如何解决取无限结构的有限部分
我必须定义一个无限的自行车手enumInts::Cyclist Integer
data Cyclist a=Elem (Cyclist a) a (Cyclist a)
enumInts:: Cyclist Integer
enumInts=Elem prev 0 next
where
prev=help2 enumInts 0
next=help1 enumInts 0
-- Create positive part
help1::Cyclist Integer -> Integer -> Cyclist Integer
help1 prev n=present
where present=Elem prev (n+1) next
where next=help1 present (n+1)
-- Create negative part
help2::Cyclist Integer -> Integer -> Cyclist Integer
help2 next n=present
where present=Elem prev (n-1) next
where prev=help2 present (n-1)
解决方法
我敢肯定，现在已经超过了您的截止日期，因此我很高兴处理倍数无限的Integer：
允许有限的部分
要使用汇整功能，我必须编辑您的类型，使其可以是有限的：
data Cyclist a=Elem (Cyclist a) a (Cyclist a) | Empty
deriving Show
takeToDepth :: Int -> Cyclist a -> Cyclist a
takeToDepth 0 _ = Empty
takeToDepth n (Elem c1 a c2)
| n >0 = Elem (takeToDepth (n-1) c1) a (takeToDepth (n-1) c2)
| otherwise = Empty
takeToDepth n Empty = Empty
*Main> takeToDepth 1 enumInts
Elem Empty 0 Empty
0 -- I\'ve drawn the tree
*Main> takeToDepth 2 enumInts
Elem (Elem Empty (-1) Empty) 0 (Elem Empty 1 Empty)
0
| -- looks OK
--- -- see the end of the answer for how I pretty printed
/ \\
-1 1
*Main> takeToDepth 3 enumInts
Elem (Elem (Elem Empty (-2) Empty) (-1) (Elem Empty 0 Empty))
0 (Elem (Elem Empty 0 Empty) 1 (Elem Empty 2 Empty))
0
|
-----
/ \\
-1 1
| |
--- --
/ \\ / \\
-2 0 0 2 -- oops! We\'ve re-created zero for 1 and -1
0
*Main> takeToDepth 4 enumInts
Elem (Elem (Elem (Elem Empty (-3) Empty) (-2) (Elem Empty (-1) Empty)) (-1)
(Elem (Elem Empty (-1) Empty) 0 (Elem Empty 1 Empty))) 0
(Elem (Elem (Elem Empty (-1) Empty) 0 (Elem Empty 1 Empty)) 1
(Elem (Elem Empty 1 Empty) 2 (Elem Empty 3 Empty)))
0
|
--------------------------
/ \\
-1 1
| |
------------- -----------
/ \\ / \\
-2 0 0 2
| | | |
------- ----- ----- -----
/ \\ / \\ / \\ / \\
-3 -1 -1 1 -1 1 1 3
| | | | | | | |
--- --- --- -- --- -- -- --
/ \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\
-4 -2 -2 0 -2 0 0 2 -2 0 0 2 0 2 2 4
this = Elem (Elem (Elem (Elem Empty (-3) Empty) (-2) Empty) (-1) Empty)
0 (Elem Empty 1 (Elem Empty 2 (Elem Empty 3 Empty)))
0
|
---
/ \\
-1 1
| |
-2 2
| |
-3 3
data InfiniteList a = IL a (InfiniteList a) deriving Show
tailIL (IL _ therest) = therest
headIL (IL a _ ) = a
fromList [] = error \"fromList: finite list supplied\"
fromList (x:xs) = IL x (fromList xs)
toList (IL a therest) = a:toList therest
data DoublyInfiniteList a = DIL {left :: InfiniteList a,here :: a,right :: InfiniteList a}
deriving Show
enumIntsDIL = DIL {left = fromList [-1,-2..],here = 0,right = fromList [1..]}
0
|
---
/ \\
-1 1
| |
-2 2
| |
-3 3
| |
-4 4
reverse
toList
fromList
go :: Int -> DoublyInfiniteList a -> DoublyInfiniteList a
go 0 dil = dil
go n dil | n < 0 = go (n+1) DIL {left = tailIL . left $ dil,here = headIL . left $ dil,right = IL (here dil) (right dil)}
go n dil | n > 0 = go (n-1) DIL {left = IL (here dil) (left dil),here = headIL . right $ dil,right = tailIL . right $ dil}
data LeftRightList a = LRL {left\'::[a],here\'::a,right\'::[a]} -- deriving Show
toLRL :: Int -> DoublyInfiniteList a -> LeftRightList a
toLRL n dil = LRL {left\' = take n . toList . left $ dil,here\' = here dil,right\' = take n . toList . right $ dil}
*Main> toLRL 10 enumIntsDIL
LRL {left\' = [-1,-2,-3,-4,-5,-6,-7,-8,-9,-10],here\' = 0,right\' = [1,2,3,4,5,6,7,8,9,10]}
import Data.List -- (Put this import at the top of the file,not here.)
