Week 2

--Assignment 1

module SquareRoot where

eps :: Double
eps = 0.001

improve :: Double -> Double -> Double
improve x y_old = (y_old+(x/y_old))/2 --implement as defined   

goodEnough :: Double -> Double -> Bool
goodEnough y_old y_new 
  | abs((y_new - y_old)/y_new)<eps = True -- if approximation is below<eps => Good enough
  | otherwise = False -- else, not good enough

root :: Double -> Double
root x = aux x 1 --helper function defined below

aux :: Double -> Double -> Double
aux x y
 | goodEnough y (improve x y) = improve x y --if approximation is good enough, done
 | otherwise = aux x (improve x y) --else recurse

main :: IO ()
main = do 
  putStrLn "Compute the root of:"
  input <- getLine -- <- to assign in do block from getLine
  let x = read input -- let to assign in do block, read to convert to double
  if x<0
    then return() -- abort if negative
    else do -- do not forget do block
     putStrLn ("Square root: " ++ show(root x)) -- else compute root
     main --loop back to main
     
--Assignment 2

module Coins where

ls = [500, 200, 100, 50, 20, 10, 5]

cntChange :: Int -> Int
cntChange x = aux x ls

aux :: Int -> [Int] -> Int
aux x (d:ds)
 | x<0 = 0 -- BC1
 | x==0 = 1 --BC2
 | ds==[] && x `mod` d == 0 = 1 --BC3
 | ds==[] && x `mod` d /= 0 = 0 --BC4
 | otherwise = (aux x ds) + (aux (x-d) (d:ds)) --recursion