ðŸŽ‰ Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io ðŸŽ‰

# Wows's solution

## to Zipper in the Scala Track

Published at Mar 21 2019 · 0 comments
Instructions
Test suite
Solution

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)

The Scala exercises assume an SBT project scheme. The exercise solution source should be placed within the exercise directory/src/main/scala. The exercise unit tests can be found within the exercise directory/src/test/scala.

To run the tests simply run the command `sbt test` in the exercise directory.

For more detailed info about the Scala track see the help page.

## Submitting Incomplete Solutions

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

### ZipperTest.scala

``````import org.scalatest.{FunSuite, Matchers}

/** @version created manually **/
class ZipperTest extends FunSuite with Matchers {
def empty[A]: Option[BinTree[A]] = None

def bt[A](v: A, l: Option[BinTree[A]], r: Option[BinTree[A]]): Option[BinTree[A]] =
Some(BinTree(v, l, r))

def leaf[A](v: A): Option[BinTree[A]] =
Some(BinTree(v, None, None))

val t1: BinTree[Int] = BinTree(1, bt(2, empty,   leaf(3)), leaf(4))
val t2: BinTree[Int] = BinTree(1, bt(5, empty,   leaf(3)), leaf(4))
val t3: BinTree[Int] = BinTree(1, bt(2, leaf(5), leaf(3)), leaf(4))
val t4: BinTree[Int] = BinTree(1, leaf(2),                 leaf(4))

def fromSome[T](o: Option[T]) = o.get

val z = Zipper

test("data is retained") {
z.toTree(z.fromTree(t1)) should be (t1)
}

test("left, right and value") {
pending
z.value(fromSome(z.right(fromSome(z.left(z.fromTree(t1)))))) should be (3)
}

pending
(z.left(fromSome(z.left(z.fromTree(t1))))) should be (None)
}

test("tree from deep focus") {
pending
z.toTree(fromSome(z.right(fromSome(z.left(z.fromTree(t1)))))) should be (t1)
}

test("setValue") {
pending
z.toTree(z.setValue(5, (fromSome(z.left(z.fromTree(t1)))))) should be (t2)
}

test("setLeft with Some") {
pending
z.toTree(z.setLeft(Some(BinTree(5, None, None)),
(fromSome(z.left(z.fromTree(t1)))))) should be (t3)
}

test("setRight with None") {
pending
z.toTree(z.setRight(None, (fromSome(z.left(z.fromTree(t1)))))) should be (t4)
}

test("different paths to same zipper") {
pending
z.right(fromSome(z.up(fromSome(z.left(z.fromTree(t1)))))) should be
(z.right(z.fromTree(t1)))
}
}``````
``````case class BinTree[A](value: A, left: Option[BinTree[A]], right: Option[BinTree[A]])

case class Zipper[A](tree: BinTree[A], context: Context[A])

sealed trait Context[A]

case class Top[A]() extends Context[A]

case class Right[A](v: A, l: Option[BinTree[A]], context: Context[A]) extends Context[A]

case class Left[A](v: A, r: Option[BinTree[A]], context: Context[A]) extends Context[A]

object Zipper {

def fromTree[A](bt: BinTree[A]): Zipper[A] = Zipper(bt, Top())

@annotation.tailrec
def toTree[A](zipper: Zipper[A]): BinTree[A] = zipper match {
case Zipper(t, Top()) => t
case Zipper(t, Left(v, r, context)) => toTree(Zipper(BinTree(v, Some(t), r), context))
case Zipper(t, Right(v, l, context)) => toTree(Zipper(BinTree(v, l, Some(t)), context))
}

def value[A](zipper: Zipper[A]): A = zipper.tree.value

def left[A](zipper: Zipper[A]): Option[Zipper[A]] = zipper.tree.left.map(
Zipper(_, Left(zipper.tree.value, zipper.tree.right, zipper.context)))

def right[A](zipper: Zipper[A]): Option[Zipper[A]] = zipper.tree.right.map(
Zipper(_, Right(zipper.tree.value, zipper.tree.left, zipper.context)))

def up[A](zipper: Zipper[A]): Option[Zipper[A]] = zipper match {
case Zipper(t, Top()) => None
case Zipper(t, Left(v, r, context)) => Some(Zipper(BinTree(value = v, left = Some(t), right = r),
context))
case Zipper(t, Right(v, l, context)) => Some(Zipper(BinTree(value = v, left = l, right = Some(t)),
context))
}

def setValue[A](v: A, zipper: Zipper[A]): Zipper[A] = zipper match {
case Zipper(t, c) => Zipper(t.copy(v), c)
}

def setLeft[A](l: Option[BinTree[A]], zipper: Zipper[A]): Zipper[A] = zipper match {
case Zipper(t, c) => Zipper(t.copy(left = l), c)
}

def setRight[A](r: Option[BinTree[A]], zipper: Zipper[A]): Zipper[A] = zipper match {
case Zipper(t, c) => Zipper(t.copy(right = r), c)
}
}``````