Binary Trees: Introduction | DSA in C++ - Software Development PDF Download

Introduction

Binary trees are an essential data structure in computer science, widely used for organizing and manipulating hierarchical data. They consist of nodes connected through edges, forming a tree-like structure. In this article, we will explore the basics of binary trees, understand their properties, and learn how to implement them in C++.

Binary Tree Basics

• A binary tree is a collection of nodes, where each node contains a value and can have at most two child nodes: a left child and a right child.
• The topmost node in a binary tree is called the root node, and it serves as the entry point for accessing the entire tree.
• Nodes that do not have any child nodes are called leaf nodes.
• The height of a binary tree is the maximum number of edges between the root node and any leaf node.
• Binary trees can be categorized as full binary trees, complete binary trees, or balanced binary trees based on certain properties.

Binary Tree Implementation in C++:

Let's start by implementing a binary tree in C++. We will create a structure called 'Node' to represent each node in the tree.

struct Node {

    int value;

    Node* left;

    Node* right;

    Node(int val) {

        value = val;

        left = nullptr;

        right = nullptr;

    }

};

The 'Node' structure contains an integer value to store the data, and two pointers 'left' and 'right' to point to the left and right child nodes, respectively.

The constructor initializes the value and sets the child pointers to 'nullptr'.

Creating Binary Trees:

To create a binary tree, we need to allocate memory for each node and establish the appropriate connections.

// Create a binary tree with root node having value 1

Node* root = new Node(1);

// Create left and right child nodes

root->left = new Node(2);

root->right = new Node(3);

In the above code, we create a binary tree with the root node having a value of 1. We then create two child nodes with values 2 and 3, respectively, and connect them to the root node.

Traversing Binary Trees:

Traversing a binary tree allows us to visit each node in a specific order. There are three common traversal techniques: in-order, pre-order, and post-order.

In-order traversal: In this traversal, we first visit the left subtree, then the root node, and finally the right subtree.

void inorderTraversal(Node* node) {

    if (node == nullptr) return;

    inorderTraversal(node->left);

    cout << node->value << " ";

    inorderTraversal(node->right);

}

Pre-order traversal: In this traversal, we first visit the root node, then the left subtree, and finally the right subtree.

void preorderTraversal(Node* node) {

    if (node == nullptr) return;

    cout << node->value << " ";

    preorderTraversal(node->left);

    preorderTraversal(node->right);

}

Post-order traversal: In this traversal, we first visit the left subtree, then the right subtree, and finally the root node.

void postorderTraversal(Node* node) {

    if (node == nullptr) return;

    postorderTraversal(node->left);

    postorderTraversal(node->right);

    cout << node->value << " ";

}

You can call these traversal functions by passing the root node as an argument to print the values in the desired order.

Sample Problems:

Here are a few sample problems you can try to deepen your understanding of binary trees:

• Problem 1: Given a binary tree, determine if it is a valid binary search tree.
• Problem 2: Find the maximum depth of a binary tree.
• Problem 3: Given two binary trees, check if they are identical.
• Problem 4: Convert a binary tree into its mirror image.

Solution hints for these problems can be found in various online coding platforms and algorithm textbooks.

Conclusion

Binary trees are powerful data structures for organizing hierarchical data. In this article, we covered the basics of binary trees, their implementation in C++, tree traversal techniques, and provided sample problems to enhance your understanding. With this knowledge, you can begin exploring more advanced concepts related to binary trees and their applications in various algorithms and data structures.