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# Minth-11's solution

## to Zipper in the Haskell Track

Published at Apr 09 2020 · 0 comments
Instructions
Test suite
Solution

#### Note:

This exercise has changed since this solution was written.

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)

## Getting Started

Please refer to the installation and learning help pages.

## Running the tests

To run the test suite, execute the following command:

``````stack test
``````

#### If you get an error message like this...

``````No .cabal file found in directory
``````

You are probably running an old stack version and need to upgrade it.

#### Otherwise, if you get an error message like this...

``````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
``````

## Running GHCi

If you want to play with your solution in GHCi, just run the command:

``````stack ghci
``````

## Feedback, Issues, Pull Requests

The exercism/haskell repository on GitHub is the home for all of the Haskell exercises.

If you have feedback about an exercise, or want to help implementing a new one, head over there and create an issue. We'll do our best to help you!

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

### Tests.hs

``````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

(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``````
``````module Zipper
( BinTree(BT)
, fromTree
, left
, right
, setLeft
, setRight
, setValue
, toTree
, up
, value
) where

import qualified Data.Maybe as Maybe

data LeftOrRight = L | R deriving (Eq, Show)

data BinTree a = BT { btValue :: a
, btLeft  :: Maybe (BinTree a)
, btRight :: Maybe (BinTree a)
} deriving (Eq, Show)

data Zipper a = Zipper { zipp :: [LeftOrRight]
, tree :: BinTree a
} deriving (Eq, Show)

extendendTree :: Zipper a -> Maybe (BinTree a)
extendendTree (Zipper ls tr) = helper ls (Just tr)
where
helper _ Nothing = Nothing
helper (R:xs) (Just tr) = helper xs (btRight tr)
helper (L:xs) (Just tr) = helper xs (btLeft tr)
helper [] x = x

fromTree :: BinTree a -> Zipper a
fromTree tree = Zipper [] tree

toTree :: Zipper a -> BinTree a
toTree = tree

value :: Zipper a -> a
value zipper = btValue \$ f et
where
f Nothing = error "Zipper list extends beyond tree."
f (Just x) = x
et = extendendTree zipper

goFurther :: LeftOrRight -> (Zipper a) -> Maybe (Zipper a)
goFurther n zipper
| Maybe.isNothing \$ extendendTree u = Nothing
| otherwise = Just \$ u
where
u = Zipper ((zipp zipper) ++ [n]) (tree zipper)

left :: Zipper a -> Maybe (Zipper a)
left = goFurther L

right :: Zipper a -> Maybe (Zipper a)
right = goFurther R

up :: Zipper a -> Maybe (Zipper a)
up zipper
| zipp zipper == [] = Nothing
| otherwise = Just \$ Zipper (init (zipp zipper)) (tree zipper)

setValue :: a -> Zipper a -> Zipper a
setValue x (Zipper a b) = Zipper a (Maybe.fromJust (f g (Just b) a))
where
g (BT v l r) = BT x l r

setLeft :: Maybe (BinTree a) -> Zipper a -> Zipper a
setLeft tree (Zipper a b) = Zipper a (Maybe.fromJust (f g (Just b) a))
where
g (BT v l r) = BT v tree r

setRight :: Maybe (BinTree a) -> Zipper a -> Zipper a
setRight tree (Zipper a b) = Zipper a (Maybe.fromJust (f g (Just b) a))
where
g (BT v l r) = BT v l tree

f :: (BinTree a -> BinTree a) -> Maybe (BinTree a) -> [LeftOrRight] -> Maybe (BinTree a)
f g (Just (BT v l r)) [] = Just \$ g \$ BT v l r
f g (Just (BT v l r)) (y:ys)
| y == L = Just \$ BT v (f g l ys) r
| y == R = Just \$ BT v l (f g r ys)``````