Tree – Understanding Hierarchical Data Structures

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Introduction

A tree is a widely used abstract data structure that represents hierarchical relationships. Unlike linear structures like arrays, stacks, or linked lists, trees allow us to model complex, nested data in a natural and efficient way.

Consider the following real-world hierarchies:

• A company with departments, teams, and employees.

• A file system with folders and subfolders.

• A family tree with generations and descendants.

All of these can be represented as trees, where each entity relates to its "parent" and "children".

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Basic Terminology

Before diving deep, let’s get familiar with core terms:

• Node: A single element in a tree.

• Root: The topmost node (starting point).

• Parent: A node that has children.

• Child: A node that descends from another node.

• Leaf: A node with no children.

• Subtree: Any node along with its descendants.

• Level: Distance from the root (root is at level 0).

• Height: The length of the longest path from the root to a leaf.

Example Tree:

         A (Root)
        /   \
      B       C
     / \     / \
    D   E   F   G

• A is the root.

• B and C are children of A.

• D, E, F, G are leaf nodes.

• Height = 2 (longest path A → B → D or A → C → F).

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Types of Trees

Trees come in many forms depending on the number of children allowed or specific properties.

1. General Tree
   Each node can have any number of children.

2. Binary Tree
   Each node can have at most two children (commonly referred to as left and right).

3. Binary Search Tree (BST)
   A binary tree with an order:

   • Left child < Parent < Right child

   • Allows efficient search, insertion, and deletion.

4. Balanced Trees
   Special BSTs where height is minimized:

   • AVL Tree – balances using rotations.

   • Red-Black Tree – self-balancing using color properties.

5. N-ary Tree
   A tree where nodes can have up to N children. Useful in modeling file systems, DOM trees, etc.

6. Trie (Prefix Tree)
   A specialized tree used for string storage and lookup, especially in autocomplete features.

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Properties of Trees

Let’s cover some key mathematical and structural properties:

• A tree with n nodes has n - 1 edges.

• In a binary tree of height h, the maximum number of nodes is 2^(h+1) - 1.

• A full binary tree has nodes with either 0 or 2 children.

• A complete binary tree is fully filled except possibly for the last level, filled left to right.

• The height of a balanced BST is O(log n), ensuring efficient operations.

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🌳 Tree Traversals (with Java Code)

1. Inorder Traversal (Left → Root → Right)

void inorder(Node node) {
    if (node == null) return;
    inorder(node.left);
    System.out.print(node.data + " ");
    inorder(node.right);
}

2. Preorder Traversal (Root → Left → Right)

void preorder(Node node) {
    if (node == null) return;
    System.out.print(node.data + " ");
    preorder(node.left);
    preorder(node.right);
}

3. Postorder Traversal (Left → Right → Root)

void postorder(Node node) {
    if (node == null) return;
    postorder(node.left);
    postorder(node.right);
    System.out.print(node.data + " ");
}

4. Level Order Traversal (Breadth-First Search)

void levelOrder(Node root) {
    if (root == null) return;
    Queue<Node> queue = new LinkedList<>();
    queue.add(root);
    while (!queue.isEmpty()) {
        Node current = queue.poll();
        System.out.print(current.data + " ");
        if (current.left != null) queue.add(current.left);
        if (current.right != null) queue.add(current.right);
    }
}

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Common Operations & Time Complexities

In practice, always use balanced trees for performance-critical applications.

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Use Cases of Trees

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Visual Representation

Here’s an illustration of different tree types:

• Binary Tree

         5
        / \
       3   8
  

• BST (Sorted)

         10
        /  \
       5    15
      / \     \
     2   7     20
  

• Trie (for “top”, “toy”, “to”)

      t
      |
      o
     / \
    p   y
  

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LeetCode Practice Problems

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💡 Tips for Interview Preparation

• Start with traversal problems like LeetCode#94 (Inorder Traversal) – These are beginner-friendly and help you build a strong foundation in recursion and tree structure understanding.

• Draw the tree on paper for problems like LeetCode#235 (Lowest Common Ancestor) – Visualizing parent-child relationships helps in figuring out the right traversal and logic path.

• Practice both recursive and iterative approaches – Some companies (e.g., Google, Meta) often ask for iterative solutions too, especially for problems like LeetCode#104 (Maximum Depth).

• Be ready to construct trees from input – Problems like Build Tree from Inorder and Preorder Traversals are common in technical rounds. Practice these to strengthen tree construction logic.

• Understand how to handle edge cases – For example, test your solution on a single-node tree or a completely skewed tree (like a linked list). These often help spot recursion depth and null pointer bugs.

• Don’t ignore serialization problems like LeetCode#297 – These appear in system design-focused interviews or when assessing understanding of tree-to-string conversions.

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🔚 Wrapping Up

Trees are one of the most fundamental data structures in computer science, and mastering them opens the door to solving a wide variety of complex real-world and interview problems.

In this post, we covered everything from the basic building blocks of trees, to various types (Binary Tree, BST, Trie, etc.), to common traversals with Java code, and even tackled real LeetCode problems that frequently show up in interviews.

Understanding trees is not just about passing interviews, but also about building better mental models for solving hierarchical problems—be it representing a file system, constructing a decision engine, or implementing autocomplete in search engines.

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🙌 Enjoying the Series?

This blog is part of my DSA series — “Level Up Your Programming with Nitin”, where I break down core data structures and algorithms with clear explanations, real-world analogies, Java code snippets, and curated LeetCode problems.

You can explore the entire series anytime here:
🔗 DS Interview Prep Series

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Thanks for reading, and happy coding! 💻🌳

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