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SergiiVlasiuk's solution

to Binary Search Tree in the Scala Track

Published at Aug 26 2019 · 0 comments
Instructions
Test suite
Solution

Insert and search for numbers in a binary tree.

When we need to represent sorted data, an array does not make a good data structure.

Say we have the array [1, 3, 4, 5], and we add 2 to it so it becomes [1, 3, 4, 5, 2] now we must sort the entire array again! We can improve on this by realizing that we only need to make space for the new item [1, nil, 3, 4, 5], and then adding the item in the space we added. But this still requires us to shift many elements down by one.

Binary Search Trees, however, can operate on sorted data much more efficiently.

A binary search tree consists of a series of connected nodes. Each node contains a piece of data (e.g. the number 3), a variable named left, and a variable named right. The left and right variables point at nil, or other nodes. Since these other nodes in turn have other nodes beneath them, we say that the left and right variables are pointing at subtrees. All data in the left subtree is less than or equal to the current node's data, and all data in the right subtree is greater than the current node's data.

For example, if we had a node containing the data 4, and we added the data 2, our tree would look like this:

  4
 /
2

If we then added 6, it would look like this:

  4
 / \
2   6

If we then added 3, it would look like this

   4
 /   \
2     6
 \
  3

And if we then added 1, 5, and 7, it would look like this

      4
    /   \
   /     \
  2       6
 / \     / \
1   3   5   7

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.

Source

Josh Cheek https://twitter.com/josh_cheek

Submitting Incomplete Solutions

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

BstTest.scala

import org.scalatest.{Matchers, FlatSpec}

/** @version created manually **/
class BstTest extends FlatSpec with Matchers {
  val bst4 = Bst(4)

  it should "retain data" in {
    bst4.value should equal(4)
  }

  it should "retain data - char" in {
    pending
    Bst('d').value should equal('d')
  }

  it should "insert less" in {
    pending
    bst4.insert(2).left.get.value should equal(2)
  }

  it should "insert less - char" in {
    pending
    Bst('d').insert('a').left.get.value should equal('a')
  }

  it should "insert same" in {
    pending
    bst4.insert(4).left.get.value should equal(4)
  }

  it should "insert greater than" in {
    pending
    bst4.insert(5).right.get.value should equal(5)
  }

  it should "handle complex tree - sort out of order list" in {
    pending
    val bst = Bst.fromList(List(4, 2, 6, 1, 3, 7, 5))
    Bst.toList(bst) should equal((1 to 7).toList)

    bst.value should equal(4)
    bst.left.get.value should equal(2)
    bst.left.get.left.get.value should equal(1)
    bst.left.get.right.get.value should equal(3)
    bst.right.get.value should equal(6)
    bst.right.get.left.get.value should equal(5)
    bst.right.get.right.get.value should equal(7)
  }

  it should "iterating one element" in {
    pending
    Bst.toList(bst4) should equal(List(4))
  }

  it should "iterating over smaller element" in {
    pending
    Bst.toList(Bst.fromList(List(4, 2))) should equal(List(2, 4))
  }

  it should "iterating over larger element" in {
    pending
    Bst.toList(Bst.fromList(List(4, 5))) should equal(List(4, 5))
  }

  it should "iterating over complex tree" in {
    pending
    Bst.toList(Bst.fromList(List(4, 2, 1, 3, 6, 7, 5))) should equal((1 to 7).toList)
  }

  it should "iterating over complex tree - chars" in {
    pending
    Bst.toList(Bst.fromList(List('d', 'b', 'a', 'c', 'f', 'g', 'e'))) should
      equal(('a' to 'g').toList)
  }
}
object Bst {
  def fromList(l: List[Int]): Bst = l match {
    case Nil => throw new IllegalArgumentException("At least 1 item in the list is required")
    case x :: xs => xs.foldLeft(Bst(x))((agg, x) => agg.insert(x))
  }

  def toList(bst: Bst): List[Int] = bst match {
    case Bst(v, Some(left), Some(right)) => toList(left) ++ (v :: toList(right))
    case Bst(v, None, Some(right)) => v :: toList(right)
    case Bst(v, Some(left), None) => toList(left) ++ (v :: Nil)
    case Bst(v, None, None) => v :: Nil
  }
}

case class Bst(value: Int, left: Option[Bst] = None, right: Option[Bst] = None) {
  def insert(item: Int): Bst = if (item <= value) { // to left
    val newLeft = if (left == None) Bst(item) else left.get.insert(item)
    Bst(value, Some(newLeft), right)
  } else { //to right
    val newRight = if (right == None) Bst(item) else right.get.insert(item)
    Bst(value, left, Some(newRight))
  }
}

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