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to Zipper in the Scala Track

Published at Jun 26 2020 · 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.

Please see the learning and installation pages if you need any help.

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)))
  }
}
// A binary tree.
case class BinTree[A](value: A, left: Option[BinTree[A]], right: Option[BinTree[A]])

case class Zipper[A](var tree: BinTree[A], var up: Option[Zipper[A]] = None) {
  var value: A = tree.value
  var right: Option[Zipper[A]] = tree.right match {
    case Some(a) => Some(Zipper(a, Some(this)))
    case None => None
  }
  var left: Option[Zipper[A]] = tree.left match {
    case Some(a) => Some(Zipper(a, Some(this)))
    case None => None
  }
}

object BinTree {
  def apply[A](zipper: Zipper[A]): BinTree[A] = {
    val value = zipper.value
    val left = if (zipper.left.isDefined) Some(BinTree[A](zipper.left.get)) else None
    val right = if (zipper.right.isDefined) Some(BinTree[A](zipper.right.get)) else None
    BinTree[A](value, left, right)
  }
}

object Zipper {
  // Get a zipper focussed on the root node.
  def fromTree[A](bt: BinTree[A]): Zipper[A] = Zipper(bt)

  // Get the complete tree from a zipper.
  def toTree[A](zipper: Zipper[A]): BinTree[A] = {
    var up = zipper
    while (up.up.isDefined) {
      up = up.up.get
    }
    BinTree[A](up)
  }

  // Get the value of the focus node.
  def value[A](zipper: Zipper[A]): A = zipper.value

  // Get the left child of the focus node, if any.
  def left[A](zipper: Zipper[A]): Option[Zipper[A]] = zipper.left

  // Get the right child of the focus node, if any.
  def right[A](zipper: Zipper[A]): Option[Zipper[A]] = zipper.right

  // Get the parent of the focus node, if any.
  def up[A](zipper: Zipper[A]): Option[Zipper[A]] = zipper.up

  // Set the value of the focus node.
  def setValue[A](v: A, zipper: Zipper[A]): Zipper[A] = {
    zipper.value = v
    zipper
  }

  // Replace a left child tree.
  def setLeft[A](l: Option[BinTree[A]], zipper: Zipper[A]): Zipper[A] = {
    l match {
      case Some(a) => zipper.left = Some(Zipper(a))
      case None => zipper.left = None
    }
    zipper
  }

  // Replace a right child tree.
  def setRight[A](r: Option[BinTree[A]], zipper: Zipper[A]): Zipper[A] = {
    r match {
      case Some(a) => zipper.right = Some(Zipper(a))
      case None => zipper.right = None
    }
    zipper
  }
}

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