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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)
  }

  test("dead end") {
    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)
  }
}

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