The document provides an introduction to trees in data structures, emphasizing their hierarchical nature and key terms associated with them. It details binary trees, including their properties, types, and implementations in Python, as well as various tree traversal methods. The explanation includes both linked and array representations of binary trees and offers Python code snippets for traversal techniques.

1. Introduction to Trees in Data
Structures
• • Trees are hierarchical data structures
consisting of nodes.
• • Root node is the topmost node; it has no
parent.
• • Nodes have parent-child relationships.
• • Key terms: Root, Parent, Child, Sibling, Leaf,
Path, Depth, Height.
• • Trees are used in file systems, databases,
and hierarchical data organization.

2. Binary Tree and Its Properties
• • A Binary Tree is a tree where each node has
at most two children.
• • Properties:
• - Maximum nodes at level i = 2^i.
• - Maximum nodes in a tree of height h =
2^(h+1) - 1.
• - Minimum height for n nodes = log2(n+1) .
⌈ ⌉
• - Perfect Binary Tree: All levels are
completely filled.

3. Types of Binary Trees
• • Full Binary Tree: Every node has 0 or 2
children.
• • Complete Binary Tree: All levels except the
last are filled.
• • Perfect Binary Tree: All internal nodes have 2
children, and all leaves are at the same level.
• • Degenerate Tree: Each parent has only one
child, resembling a linked list.
• • Balanced Binary Tree: Height difference
between left and right subtree is minimal.

4. Binary Tree Implementation
(Python)
• Algorithm:
• 1. Define a Node class with data, left, and right
pointers.
• 2. Initialize the root node.
• 3. Add methods for insertion and traversal.
• Code:
• class Node:
• def __init__(self, data):

5. Binary Tree Representation
• • Linked Representation:
• - Nodes are linked using pointers.
• - Efficient for dynamic memory allocation.
• • Array Representation:
• - Nodes are stored in an array sequentially.
• - Parent-Child relationships determined using
indices:
• * Parent = (i-1)/2
⌊ ⌋

6. Binary Tree Traversals
• • In-order Traversal (Left, Root, Right):
• - Used for retrieving sorted elements from
BST.
• • Pre-order Traversal (Root, Left, Right):
• - Used for creating a copy of the tree.
• • Post-order Traversal (Left, Right, Root):
• - Used for deleting the tree.

7. Traversals with Code (Python)
• Code:
• def inorder(root):
• if root:
• inorder(root.left)
• print(root.data, end=' ')
• inorder(root.right)
• def preorder(root):
• if root: