Introduction to Trees in Data Structures | DWP

Trees are one of the most important and widely used data structures in computer science. They help represent hierarchical data efficiently and are the foundation for many advanced concepts such as file systems, databases, compilers, operating systems, and search algorithms.

Unlike arrays and linked lists, trees are non-linear data structures, meaning data is not stored sequentially. Instead, elements are organized in a parent-child relationship, forming a structure similar to an inverted tree.

Understanding trees is essential for mastering topics like Binary Trees, Binary Search Trees, Heaps, Tries, Graphs, and even System Design concepts.

What is a Tree?

A tree is a hierarchical data structure consisting of nodes connected by edges.

• The topmost node is called the root

• Each node can have zero or more child nodes

• Nodes without children are called leaf nodes

In simple words, a tree starts from a root and branches out into subtrees.

Example representation

        A
       / \
      B   C
     / \
    D   E

Here, A is the root, B and C are children of A, and D and E are leaf nodes.

Key Terminologies in Trees

Before diving deeper, it is important to understand some common tree terminologies.

Root

The topmost node of the tree.

Parent

A node that has child nodes.

Child

Nodes directly connected below a parent.

Leaf Node

A node with no children.

Edge

The connection between two nodes.

Height of a Tree

The maximum number of edges from the root to any leaf.

Depth of a Node

The number of edges from the root to that node.

Subtree

A tree formed by any node and its descendants.

Why Do We Need Trees?

Trees are used when data needs to be stored and accessed hierarchically.

Some real-world use cases include

• File system structure (folders and files)

• HTML DOM structure

• Organization hierarchy in companies

• Database indexing (B-Trees, B+ Trees)

• Searching and sorting data efficiently

Trees allow faster search, insertion, and deletion compared to linear data structures in many scenarios.

Tree vs Linear Data Structures

Arrays and Linked Lists store data linearly, one after another.

Trees store data hierarchically.

Key differences

• Arrays and linked lists have a single level, trees have multiple levels

• Searching in arrays can take O(n), trees can optimize this to O(log n)

• Trees naturally represent parent-child relationships

This makes trees powerful for complex data modeling.

Types of Trees (High-Level Overview)

There are many types of trees, each designed for specific problems.

Binary Tree

Each node can have at most two children.

Binary Search Tree (BST)
A binary tree where left child < root < right child.

Balanced Trees

Trees that maintain height balance for performance (AVL, Red-Black Tree).

Heap

A complete binary tree used in priority queues.

Trie

A tree used for efficient string searching and autocomplete.

General Tree

A tree where nodes can have any number of children.

This article focuses on understanding the basics before diving into these specialized trees.

Basic Tree Node Structure

A simple tree node typically contains

• A value

• References to child nodes

Example in JavaScript

class TreeNode {
  constructor(value) {
    this.value = value;
    this.children = [];
  }
}

For binary trees

class TreeNode {
  constructor(value) {
    this.value = value;
    this.left = null;
    this.right = null;
  }
}

Tree Traversal (Preview)

Traversal means visiting all nodes of the tree in a specific order.

Common traversal techniques

Depth First Traversal

• Preorder

• Inorder

• Postorder

Breadth First Traversal

• Level Order Traversal

Traversal techniques are fundamental and will be covered in detail in upcoming topics.

Time Complexity in Trees

Time complexity in trees often depends on the height of the tree.

• Balanced tree operations: O(log n)
• Skewed tree operations: O(n)

This is why balanced trees are preferred in real-world systems.

Common Mistakes Beginners Make

• Confusing tree height with depth

• Forgetting base cases in recursive tree traversal

• Assuming all trees behave like BSTs

• Not handling null nodes properly

Understanding these early avoids many bugs later.

Where Trees Are Used in Interviews

Trees are one of the most frequently asked topics in coding interviews.

Typical interview problems include

• Tree traversal

• Height and depth calculation

• Lowest Common Ancestor

• Diameter of a tree

• Binary Search Tree validation

Mastering tree basics gives a strong foundation for these problems.

Conclusion

Trees are a powerful and essential data structure for organizing and processing hierarchical data efficiently. They form the backbone of many advanced algorithms and real-world systems.

Before jumping into complex tree problems, it is crucial to understand tree structure, terminology, and basic operations clearly. Once the fundamentals are strong, advanced topics like BSTs, Heaps, Tries, and Graphs become much easier to learn.

In the next topics, we will dive deeper into Binary Trees, Tree Traversals, and Binary Search Trees with hands-on examples and interview questions. - DSA WITH PIYUSH | DWP