-- sample solutions for Revision Tutorial 3, 28 Nov 2012

import Test.QuickCheck

-- Problem 2010 resit - 2
f1 :: [a] -> [a]
f1 xs = [xs !! i | i <- [0,3..length xs - 1]]

g1 :: [a] -> [a]
g1 [] = []
g1 (x:y:z:rest) = x : g1 rest
g1 small_list = [head small_list]

h1 :: [a] -> [a]
h1 xs = map (\i -> xs !! i) [0,3..length xs - 1]

test1 = 
    f1 "abcdefghij"    == "adgj" &&
    f1 [1, 2, 3, 4, 5] == [1, 4] &&
    f1 [0, 0, 0, 0, 0] == [0, 0] &&
    f1 ([]::[Integer]) == [] -- there is an ambiguity if [] is not casted

prop1 :: Eq a => [a] -> Bool
prop1 xs = f1 xs == g1 xs && f1 xs == h1 xs


-- Problem 2009 sitting 2 - 2
f2 :: [a] -> [a]
f2 xs = concat [[xs !! (i+1), xs !! i]| i <- [0,2..length xs - 1]]

g2 :: [a] -> [a]
g2 [] = []
g2 (x:y:rest) = y:x:(g2 rest)

h2 :: [a] -> [a]
h2 xs = concat (map (\i -> [xs !! (i+1), xs !! i]) [0,2..length xs - 1])

test2 = 
    f2 "swapping"      == "wspaipgn" &&
    f2 [1, 2, 3, 4]    == [2, 1, 4, 3] &&
    f2 ([]::[Integer]) == []

prop2 :: (Eq a) => [a] -> Property
prop2 xs = (even (length xs)) ==> f2 xs == g2 xs && f2 xs == h2 xs


-- Problem 2011 - 2
f3 :: [Integer] -> Integer
f3 xs | even (length xs) 
 = sum [(xs !! i) * (xs !! (i+1)) | i <- [0,2..length xs - 2]]

g3 :: [Integer] -> Integer
g3 [] = 0
g3 (x:y:rest) = x * y + (g3 rest)

h3 :: [Integer] -> Integer
h3 xs | even (length xs)
 = foldr (+) 0 (map (\i -> (xs !! i) * (xs !! (i+1))) [0,2..length xs - 2])

test3 = 
    f3 [1, 2, 3, 4] == 14 &&
    f3 [3, 5, 7, 5, -2, 4] == 42 &&
    f3 [] == 0
-- f3 [1, 2, 3] gives an error

prop3 :: [Integer] -> Property
prop3 xs = even (length xs) ==> f3 xs == g3 xs && f3 xs == h3 xs