module Exercise_1_Sol where

import Test.QuickCheck

{-G1.1-}

threeAscending :: Integer -> Integer -> Integer -> Bool
threeAscending x y z = x < y && y < z

fourEqual :: Integer -> Integer -> Integer -> Integer -> Bool
fourEqual w x y z = w == x && x == y && y == z

{-
 - threeAscending (2+3) 5 (11 `div` 2)
 - = (2+3) < 5 && 5 < (11 `div` 2)
 - = 5 < 5 && 5 < (11 `div` 2)
 - = False && 5 < (11 `div` 2)
 - = False
 -
 - fourEqual (2 + 3) 5 (11 `div` 2) (21 `mod` 11)
 - = (2 + 3) == 5 && 5 == (11 `div` 2) && (11 `div 2) == (21 `mod` 11)
 - = 5 == 5 && 5 == (11 `div` 2) && (11 `div 2) == (21 `mod` 11)
 - = True && 5 == (11 `div` 2) && (11 `div 2) == (21 `mod` 11)
 - = 5 == (11 `div` 2) && (11 `div 2) == (21 `mod` 11)
 - = 5 == 5 && 5 == (21 `mod` 11)
 - = True && 5 == (21 `mod` 11)
 - = 5 == (21 `mod` 11)
 - = 5 == 10
 - = False
 -}


{- G1.2 -}
fac :: Integer -> Integer
fac n | n > 0 = n * fac (n - 1)
      | otherwise = 1

sum_eleven :: Integer -> Integer
sum_eleven n = sum_eleven' n 10

sum_eleven' :: Integer -> Integer -> Integer
sum_eleven' n 0 = n
sum_eleven' n m = n + m + sum_eleven' n (m - 1)


{- G1.3 -}
g :: Integer -> Integer
g n = if n < 10 then n*n else n

max_g :: Integer -> Integer
max_g 0 = 0
max_g n | n > 0 = if (g mg > g n) then mg else n
        | otherwise = 0
            where mg = max_g (n - 1)

max_g' :: Integer -> Integer
max_g' n | n < 0 = 0
         | n >= 10 && n < 81 = 9
         | otherwise = n

prop_max_g n = max_g n == max_g' n


{-H1.1-}

{-WETT-}
allDistinct :: Integer -> Integer -> Integer -> Integer -> Integer -> Bool
allDistinct a b c d e =
  a /= b && a /= c && a /= d && a /= e &&
            b /= c && b /= d && b /= e &&
                      c /= d && c /= e &&
                                d /= e
{-TTEW-}


{-H1.2-}

f :: Integer -> Integer -> Integer
f 0 _ = 0
f _ 0 = 0
f m n = 1 + f (f (n - 1) m) (f (m - 1) n)

prop_f m n = m >= 0 ==> n >= 0 ==> f m n == min m n

{-H1.3-}

isPower' :: Integer -> Integer -> Integer -> Bool
isPower' x a b | b > x = False
               | otherwise = x == a ^ b || isPower' x a (b+1)

isPower :: Integer -> Integer -> Bool
isPower x a = isPower' x a 0