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A tree
A tree

The tree is a data structure of profound importance. It is used in numerous facets of software development, such as:

  • Representing hierarchical relationships.
  • Managing sorted data.
  • Facilitating fast lookup operations.

There are many types of trees, and they come in various shapes and sizes. In this chapter, you will learn the basics of using and implementing a tree.

Terminology

There are many terms associated with trees, so you will get acquainted with a couple right off the bat.

Node

Like the linked list, trees are made up of nodes.

Parent and child

Trees are viewed starting from the top and branching towards the bottom, just like a real tree, only upside-down.

Root

The topmost node in the tree is called the root of the tree. It is the only node that has no parent:

Leaf

A node is a leaf if it has no children:

Implementation

Open up the starter playground for this chapter to get started. A tree is made up of nodes, so your first task is to create a TreeNode class.

public class TreeNode<T> {
  public var value: T
  public var children: [TreeNode] = []

  public init(_ value: T) {
    self.value = value
  }
}
public func add(_ child: TreeNode) {
  children.append(child)
}
example(of: "creating a tree") {
  let beverages = TreeNode("Beverages")

  let hot = TreeNode("Hot")
  let cold = TreeNode("Cold")

  beverages.add(hot)
  beverages.add(cold)
}

Traversal algorithms

Iterating through linear collections such as arrays or linked lists is straightforward. Linear collections have a clear start and end:

Depth-first traversal

Write the following at the bottom of TreeNode.swift:

extension TreeNode {
  public func forEachDepthFirst(visit: (TreeNode) -> Void) {
    visit(self)
    children.forEach {
      $0.forEachDepthFirst(visit: visit)
    }
  }
}
func makeBeverageTree() -> TreeNode<String> {
  let tree = TreeNode("Beverages")

  let hot = TreeNode("hot")
  let cold = TreeNode("cold")

  let tea = TreeNode("tea")
  let coffee = TreeNode("coffee")
  let chocolate = TreeNode("cocoa")

  let blackTea = TreeNode("black")
  let greenTea = TreeNode("green")
  let chaiTea = TreeNode("chai")

  let soda = TreeNode("soda")
  let milk = TreeNode("milk")

  let gingerAle = TreeNode("ginger ale")
  let bitterLemon = TreeNode("bitter lemon")

  tree.add(hot)
  tree.add(cold)

  hot.add(tea)
  hot.add(coffee)
  hot.add(chocolate)

  cold.add(soda)
  cold.add(milk)

  tea.add(blackTea)
  tea.add(greenTea)
  tea.add(chaiTea)

  soda.add(gingerAle)
  soda.add(bitterLemon)

  return tree
}

example(of: "depth-first traversal") {
  let tree = makeBeverageTree()
  tree.forEachDepthFirst { print($0.value) }
}
---Example of: depth-first traversal---
Beverages
hot
tea
black
green
chai
coffee
cocoa
cold
soda
ginger ale
bitter lemon
milk

Level-order traversal

Write the following at the bottom of TreeNode.swift:

extension TreeNode {
  public func forEachLevelOrder(visit: (TreeNode) -> Void) {
    visit(self)
    var queue = Queue<TreeNode>()
    children.forEach { queue.enqueue($0) }
    while let node = queue.dequeue() {
      visit(node)
      node.children.forEach { queue.enqueue($0) }
    }
  }
}

example(of: "level-order traversal") {
  let tree = makeBeverageTree()
  tree.forEachLevelOrder { print($0.value) }
}
---Example of: level-order traversal---
Beverages
hot
cold
tea
coffee
cocoa
soda
milk
black
green
chai
ginger ale
bitter lemon

Search

You already have a method that iterates through all the nodes, so building a search algorithm shouldn’t take long. Write the following at the bottom of TreeNode.swift:

extension TreeNode where T: Equatable {
  public func search(_ value: T) -> TreeNode? {
    var result: TreeNode?
    forEachLevelOrder { node in
      if node.value == value {
        result = node
      }
    }
    return result
  }
}
example(of: "searching for a node") {
  // tree from last example
  
  if let searchResult1 = tree.search("ginger ale") {
    print("Found node: \(searchResult1.value)")
  }
  if let searchResult2 = tree.search("WKD Blue") {
    print(searchResult2.value)
  } else {
    print("Couldn't find WKD Blue")
  }
}
---Example of: searching for a node---
Found node: ginger ale
Couldn't find WKD Blue

Key points

  • Trees share some similarities to linked lists, but, whereas linked-list nodes may only link to one successor node, a tree node can link to many child nodes.
  • Every tree node, except for the root node, has exactly one parent node.
  • A root node has no parent nodes.
  • Leaf nodes have no child nodes.
  • Be comfortable with the tree terminology such as parent, child, leaf and root. Many of these terms are common tongue for fellow programmers and will be used to help explain other tree structures.
  • Traversals, such as depth-first and level-order traversals, aren’t specific to the general tree. They work on other trees as well, although their implementation will be slightly different based on how the tree is structured.

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