diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,30 @@ +Copyright Wolfgang Kittenberger (c) 2016 + +All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are met: + + * Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + + * Redistributions in binary form must reproduce the above + copyright notice, this list of conditions and the following + disclaimer in the documentation and/or other materials provided + with the distribution. + + * Neither the name of Wolfgang Kittenberger nor the names of other + contributors may be used to endorse or promote products derived + from this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/antiprimes.cabal b/antiprimes.cabal new file mode 100644 --- /dev/null +++ b/antiprimes.cabal @@ -0,0 +1,35 @@ +name: antiprimes +version: 0.1.0.0 +synopsis: Initial project template from stack +description: Please see README.md +homepage: https://github.com/wokibe/antiprimes#readme +license: BSD3 +license-file: LICENSE +author: Wolfgang Kittenberger +maintainer: wolfkibe@gmail.com +copyright: Copyright: (c) wolfkibe +category: Learning Haskell +build-type: Simple +-- extra-source-files: +cabal-version: >=1.10 + +library + hs-source-dirs: src + exposed-modules: AntiPrimes + build-depends: base >= 4.7 && < 5 + , primes + default-language: Haskell2010 + +test-suite antiprimes-test + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Spec.hs + build-depends: base + , antiprimes + , hspec + ghc-options: -threaded -rtsopts -with-rtsopts=-N + default-language: Haskell2010 + +source-repository head + type: git + location: https://github.com/wokibe/antiprimes diff --git a/src/AntiPrimes.hs b/src/AntiPrimes.hs new file mode 100644 --- /dev/null +++ b/src/AntiPrimes.hs @@ -0,0 +1,127 @@ +-- | a.k.a. highliy composite numbers +module AntiPrimes + (Nui, Siz, Lst, size, dividers, proof, list) where + +import Data.List (foldr1, group, nub, sort, tails) +import Data.Numbers.Primes (primeFactors) + +-- | Number under investigation +type Nui = Int +-- | number of divisors of Nui +type Siz = Int +-- | list of tuples: numbers and their divisor sizes +type Lst = [(Nui, Siz)] + +-- calculate the frequencies of the list elements +frequ :: [Int] -> [(Int, Int)] +frequ list = map (\l -> (head l, length l)) (group (sort list)) + +-- good old combinatorics: combine n elements of a list without repetitions +comb :: (Eq a, Num a) => a -> [a1] -> [[a1]] +comb 0 lst = [[]] +comb n lst = do + (x:xs) <- tails lst + rest <- comb (n-1) xs + return $ x:rest + +-- all possible combinations of a list +combAll :: (Eq a, Num a) => a -> [a1] -> [[a1]] +combAll 0 lst = [] +combAll n lst = (comb n lst) ++ (combAll (n-1) lst) + +-- error message +msg :: String +msg = "the number must be greater than 0" + +lst1 :: Lst +lst1 = [(1,1)] + +-- multiplication all elements of a list +mul :: (Num a, Foldable t) => t a -> a +mul x = foldr1 (*) x + +-- generate a tuple with a number and ist size +tup :: Nui -> (Nui, Siz) +tup n = (n, size n) + +-- list of (n, size) for n = [2..n] +lst :: Nui -> Lst +lst n + | n <= 0 = error msg + | n == 1 = lst1 + | otherwise = map tup rng + where rng = [2..n] -- range of interest + +-- | calculate the "size" of all possible factors of a number +-- +-- >>> import qualified AntiPrimes as AP +-- >>> AP.size 12 +-- 6 -- as [1,2,3,4,6,12] are possible +-- +size :: Nui -> Siz +size n + | n <= 0 = error msg + | n == 1 = 1 + | otherwise = foldr1 (*) incrs + where facts = primeFactors n + frequs = frequ facts + counts = map snd frequs + incrs = map (1 +) counts + +-- | calculate all possible dividers of a number +-- +-- >>> import qualified AntiPrimes as AP +-- >>> AP.dividers 12 +-- [1,2,3,4,6,12] +-- +dividers :: Nui -> [Int] +dividers n + | n <= 0 = error msg + | n == 1 = [1] + | otherwise = sort add1 + where facts = primeFactors n + len = length facts + combs = combAll len facts + multi = map mul combs + clean = nub multi + add1 = clean ++ [1] + +-- | proof if a number is an antiprime +-- +-- >>> import qualified AntiPrimes as AP +-- >>> AP.proof 4 +-- True +-- >>> AP.proof 5 +-- False +-- +proof :: Nui -> Bool +proof n + | n <= 0 = error msg + | n == 1 = True + | n == 2 = True + | otherwise = length flt == 1 + where siz = size n + flt = filter (\(a, b) -> b >= siz) $ lst n + +-- | show all (antiprimes, size) below a number +-- +-- >>> import qualified AntiPrimes as AP +-- >>> AP.list 12 +-- [(1,1),(2,2),(4,3),(6,4)] +-- +list :: Int -> Lst +list 0 = error msg +list 1 = lst1 +list n + | n <= 0 = error msg + | n == 1 = lst1 + | otherwise = list' lst1 (lst n) + +-- helper function to clean out excluded entries +list' :: Lst -> Lst -> Lst +list' aps [] = aps +list' aps rest = list' nxt est + where top = head rest + rst = tail rest + nxt = aps ++ [top] + est = filter (\(a, b) -> b > (snd top)) $ rst diff --git a/test/Spec.hs b/test/Spec.hs new file mode 100644 --- /dev/null +++ b/test/Spec.hs @@ -0,0 +1,1 @@ +{-# OPTIONS_GHC -F -pgmF hspec-discover #-}