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Binary Trees I

Learn the fundamentals of binary trees, their properties, and basic operations in Java. Master the essential concepts that form the foundation of tree data structures.

Learning Objectives

Core Concepts

  • Understanding binary tree structure
  • Tree traversal methods
  • Binary search tree properties
  • Basic tree operations

Skills Development

  • Implementing tree nodes in Java
  • Tree manipulation algorithms
  • Recursive problem-solving
  • Tree visualization techniques

Prerequisites

Required Knowledge

  • Basic Java programming
  • Understanding of classes and objects
  • Familiarity with recursion
  • Basic data structures concepts

Recommended Preparation

  • Review linked list concepts
  • Practice recursive functions
  • Understand time complexity
  • Study Java generics and inheritance

Video Lectures

1. Binary Tree Basics

Key Topics Covered:

  • What is a binary tree?
  • Tree terminology (root, nodes, leaves)
  • Properties of binary trees
  • Common applications in Java

2. BST Search

Key Topics Covered:

  • Binary Search Tree properties
  • Search algorithm implementation in Java
  • Time complexity analysis
  • Recursive search approach

3. BST Insert

Key Topics Covered:

  • Insertion algorithm for BST
  • Maintaining BST properties
  • Handling duplicate values
  • Java implementation walkthrough

Code Implementation

Tree Node Implementation

public class TreeNode> {
    private T value;
    private TreeNode left;
    private TreeNode right;
    
    public TreeNode(T value) {
        this.value = value;
        this.left = null;
        this.right = null;
    }
    
    // Getters and setters
    public T getValue() { return value; }
    public TreeNode getLeft() { return left; }
    public TreeNode getRight() { return right; }
    public void setLeft(TreeNode left) { this.left = left; }
    public void setRight(TreeNode right) { this.right = right; }
}

Binary Search Tree Implementation

public class BinarySearchTree> {
    private TreeNode root;
    
    public BinarySearchTree() {
        this.root = null;
    }
    
    public void insert(T value) {
        if (root == null) {
            root = new TreeNode<>(value);
            return;
        }
        
        insertHelper(root, value);
    }
    
    private TreeNode insertHelper(TreeNode current, T value) {
        if (current == null) {
            return new TreeNode<>(value);
        }
        
        int compareResult = value.compareTo(current.getValue());
        
        if (compareResult < 0) {
            current.setLeft(insertHelper(current.getLeft(), value));
        } else if (compareResult > 0) {
            current.setRight(insertHelper(current.getRight(), value));
        }
        
        return current;
    }
    
    public boolean search(T value) {
        return searchHelper(root, value);
    }
    
    private boolean searchHelper(TreeNode current, T value) {
        if (current == null) {
            return false;
        }
        
        int compareResult = value.compareTo(current.getValue());
        
        if (compareResult == 0) {
            return true;
        } else if (compareResult < 0) {
            return searchHelper(current.getLeft(), value);
        } else {
            return searchHelper(current.getRight(), value);
        }
    }
}

Guided Practice

For additional hands-on practice and exercises on binary trees, check out our comprehensive guided project:

Practice Exercises

BST Operations

Implement these basic BST operations:

  • Find the minimum value in a BST
  • Find the maximum value in a BST
  • Count the number of nodes in a BST
  • Calculate the height of a BST

Tree Traversals

Implement all three tree traversal methods:

  • In-order traversal
  • Pre-order traversal
  • Post-order traversal

Advanced Challenges

Try these more challenging exercises:

  • Check if a binary tree is a valid BST
  • Find the lowest common ancestor of two nodes
  • Implement tree deletion (with all cases)
  • Convert a sorted array to a balanced BST

Online Resources: