====== Recursion ======
===== Q.1 =====
从一个长方形中剪下一个最大的正方形，剩下部分是一个新的长方形；从这个新的长方形中再次剪下一个最大的正方形，剩下部分依然是一个长方形；从这个新的长方形中第三次剪下一个最大的正方形，此时剩余部分是一个长为23cm，宽为20cm的长方形，则原长方形的周长是多少？

&HS
++++ Solution by Josh|
<code haskell>
data Rect = Rect Int Int deriving Show

flatMap :: (a -> [b]) -> [a] -> [b]
flatMap _ [] = []
flatMap f (x:xs) = (f x) ++ flatMap f xs 

expand :: Rect -> [Rect]
expand (Rect a b) = [(Rect (a + b) b), (Rect a (a + b))] 

nExpand :: Int -> [Rect] -> [Rect]
nExpand 0 = id 
nExpand n = nExpand (n - 1) . (flatMap expand)

perimeter :: Rect -> Int
perimeter (Rect a b) = 2 * (a + b)

main =  
    (print . (map perimeter) . (nExpand 3)) [(Rect 23 20)]
</code>
++++