Creating a zipper for a binary tree.
Zippers are a purely functional way of navigating within a data structure and manipulating it. They essentially contain a data structure and a pointer into that data structure (called the focus).
For example given a rose tree (where each node contains a value and a list of child nodes) a zipper might support these operations:
from_tree
(get a zipper out of a rose tree, the focus is on the root node)to_tree
(get the rose tree out of the zipper)value
(get the value of the focus node)prev
(move the focus to the previous child of the same parent,
returns a new zipper)next
(move the focus to the next child of the same parent, returns a
new zipper)up
(move the focus to the parent, returns a new zipper)set_value
(set the value of the focus node, returns a new zipper)insert_before
(insert a new subtree before the focus node, it
becomes the prev
of the focus node, returns a new zipper)insert_after
(insert a new subtree after the focus node, it becomes
the next
of the focus node, returns a new zipper)delete
(removes the focus node and all subtrees, focus moves to the
next
node if possible otherwise to the prev
node if possible,
otherwise to the parent node, returns a new zipper)Please refer to the installation and learning help pages.
To run the test suite, execute the following command:
stack test
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No compiler found, expected minor version match with...
Try running "stack setup" to install the correct GHC...
Just do as it says and it will download and install the correct compiler version:
stack setup
If you want to play with your solution in GHCi, just run the command:
stack ghci
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import Data.Maybe (fromJust)
import Test.Hspec (Spec, it, shouldBe)
import Test.Hspec.Runner (configFastFail, defaultConfig, hspecWith)
import Zipper
( BinTree(BT)
, fromTree
, left
, right
, setLeft
, setRight
, setValue
, toTree
, up
, value
)
main :: IO ()
main = hspecWith defaultConfig {configFastFail = True} specs
specs :: Spec
specs = do
let leaf v = node v Nothing Nothing
node v l r = Just (BT v l r :: BinTree Int)
t1 = BT 1 (node 2 Nothing $ leaf 3) $ leaf 4
t2 = BT 1 (node 5 Nothing $ leaf 3) $ leaf 4
t3 = BT 1 (node 2 (leaf 5) $ leaf 3) $ leaf 4
t4 = BT 1 (leaf 2 ) $ leaf 4
t5 = BT 6 (leaf 7 ) $ leaf 8
t6 = BT 1 (node 2 Nothing $ leaf 3) $ node 6 (leaf 7) (leaf 8)
t7 = BT 1 (node 2 Nothing $ leaf 5) $ leaf 4
it "data is retained" $
toTree (fromTree t1)
`shouldBe` t1
it "left, right and value" $
(value . fromJust . right . fromJust . left . fromTree) t1
`shouldBe` 3
it "dead end" $
(left . fromJust . left . fromTree) t1
`shouldBe` Nothing
it "traversing up from top" $
(up . fromTree) t1
`shouldBe` Nothing
it "left, right, and up" $
(value . fromJust . right . fromJust . left . fromJust . up . fromJust . right . fromJust . up . fromJust . left . fromTree) t1
`shouldBe` 3
it "tree from deep focus" $
(toTree . fromJust . right . fromJust . left . fromTree) t1
`shouldBe` t1
it "setValue" $
(toTree . setValue 5 . fromJust . left . fromTree) t1
`shouldBe` t2
it "setValue after traversing up" $
(toTree . setValue 5 . fromJust . up . fromJust . right . fromJust . left . fromTree) t1
`shouldBe` t2
it "setLeft with Just" $
(toTree . setLeft (leaf 5) . fromJust . left . fromTree) t1
`shouldBe` t3
it "setRight with Nothing" $
(toTree . setRight Nothing . fromJust . left . fromTree) t1
`shouldBe` t4
it "setRight with subtree" $
(toTree . setRight (Just t5) . fromTree) t1
`shouldBe` t6
it "setValue on deep focus" $
(toTree . setValue 5 . fromJust . right . fromJust . left . fromTree) t1
`shouldBe` t7
it "different paths to same zipper" $
(right . fromJust . up . fromJust . left . fromTree) t1
`shouldBe` (right . fromTree) t1
-- 59c9e4719c6f47c505bf531de711bb3e8a429141
module Zipper
( BinTree(BT)
, fromTree
, left
, right
, setLeft
, setRight
, setValue
, toTree
, up
, value
) where
import Data.Maybe
data BinTree a = BT { btValue :: a
, btLeft :: Maybe (BinTree a)
, btRight :: Maybe (BinTree a)
} deriving (Eq, Show)
data Ctx a = Top | L (Ctx a) a (Maybe (BinTree a)) | R (Ctx a) a (Maybe (BinTree a))
deriving (Eq, Show)
data Zipper a = Z (Ctx a) (BinTree a)
deriving (Eq, Show)
fromTree :: BinTree a -> Zipper a
fromTree tree = Z Top tree
toTree :: Zipper a -> BinTree a
toTree (Z Top t) = t
toTree zipper = toTree $ fromJust $ up zipper
value :: Zipper a -> a
value (Z _ t) = btValue t
left :: Zipper a -> Maybe (Zipper a)
left (Z ctx t)= btLeft t >>= Just . Z (L ctx (btValue t) (btRight t))
right :: Zipper a -> Maybe (Zipper a)
right (Z ctx t)= btRight t >>= Just . Z (R ctx (btValue t) (btLeft t))
up :: Zipper a -> Maybe (Zipper a)
up (Z Top t) = Nothing
up (Z (L ctx v t') t) = Just $ Z ctx (BT v (Just t) t')
up (Z (R ctx v t') t) = Just $ Z ctx (BT v t' (Just t))
setValue :: a -> Zipper a -> Zipper a
setValue x (Z ctx t) = Z ctx $ t { btValue = x }
setLeft :: Maybe (BinTree a) -> Zipper a -> Zipper a
setLeft tree (Z ctx t) = Z ctx $ t { btLeft = tree }
setRight :: Maybe (BinTree a) -> Zipper a -> Zipper a
setRight tree (Z ctx t) = Z ctx $ t { btRight = tree }
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