11. ITMO University's wiki: https://neerc.ifmo.ru/wiki/index.php?title=Лямбда-исчисление (Russian)