-- Solutions to CSE 341 Haskell Discussion Questions #3

mystery = 1 : map (+2) mystery 
-- mystery is the list [1,3 ..]
-- in other words, all the odd numbes

-- version of repeat from the Prelude
repeat' :: a -> [a]
repeat' x = x : repeat' x

-- version of cycle from the Prelude
cycle' :: [a] -> [a]
cycle' xs = xs ++ cycle xs

{- Give a recursive definition of a variable doubles whose first element is
 10, and whose n-th element is twice the n-1 st, i.e
     [10, 20, 40, 80, 160, 320, ....]
 Use a helper function doubles_from that returns a list of all the doubles starting at n. -}
doubles :: [Integer]
doubles = doubles_from 10
doubles_from :: Integer -> [Integer]
doubles_from n = n : doubles_from (2*n)

-- other versions of doubles
doubles2 :: [Integer]
doubles2 = 10 : map (*2) doubles

-- using iterate:
doubles3 :: [Integer]
doubles3 = iterate (*2) 10


{- Write a Haskell function to return the infinite list of amounts of
 money you have every year, assuming you start with $100 and get paid 5%
 interest, compounded yearly. -}

-- simple but not general version:
dollars :: [Double]
dollars = 100 : map (\d -> 1.05*d) dollars

-- or using iterate:
idollars = iterate (1.05*) 100

-- more general recursive version:
better_dollars :: [Double]
better_dollars = dollar_growth 100.0 0.05

dollar_growth :: Double -> Double -> [Double]
dollar_growth p rate = p : dollar_growth (p*(1+rate)) rate


{- infinite list of all integers, ordered in such a way that you can find
   any given integer after searching a finite number of elements -}

ints :: [Integer]
ints = 0 : intsfrom 1
intsfrom n = n : (-n) : intsfrom (n+1)

{- or an alternate version: -}
otherints = 0: interleave [1..] [-1, -2 ..]
interleave (x:xs) (y:ys) = x : y : interleave xs ys