PureScript by Example - 4.11 Guards - Exercise 1-4 Solutions

Guards.purs

module Guards where

-- 4.11 Guards of PureScript by Example

-- Boilerplate code provided by PureScript by Example

import Prelude
import Data.Array
import Control.MonadZero (guard)

factors :: Int -> Array (Array Int)
factors n = do
  i <- 1 .. n
  j <- i .. n
  guard (i * j == n)
  pure [i, j]

-- Exercise 1
isPrime :: Int -> Boolean
isPrime n = n /= 1 && length (factors n) == 1

-- Exercise 2
cartesianProduct :: forall a. Array a -> Array a -> Array (Array a)
cartesianProduct arr1 arr2 = do
  a <- arr1
  b <- arr2
  pure [a, b]

-- Exercise 3
pythagoreanTriples :: Int -> Array (Array Int)
pythagoreanTriples n = do
  a <- 1 .. n
  b <- a .. n
  c <- b .. n
  guard (a * a + b * b == c * c)
  pure [a, b, c]

-- Exercise 4
factorizations :: Int -> Array (Array Int)
factorizations 1 = [[1]]
factorizations n = nubEq $ map sort $
  map (filter (\m -> m /= 1)) $
  concatMap (\m -> map (\arr -> m : arr) (factorizations (div n m))) $
  filter (\m -> mod n m == 0) (2 .. n)