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

ErikSchierboom's solution

to Zipper in the Scala Track

Published at Jul 13 2018 · 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)))
}
}``````
``````trait Crumb[A]
case class LeftCrumb[A](value: A, tree: Option[BinTree[A]]) extends Crumb[A]
case class RightCrumb[A](value: A, tree: Option[BinTree[A]]) extends Crumb[A]

case class Zipper[A](value: A, left: Option[BinTree[A]], right: Option[BinTree[A]], crumbs: List[Crumb[A]])
case class BinTree[A](value: A, left: Option[BinTree[A]], right: Option[BinTree[A]])

object Zipper {
def fromTree[A](bt: BinTree[A]): Zipper[A] = Zipper[A](bt.value, bt.left, bt.right, Nil)

def toTree[A](zipper: Zipper[A]): BinTree[A] = {
def loop(crumbs: List[Crumb[A]], t: BinTree[A]): BinTree[A] =
crumbs match {
case Nil => t
case (LeftCrumb(tv, tr)::cs) => loop(cs, BinTree(tv, Some(t), tr))
case (RightCrumb(tv, tl)::cs) => loop(cs, BinTree(tv, tl, Some(t)))
}

val tree = BinTree(zipper.value, zipper.left, zipper.right)
loop(zipper.crumbs, tree)
}

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

def left[A](zipper: Zipper[A]): Option[Zipper[A]] =
zipper.left.map(l => fromTree(l).copy(crumbs = LeftCrumb(zipper.value, zipper.right) :: zipper.crumbs))

def right[A](zipper: Zipper[A]): Option[Zipper[A]] =
zipper.right.map(r => fromTree(r).copy(crumbs = RightCrumb(zipper.value, zipper.left) :: zipper.crumbs))

def up[A](zipper: Zipper[A]): Option[Zipper[A]] =
zipper.crumbs match {
case Nil => None
case LeftCrumb(tv, tr)::cs => Some(Zipper(tv, Some(toTree(zipper)), tr, cs))
case RightCrumb(tv, tl)::cs => Some(Zipper(tv, tl, Some(toTree(zipper)), cs))
}

def setValue[A](v: A, zipper: Zipper[A]): Zipper[A] =  zipper.copy(value = v)

def setLeft[A](l: Option[BinTree[A]], zipper: Zipper[A]): Zipper[A] = zipper.copy(left = l)

def setRight[A](r: Option[BinTree[A]], zipper: Zipper[A]): Zipper[A] = zipper.copy(right = r)
}``````

What can you learn from this solution?

A huge amount can be learned from reading other peopleâ€™s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

• What compromises have been made?