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## to Zipper in the Scala Track

Published at Apr 28 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)))
}
}``````
``````import scala.language.postfixOps

sealed trait Path[+A]

case object Root extends Path[Nothing]

case class Right[A](zipper: Zipper[A]) extends Path[A]

case class Left[A](zipper: Zipper[A]) extends Path[A]

case class Zipper[A](focus: BinTree[A],
valueUpdate: Option[A] = None,
leftUpdate: Option[Option[BinTree[A]]] = None,
rightUpdate: Option[Option[BinTree[A]]] = None,
path: Path[A] = Root)

object Zipper {
// A zipper for a binary tree.
// ??? Zipper[A] ???

// 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] = {
val tree = updatedTree(zipper)

zipper.path match {
case Root => tree
case Left(z: Zipper[A]) => toTree(setLeft(Some(tree), z))
case Right(z: Zipper[A]) => toTree(setRight(Some(tree), z))
}
}

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

// Get the left child of the focus node, if any.
def left[A](zipper: Zipper[A]): Option[Zipper[A]] =
zipper.leftUpdate getOrElse zipper.focus.left map (Zipper(_, path = Left(zipper)))

// Get the right child of the focus node, if any.
def right[A](zipper: Zipper[A]): Option[Zipper[A]] =
zipper.rightUpdate getOrElse zipper.focus.right map (Zipper(_, path = Right(zipper)))

// Get the parent of the focus node, if any.
def up[A](zipper: Zipper[A]): Option[Zipper[A]] = zipper.path match {
case Root => None
case Left(z: Zipper[A]) => Some(setLeft(Some(updatedTree(zipper)), z))
case Right(z: Zipper[A]) => Some(setRight(Some(updatedTree(zipper)), z))
}

// Set the value of the focus node.
def setValue[A](v: A, zipper: Zipper[A]): Zipper[A] = zipper.copy(valueUpdate =
if (v == zipper.focus.value) {
None
} else Some(v)
)

// Replace a left child tree.
def setLeft[A](l: Option[BinTree[A]], zipper: Zipper[A]): Zipper[A] = zipper.copy(leftUpdate =
if (l == zipper.focus.left) {
None
} else Some(l)
)

// Replace a right child tree.
def setRight[A](r: Option[BinTree[A]], zipper: Zipper[A]): Zipper[A] = zipper.copy(rightUpdate =
if (r == zipper.focus.right) {
None
} else Some(r)
)

def updatedTree[A](zipper: Zipper[A]): BinTree[A] =
if (zipper.valueUpdate orElse zipper.leftUpdate orElse zipper.rightUpdate nonEmpty) {
BinTree(
value(zipper),
zipper.leftUpdate.getOrElse(zipper.focus.left),
zipper.rightUpdate.getOrElse(zipper.focus.right)
)
} else zipper.focus
}

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