factorisation

Factorisation.purs

module Factorisation where

import Control.MonadZero (guard)
import Data.Array (concatMap, cons, nub, sort, (..))
import Data.Functor (map)
import Data.Tuple (Tuple(..))
import Prelude (bind, pure, ($), (==), discard, (*))

factors :: Int -> Array (Tuple Int Int)
factors n = do
  i <- 2 .. n
  j <- i .. n
  guard $ i * j == n
  pure $ Tuple i j

factorisation :: Int -> Array (Array Int)
factorisation n = nub $ map sort $ concatMap (\(Tuple h t) -> cons [h,t] $ map (cons h) (factorisation t)) (factors n)

-- > factorisation 12
-- [[2,6],[2,2,3],[3,4]]