[plt-scheme] Teaching Scheme

And, for good measure, a Haskell version of the same program:

doorOpen :: Int -> Bool
doorOpen door = doh door door

doh :: Int -> Int -> Bool
doh door 0 = True
doh door pass =
	if (door `rem` (pass+1)) == pass
	then not (doh door (pass-1))
	else doh door (pass-1)

doors :: [Bool]
doors = [doorOpen n | n <- [0..]]

printDoor :: (Int,Bool) -> IO ()
printDoor (door,open) =
	putStrLn ("Door #" ++ (show door) ++ " is " ++
		if open then "open.." else "closed..")

printUpTo :: Int -> IO ()
printUpTo n =
	mapM_ printDoor (zip [0..(n-1)] doors)


You can call printUpTo 50, then printUpTo 20, then printUpTo 300, and it'll compute the right answer for each of the numbers 0..299 only once -- not the numbers 0..19 three times, 20..49 twice, and 50..299 once each.


Stephen Bloch
sbloch at adelphi.edu