import Control.Monad
-- factorial x = product [1..x]
factorial 0 = 1
factorial n = n * factorial (n-1)

-- choose n k = if n < 0 then error "n should be positive" else factorial n `div` factorial k `div` factorial (n-k)

choose n k
    | n < 0 = error "n should be nonnegative"
    | k < 0 = error "k should be nonnegative"
    | k > n = error "k should be <= n"
    | otherwise = factorial n `div` factorial k `div` factorial (n-k)

foo = 12345

fibo 0 = 0
fibo 1 = 1
fibo n = fibo (n - 1) + fibo (n - 2)

--      i = 0, 1, 2, 3, 4, 5, 6, 7 , 8,  ...
-- fibo i = 0, 1, 1, 2, 3, 5, 8, 13, 21, ...
-- (0, 1) -> (1, 1) -> (
-- fibo2 k = (kth fibo number, (k+1)th fibo number)
fibo2 0 = (0, 1)
fibo2 n = let (x, y) = fibo2 (n-1) in (y, x + y)
-- if n = 8
-- then x = 13
-- and y = 21

fiboList = 0 : 1 : zipWith (+) fiboList (tail fiboList)

mymap f [] = []
mymap f (x:xs) = f x : mymap f xs

spliceOne [] = []
spliceOne (x:xs) = (x, xs) : [(y, x:ys) | (y, ys) <- spliceOne xs]

permutations [] = [[]]
permutations xs = [y : p | (y, ys) <- spliceOne xs, p <- permutations ys]

-- rollFiveDice = [[d1, d2, d3, d4, d5] | d1 <- [1..6], d2 <- [1..6], d3 <- [1..6], d4 <- [1..6], d5 <- [1..6]]
rollFiveDice = replicateM 5 [1..6]