module Exercise03 where

import Text.Printf (printf)
import Data.List (intercalate)
-- HA 3.1a) i
selectRow :: [[Int]] -> Int -> [Int]
selectRow xss i = xss!!i

-- HA 3.1a) ii
selectColumn :: [[Int]] -> Int -> [Int]
selectColumn xss i = [y!!i | y<-xss]

-- HA 3.1a) iii
intRoot :: Int -> Int
intRoot = floor . sqrt . fromIntegral

--return numbers in square as a list. squares are numbered  from left to right and top to bottom
--e.g. :
--[0,1,2]
--[3,4,5]
--[6,7,8]
selectSquare :: [[Int]] -> Int -> [Int]
selectSquare xss i = [selectRow xss y !! z | y<-[num| num <- [0..length (selectRow xss 0)], num >= div i (intRoot (length (selectRow xss 0))) * intRoot (length (selectRow xss 0)), num < (div i (intRoot (length (selectRow xss 0)))+1) * intRoot (length (selectRow xss 0))], z <- [num| num <- [0..length (selectRow xss 0)], num >= mod i (intRoot (length (selectRow xss 0))) * intRoot (length (selectRow xss 0)), num < (mod i (intRoot (length (selectRow xss 0)))+1) * intRoot (length (selectRow xss 0))]]

-- HA 3.1b)
isValidSubsection :: [Int] -> Bool
isValidSubsection xs = null [x | x <- xs, x /= 0, x < 0 || x > length xs || length [y | y <- xs, x == y] > 1]

isValidSudoku :: [[Int]] -> Bool
isValidSudoku xss = null [y |y <- [0..length (selectRow xss 0)-1], not(isValidSubsection (selectRow xss y) && isValidSubsection(selectColumn xss y) && isValidSubsection(selectSquare xss y))]

-- HA 3.1c)
setCell :: [[Int]] -> (Int,Int) -> Int -> [[Int]]
setCell xss (j, k) n 
 | j == 0 = [[x|y <- [0..length (selectRow xss 0) - 1], x <- [0..length (selectRow xss 0)], (y /= k && x == selectRow xss j !! y) || (x == n && y == k)]] ++ [selectRow xss i|i<- [j+1..length (selectRow xss 0)-1]]
 | j == length(selectRow xss 0) - 1= [selectRow xss i |i<- [0..j-1]] ++ [[x|y <- [0..length (selectRow xss 0) - 1], x <- [0..length (selectRow xss 0)], (y /= k && x == selectRow xss j !! y) || (x == n && y == k)]]
 | otherwise = [selectRow xss i |i<- [0..j-1]] ++ [[x|y <- [0..length (selectRow xss 0) - 1], x <- [0..length (selectRow xss 0)], (y /= k && x == selectRow xss j !! y) || (x == n && y == k)]] ++[selectRow xss i|i<- [j+1..length (selectRow xss 0)-1]]

-- HA 3.1d)
{-WETT-}
customHeadFunc :: [[[Int]]] -> [[Int]]
customHeadFunc xsss
  | null xsss = []
  | otherwise = head xsss

solveSudoku :: [[Int]] -> [[Int]]
solveSudoku xss 
--  | trace ("solver " ++ show xss) False = undefined
  | not (isValidSudoku xss) = []
  | null[x | i <- [0..length (selectRow xss 0)-1], x <- selectRow xss i, x == 0] = xss
  | otherwise = customHeadFunc [yss | j <- [0..length (selectRow xss 0)-1], j == head [x | x<-[0..length (selectRow xss 0)-1], not (null [y | y<- selectRow xss x, y == 0])], k <- [0..length (selectRow xss 0)-1], k == head[x | x<-[0..length (selectRow xss 0)-1], selectRow xss j !! x == 0], i <- [x | x <- [1..length (selectRow xss 0)], null[y |y <- selectRow xss j, x == y], null[y | y <- selectColumn xss k, x == y]],yss <- [solveSudoku (setCell xss (j,k) i)], not(null yss)]
{-TTEW-}

hardSudoku :: [[Int]]
hardSudoku = [[8,0,0,0,0,0,0,0,0],
              [0,0,3,6,0,0,0,0,0],
              [0,7,0,0,9,0,2,0,0],
              [0,5,0,0,0,7,0,0,0],
              [0,0,0,0,4,5,7,0,0],
              [0,0,0,1,0,0,0,3,0],
              [0,0,1,0,0,0,0,6,8],
              [0,0,8,5,0,0,0,1,0],
              [0,9,0,0,0,0,4,0,0]]

-- Utility method to show a sudoku
-- show sudoku with
-- >>> putStr (showSudoku sudoku)
showSudoku :: [[Int]] -> String
showSudoku xss = unlines $ intercalate [showDivider] $ chunksOf squareSize $ map showRow xss
  where
    size = length xss
    squareSize = intRoot size 
    numberSize = size `div` 10 + 1

    showRowSection xs = unwords $ map (printf ("%0" ++ show numberSize ++ "d")) xs
    showRow xs = intercalate "|" $ map showRowSection $ chunksOf squareSize xs
    showDivider = intercalate "+" $ replicate squareSize $ replicate ((numberSize + 1) * squareSize - 1) '-'

    chunksOf :: Int -> [e] -> [[e]]
    chunksOf i [] = []
    chunksOf i ls = take i ls : chunksOf i (drop i ls)