instance Show a => Show (LeftRightList a) where
show lrl = (show\'.reverse.left\' $ lrl) -- doesn\'t work for infinite ones!
++ \",\" ++ show (here\' lrl) ++ \",\"
++ (show\' $ right\' lrl) where
show\' = concat.intersperse \",\" . map show
*Main> toLRL 10 enumIntsDIL
-10,-1,1,10
*Main> toLRL 10 $ go 7 enumIntsDIL
-3,10,11,12,13,14,15,16,17
import Data.Tree
import Data.Tree.Pretty
class TreeLike t where
toTree :: t a -> Tree a
treeTake :: Int -> Tree a -> Tree a
treeTake 1 (Node a _) = Node a []
treeTake n (Node a ts) | n > 1 = Node a (map (treeTake (n-1)) ts)
| otherwise = error \"treeTake: attemt to take non-positive number of elements\"
see :: (TreeLike t,Show a) => Int -> t a -> IO ()
see n = putStrLn.drawVerticalTree.fmap show.treeTake n.toTree
*Main> see 5 $ go (-2) enumIntsDIL
-2
|
---
/ \\
-3 -1
| |
-4 0
| |
-5 1
| |
-6 2
instance TreeLike Cyclist where
toTree Empty = error \"toTree: error - Empty\"
toTree (Elem Empty a Empty) = Node a []
toTree (Elem Empty a c2) = Node a [toTree c2]
toTree (Elem c1 a Empty) = Node a [toTree c1]
toTree (Elem c1 a c2) = Node a [toTree c1,toTree c2]
instance TreeLike InfiniteList where
toTree (IL a therest) = Node a [toTree therest]
instance TreeLike DoublyInfiniteList where
toTree dil = Node (here dil) [toTree $ left dil,toTree $ right dil]
instance TreeLike [] where
toTree [] = error \"toTree: can\'t make a tree out of an empty list\"
toTree [x] = Node x []
toTree (x:ys) = Node x [toTree ys]
instance TreeLike LeftRightList where
toTree lrl = Node (here\' lrl) [toTree $ left\' lrl,toTree $ right\' lrl]
enumInts :: Integer -> [Integer]
enumInts n = [-(n`div`2)..(n`div`2)]
data [a] = [] | a : [a]
take
take 0 xs = []
take n (x:xs) = x:take (n-1) xs
take
myList = ([0] ++ ) $ concat $ [[x] ++ [-x] | x <- [1..]]
takeOnly n = sort $ take n myList
enumInts :: Cyclist Integer
enumInts = Elem (goLeft enumInts) 0 (goRight enumInts)
where
goLeft this@(Elem left n _) = let left = Elem (goLeft left) (n-1) this in left
goRight this@(Elem _ n right) = let right = Elem this (n+1) (goRight right) in right
label . forward . backward . forward . forward $ enumInts
label (Elem _ x _) = x
forward (Elem _ _ x) = x
backward (Elem x _ _) = x
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