Understanding Binary Tree and Binary Search Tree with Examples

When learning data structures and algorithms, one of the most important concepts is the tree. Among different types of trees, the Binary Tree and the Binary Search Tree (BST) are widely used in programming, databases, and problem-solving. At first, they may sound similar, but they serve different purposes and have unique properties. In this article, we will explore what Binary Trees and Binary Search Trees are, their differences, and some practical examples.

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 What is a Binary Tree?

A Binary Tree is a hierarchical data structure where each node can have at most two children, often referred to as the left child and the right child.

Key Characteristics of a Binary Tree:

1. Each node contains data and references to its children.

2. A node can have 0, 1, or 2 children.

3. The topmost node is called the root.

4. A leaf node is a node with no children.

Example of a Binary Tree:

        10
       /  \
      20   30
     / \   /
    40 50 60

• Root node → 10

• Children of 10 → 20 (left), 30 (right)

• Leaf nodes → 40, 50, 60

Types of Binary Trees:

• Full Binary Tree → Every node has 0 or 2 children.

• Complete Binary Tree → All levels are filled except possibly the last.

• Perfect Binary Tree → All internal nodes have 2 children, and all leaves are at the same level.

• Skewed Binary Tree → All nodes have only one child (either left or right).

Binary Trees are mainly used for hierarchical representation and form the basis of more advanced trees.

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 What is a Binary Search Tree (BST)?

A Binary Search Tree is a special type of Binary Tree that follows an ordering property:

• The left child’s value is always less than the parent.

• The right child’s value is always greater than the parent.

• Both left and right subtrees are also BSTs.

Example of a Binary Search Tree:

        50
       /  \
      30   70
     / \   / \
    20 40 60 80

• Root = 50

• Left subtree (values < 50) = {30, 20, 40}

• Right subtree (values > 50) = {70, 60, 80}

Key Operations in BST:

1. Search – Quickly find whether a value exists.

2. Insert – Add a new node while maintaining order.

3. Delete – Remove a node and restructure the tree.

4. Traversal – Inorder, Preorder, Postorder traversal.

BSTs are widely used in search engines, databases, and indexing systems because of their efficiency.

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 Differences Between Binary Tree and Binary Search Tree

Feature	Binary Tree	Binary Search Tree (BST)
Definition	Each node has at most 2 children.	A binary tree with ordered structure.
Ordering	No specific ordering of nodes.	Left < Root < Right.
Searching	Slower (O(n) in worst case).	Faster (O(log n) average).
Usage	Used for hierarchical representation.	Used for efficient searching & sorting.
Example	10 as root, children 20 & 30 (no order).	50 as root, left smaller, right greater.

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 Example in Programming

Binary Tree Example (Python):

class Node:
    def __init__(self, key):
        self.key = key
        self.left = None
        self.right = None

# Create a simple binary tree
root = Node(10)
root.left = Node(20)
root.right = Node(30)

Binary Search Tree Example (Python):

class BSTNode:
    def __init__(self, key):
        self.key = key
        self.left = None
        self.right = None

    def insert(self, value):
        if value < self.key:
            if self.left is None:
                self.left = BSTNode(value)
            else:
                self.left.insert(value)
        elif value > self.key:
            if self.right is None:
                self.right = BSTNode(value)
            else:
                self.right.insert(value)

# Create BST and insert values
root = BSTNode(50)
root.insert(30)
root.insert(70)
root.insert(20)
root.insert(40)

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 When to Use Which?

• Use a Binary Tree when:

  • You just need to represent hierarchical data (like a file system).

  • You don’t care about order or searching speed.

• Use a Binary Search Tree when:

  • You need fast search, insertion, and deletion.

  • You want to maintain data in sorted order.

  • You are working on problems related to range queries, indexing, or dictionaries.

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 Conclusion

The Binary Tree is the foundation of many data structures, while the Binary Search Tree is a specialized form of it, designed for faster searching and sorting.

• Binary Tree → General-purpose hierarchical structure.

• Binary Search Tree → Optimized for searching, sorting, and ordered data handling.

Understanding both is essential for programmers, as they appear frequently in technical interviews, real-world applications, and algorithm design. With practice, you’ll be able to decide when to use a simple Binary Tree and when a BST is more efficient.