import Pictures 
--
-- Code from the January 31 class.
--


-- fact n = n factorial
--   NOTE: a Program error occurs when fact is given a negative argument
fact    :: Integer -> Integer
fact n 
  | n==0 = 1
  | n>0  = n* fact (n-1)

-- power2 n = 2^n
power2 :: Int -> Int
power2 n 
    | n==0 = 1               -- base case
    | n>0  = 2 * power2(n-1) -- inductive/recursion step

-- Fibonacci numbers
fib :: Integer -> Integer
fib n
    | n==0      = 0
    | n==1      = 1
    | n>1       = fib(n-2) + fib(n-1)
    | otherwise = error "fib given a negative argument"    

-- powerOf m n 
--   returns True iff m = n^k for some nonnegative integer k
powerOf :: Integer -> Integer -> Bool
powerOf m n
    | m==1         = True                    -- case 1
    | n==1         = False                   -- case 2
    | mod m n /= 0 = False                   -- case 3
    | otherwise    = powerOf (div m n) n     -- case 4

collatz :: Integer -> Integer
collatz n
    | n == 1    = 1
    | odd n     = collatz(3*n+1)
    | otherwise = collatz(n `div` 2)

traceCollatz :: Integer -> [Integer]
traceCollatz n
    | n == 1    = [1]
    | odd n     = n:traceCollatz(3*n+1)
    | otherwise = n:traceCollatz(n `div` 2)


------------------------------------------------------------------------
-- Picture recursions
------------------------------------------------------------------------

blank, blob, horiz, vert, black, exx, what :: Picture

blank = [".....",
         ".....",
         ".....",
         ".....",
         "....."]

blob =  ["..#..",
         ".###.",
         ".###.",
         ".###.",
         "..#.."]

horiz = ["#####",
         ".....",
         "#####",
         ".....",
         "#####"]

vert  = ["#.#.#",
         "#.#.#",
         "#.#.#",
         "#.#.#",
         "#.#.#"]

exx   = ["#...#",
         ".#.#.",
         "..#..",
         ".#.#.",
         "#...#"]

what  = [".###.",
         "#...#",
         "...#.",
         "..#..",
         "..#.."]

black = invertColour blank

pp = printPicture

column :: Int -> Picture -> Picture 
-- column n pic
--   returns the picture obtained by combining n copies of pic in a column
--   An error occurs if n is less than 1
column n pic 
    | n<1 = error "Column: n < 1"
    | n==1 = pic
    | otherwise = above pic (column (n-1) pic)

row :: Int -> Picture -> Picture 
-- row n pic
--   returns the picture obtained by combining n copies of pic in a row
--   An error occurs if n is less than 1
row n pic 
    | n<1 = error "fuss"
    | n==1 = pic
    | otherwise = sideBySide pic (row (n-1) pic)

mixedRow, mixedColumn :: Int -> Picture -> Picture
-- mixedRow n pic
--   returns the picture obtained by combining n copies of pic;
--   however, each occurrence of pic has its color inverted from 
--   the previous occurrence.
--
-- For exampe: (mixedRow 4 black) returns a row of boxes of 
--   color black, blank, black, blank
mixedRow n pic
    | n<1 = error "fuss"
    | n==1 = pic
    | otherwise = sideBySide pic (mixedRow (n-1) (invertColour pic))

mixedColumn n pic 
    | n<1 = error "fuss"
    | n==1 = pic
    | otherwise = above pic (mixedColumn (n-1) (invertColour pic))


grid :: Int -> Int -> Picture -> Picture
-- grid m n pic
--  returns the picture obtained by creating an m x n grid
--  (i.e., m rows, n columns) of copies of pic
grid m n pic = column m (row n pic)

mixedGrid :: Int -> Int -> Picture -> Picture 
-- mixedGrid m n pic
--  returns the picture obtained by creating an m x n grid
--  (i.e., m rows, n columns) of copies of pic in a checkerboard
--  pattern (i.e., alternating colors)
mixedGrid m n pic = mixedColumn m (mixedRow n pic)


-- I STOPPED HERE!!!




above3 :: Picture -> Picture -> Picture -> Picture 
-- above3 pic1 pic2 pic3 
--   returns a new picture consisting of pic1 above pic2 above pic3
above3 pic1 pic2 pic3 = above pic1 (above pic2 pic3)

side3 :: Picture -> Picture -> Picture -> Picture 
-- side3 pic1 pic2 pic3 
--   returns a new picture consisting of pic1 beside pic2 beside pic3
side3 pic1 pic2 pic3 = sideBySide pic1 (sideBySide pic2 pic3)

altBox :: Int -> Picture -> Picture
-- altBox m pic
--   returns an m by m grid of pic that alternative in color
--   on successive rings
altBox n pic = error "fuss"