skyscrapers.hs

--
-- Skyscrapers: game solution checker
--


import Data.List
import System.IO


-- Read matrix values from a string
read_matrix :: String -> [[Int]]
read_matrix c = map (map read) (map words $ lines c)


-- Counts the number of visible rooftops in the given list using left folding
rooftops :: [Int] -> Int
rooftops xs = snd $ foldl (\(m,n) x -> if x > m then (x,n+1) else (m,n)) (0,0) xs


-- Checks if the constraints in the border are satisfied
check_constraints :: [[Int]] -> Bool
check_constraints [[]] = False
check_constraints m    = and $
    map (check_row_constraints . init) (tail $ init m) ++                     -- from left to right
    map (check_row_constraints . reverse . tail) (tail $ init m) ++           -- from right to left
    map (check_row_constraints . init) (tail $ init $ transpose m) ++         -- from top to down
    map (check_row_constraints . reverse . tail) (tail $ init $ transpose m)  -- from down to top

check_row_constraints :: [Int] -> Bool
check_row_constraints []    = False
check_row_constraints (n:v) = n == 0 || n == rooftops v


-- Checks if values in matrix are in the correct range and unique for each row and column
check_values :: [[Int]] -> Bool
check_values [[]] = False
check_values m    = and $ map (check_row_values . tail . init) (tail $ init m)

check_row_values :: [Int] -> Bool
check_row_values r = sort r == [1..(length r)]


-- Checks if matrix solution provided is correct
check :: [[Int]] -> IO ()
check [[]] = putStrLn "Error: empty matrix!"
check m
    | check_values m && check_constraints m = putStrLn "Your solution is correct!"
    | otherwise = putStrLn "Your solution is not correct. Try again."


main = do
    file <- readFile "game5x5.txt"    
    check $ read_matrix file