--Liz Evans
--Cs429
module Math where

type Board = [Int]

-- the slide
slide :: Int -> Int -> [Int] -> [Int]
slide x n xs = if ((inList' (x-1) xs) && (swapable x n xs))
		then swap (numOf x 1 xs) 0 xs
		else xs 


--check to make sure it's valid input
inList':: Int -> [Int] -> Bool
inList' x [] = False
inList' x (h:t) = if (x == h)
			then True
			else inList' x t

--we assume that a and b are valid
swap' :: Int -> Int -> [Int] -> [Int]
swap' a b (x:xs) = if (a == x) then b:(swap' a b xs)  
		  else if (b == x) then a:(swap' a b xs)
		  else x:(swap' a b xs)
swap' a b [] = []

swap :: Int -> Int -> [Int] -> [Int]
swap a b xs = if ((inList' a xs) && (inList' b xs)) 
		then (swap' a b xs)
		else error "arguments not on board"

-- are the two squares swapable, the validation
--helpers
swapable :: Int -> Int -> [Int] -> Bool
swapable x n ls= let px = x 
		     p0 = (posOf 0 1 ls)
		 in
			if (( ( ((p0+1) == px) &&
			      notMulOf p0 n) ||
			   
			   ( ((px+1) == p0) &&
			      notMulOf px n) 
			    ) ||
		        
			    ((p0+n) == px) ||
			    ((px+n) == p0)
			   )
			then True
			else False
			

posOf :: Int -> Int -> [Int] -> Int
posOf n acc (x:xs) = if n == x then acc else (posOf n (acc+1) xs) 

numOf :: Int -> Int -> [Int] -> Int
numOf n acc (x:xs) = if n == acc then x else (numOf n (acc+1) xs)

--X is not a multiple of Y
notMulOf :: Int -> Int -> Bool
notMulOf x y = if (x `mod` y) == 0
		then False
		else True


--board creation
boardGen :: Int ->  [Int]
boardGen n = let ls = gen 0 (n*n)
		in rshuffle ls n

shuffle :: [a] -> Int -> [a]
shuffle [] _ = []
shuffle [x] _ = x : []
shuffle (x:xs) n = x : (last xs) : shuffle (take (n-2) xs) (n-2) 

rshuffle :: [Int] -> Int -> [Int]
rshuffle xs n = let ls = (shuffle xs (n*n))
		in (filter (\x -> if (x == 0 || x == 1) then False else True) ls) 
			++ [1, 0] 
		   

gen :: Int-> Int -> [Int]
gen x n = if (x < n) then x:(gen (x+1) n) else []