-- Question 1: perfect squares between 100 and 10,000 exclusive
cpsq :: Int -> Int -> Int
cpsq m n = 0

-- Question 2 Arithmetic sequence
carith :: Int -> Int
carith n = 0

-- Question 3
q3 = 0

-- Question 4: number of ways that four positive integers can be multiplied to give 50

numways :: Int -> Int
numways target = 0

-- Question 5: sqrt12

s12n :: Int -> Float
s12n n = 0.0

-- Question 6
sum28 :: [Int] -> Bool
sum28 xs = False

-- Question 7
has22 :: [Int] -> Bool
has22 xs = False

-- Checks

check_cpsq = [ 89 == cpsq 100 10000
              ,7 == cpsq 525 900
              ,21 == cpsq 50 800]

check_carith = [ 51 == carith 259
               , 19 == carith 100
               ]

check_numways = [16 == numways 39
                ,40 == numways 50
                ,4 == numways 13
                ]

-- i do not know if max relative error and absolute error is a good way
close_h :: Float -> Float -> Bool
close_h x y = abs(x-y) <= max eps (eps*abs(y))
   where eps = 1e-4

check_s12n = [close_h 3.4641016 (s12n 1)
             , close_h 3.9324422 (s12n 2)
             , close_h 3.9915464 (s12n 3)
             , close_h 3.998943 (s12n 4)
             ]
             
             
check_sum28 = [sum28 [2,2,2,2]
              ,not $ sum28 [2,2,2,2,2]
              , sum28 [1,2,3,2,4,2,5,6,2,7]
              , not $ sum28 [10,2,30,40,2,50,2]
              , sum28 [10,2,30,40,2,50,2,60,2,70,2222]
              ]

check_has22 = [has22 [2,2]
              ,not $ has22 [2]
              ,not $ has22 []
              ,has22 [2,0,2,2]
              ,has22 [2,2,0,2,0]
              ,has22 [2,0,2,2,1,2]
              ,has22 [2,0,2,2,1,2,3]
              ,not $ has22[2,1,2,3,2,4,2,5]
              ,not $ has22 [1..20]
              ]

check = do
  putStrLn "1. cpsq"
  putStrLn $ show $ and check_cpsq
  putStrLn $ show check_cpsq
  putStrLn ""
  putStrLn "2. carith"
  putStrLn $ show $ and check_carith
  putStrLn $ show check_carith
  putStrLn ""
  putStrLn "3. how many positive three digit numbers?"
  putStrLn $ show $ 254 == q3
  putStrLn ""
  putStrLn "4. numways"
  putStrLn $ show $ and check_numways
  putStrLn $ show check_numways  
  putStrLn ""
  putStrLn "5. sqrt12"
  putStrLn $ show $ and check_s12n
  putStrLn $ show $ check_s12n  
  putStrLn ""
  putStrLn "6. sum28"
  putStrLn $ show $ and check_sum28
  putStrLn $ show $ check_sum28
  putStrLn ""
  putStrLn "7. has22"
  putStrLn $ show $ and check_has22
  putStrLn $ show $ check_has22
  

  
main = check