isConnected :: BoardSpec -> Bool
isConnected legalPositions =  checkIfAllNumberOne (infectWithGroupNumberOne (addGroupNumberToAll legalPositions))

addGroupNumberToAll :: BoardSpec -> BoardSpecGroup
addGroupNumberToAll ((a,b):xs) = ((a,b,0):(addGroupNumberToAll xs))
addGroupNumberToAll otherwise  = []

infectWithGroupNumberOne :: BoardSpecGroup -> BoardSpecGroup
infectWithGroupNumberOne ((a,b,0):xs) = infectRight (infectLeft (infectBelow (infectAbove ((a,b,1):xs) a) a) a) a
infectWithGroupNumberOne board              = board

infectAbove :: BoardSpecGroup -> Coord -> BoardSpecGroup
infectAbove board (x,y) = if (positionExists board (x,y-1)) then infectWithGroupNumberOne (bringToFrontOfList board (x,y-1)) else board

infectBelow :: BoardSpecGroup -> Coord -> BoardSpecGroup
infectBelow board (x,y) = if (positionExists board (x,y+1)) then infectWithGroupNumberOne (bringToFrontOfList board (x,y+1)) else board

infectLeft :: BoardSpecGroup -> Coord -> BoardSpecGroup
infectLeft board (x,y) = if (positionExists board (x-1,y)) then infectWithGroupNumberOne (bringToFrontOfList board (x-1,y)) else board

infectRight :: BoardSpecGroup -> Coord -> BoardSpecGroup
infectRight board (x,y) = if (positionExists board (x+1,y)) then infectWithGroupNumberOne (bringToFrontOfList board (x+1,y)) else board

positionExists :: BoardSpecGroup -> Coord -> Bool
positionExists ((cocos,_,_):xs) coords = if (cocos == coords) then (True) else (positionExists xs coords)
positionExists []               _      = False

bringToFrontOfList :: BoardSpecGroup -> Coord -> BoardSpecGroup
bringToFrontOfList board cocos = removeAllExcept board cocos ++ removeFromList board cocos

removeAllExcept :: BoardSpecGroup -> Coord -> BoardSpecGroup
removeAllExcept ((coords,a,b):board) cocos = if (coords == cocos) then ([(coords,a,b)]) else (removeAllExcept board cocos)
removeAllExcept _                   _     = []

removeFromList :: BoardSpecGroup -> Coord -> BoardSpecGroup
removeFromList ((coords,a,b):board) cocos = if (coords == cocos) then (board) else ((coords,a,b):(removeFromList board cocos))
removeFromList _                    _     = []

checkIfAllNumberOne :: BoardSpecGroup -> Bool
checkIfAllNumberOne ((_,_,1):xs) = checkIfAllNumberOne xs
checkIfAllNumberOne []           = True
checkIfAllNumberOne otherwise    = False

printBoardSpecGroup :: BoardSpecGroup -> [((Int,Int),Bool,Int)]
printBoardSpecGroup (((a,b),c,d):xs) = ((a,b),c,d):(printBoardSpecGroup xs)
printBoardSpecGroup []              = []