What is a Tree?

In computer science, a tree is a way to organize data hierarchically. Think of it like a family tree or an organizational chart: there’s a starting point (the “root”), and everything branches out from there.

Trees are super important because they make it fast and easy to find, add, and organize information—way faster than searching through everything one-by-one!

Key Parts of a Tree

  • Root: The top node where everything starts.
  • Parent: A node that has branches to other nodes.
  • Child: A node that comes from a parent.
  • Leaf: A node with no children.
  • Edge: The connection between one node and another.

Different Types of Trees

There are many kinds of trees, each good for different jobs:

  • Binary Tree: Each node has up to two children. Simple but powerful.
  • Binary Search Tree (BST): A binary tree with an extra rule—left child < parent < right child. Great for quick searching!
  • Balanced Trees (AVL, Red-Black Trees): Keep the tree height small for faster operations.
  • Heaps: Special trees used mainly to quickly find the maximum or minimum element.
  • Trie (Prefix Tree): Used to store dictionaries and autocomplete words.

Sample Code: Creating a Simple Binary Tree (in Java)

Let’s try Java this time!

class Node {
    int value;
    Node left;
    Node right;

    Node(int value) {
        this.value = value;
        left = null;
        right = null;
    }
}

public class BinaryTree {
    Node root;

    BinaryTree(int value) {
        root = new Node(value);
    }

    public static void main(String[] args) {
        BinaryTree tree = new BinaryTree(10);
        tree.root.left = new Node(5);
        tree.root.right = new Node(15);

        System.out.println("Root: " + tree.root.value);
        System.out.println("Left Child: " + tree.root.left.value);
        System.out.println("Right Child: " + tree.root.right.value);
    }
}

This simple tree has 10 at the root, 5 on the left, and 15 on the right.

How Are Trees Used?

  • Searching: Trees make it way faster to find things! (Remember our post on Searching Algorithms?)
  • Organizing Information: File systems on computers are tree-based.
  • Gaming: Decision trees are used for AI.
  • Priority Queues: Heaps (special trees) make “highest priority first” tasks super fast.

Trees and Heaps

A heap is a special kind of tree where:

  • Every parent is bigger (max-heap) or smaller (min-heap) than its children.
  • The tree is always “complete,” meaning it fills levels left-to-right without gaps.

Heaps are awesome for making fast priority queues—useful in job scheduling, game leaderboards, and more!

Complexity of Tree Operations

Understanding how fast different operations are is really important. Here’s a quick table of Big-O complexities:

Operation Binary Search Tree Balanced Tree (AVL/Red-Black) Heap
Search O(h) O(log n) O(n)
Insert O(h) O(log n) O(log n)
Delete O(h) O(log n) O(log n)

Where:

  • n = number of nodes in the tree.
  • h = height of the tree (can be up to n in the worst case for an unbalanced tree).

Balanced trees keep the height small, making operations much faster!

Heaps are super fast at finding the biggest or smallest element — but not great if you’re looking for something random!

Final Thoughts

Trees are everywhere in computer science because they mirror the way we naturally organize information: starting from one place and branching out. Mastering trees will make everything from searching to sorting feel faster and smarter.

Next up: Binary Search Trees - Search Smarter, Not Harder!