Topic: Data Structures – Trees – Part 1 of 4: Introduction and Binary Trees

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### 1. What is a Tree in Data Structures?

A tree is a non-linear hierarchical data structure consisting of nodes connected by edges. It's widely used in real-world applications like:

• File systems
• Databases (e.g., B-Trees)
• Compilers (parse trees)
• Artificial intelligence (decision trees)

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### 2. Terminologies in Trees

• Node: Basic unit of a tree
• Root: Topmost node (only one)
• Parent/Child: A node that connects to another below/above
• Leaf: A node with no children
• Edge: Connection between parent and child
• Subtree: Any child node and its descendants
• Depth: Distance from the root to a node
• Height: Longest path from a node to a leaf
• Degree: Number of children a node has

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### 3. Binary Tree Basics

A Binary Tree is a tree in which each node has at most two children, referred to as:

• Left child
• Right child

#### Real-life example:

Imagine a family tree where each person can have two children.

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### 4. Types of Binary Trees

• Full Binary Tree – every node has 0 or 2 children
• Perfect Binary Tree – all internal nodes have 2 children, and all leaves are at the same level
• Complete Binary Tree – all levels are filled except possibly the last, which is filled from left to right
• Skewed Tree – all nodes only have one child (left or right)
• Balanced Binary Tree – the height difference of left and right subtrees is minimal

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### 5. Binary Tree Representation in Python

Using Class & Object:

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

# Example
root = Node(1)
root.left = Node(2)
root.right = Node(3)

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### 6. Tree Traversals

Tree traversal means visiting all the nodes of a tree in a specific order.

• Inorder (LNR)
• Preorder (NLR)
• Postorder (LRN)
• Level Order (BFS using queue)

#### Example – Inorder Traversal (Left → Root → Right):

def inorder(root):
    if root:
        inorder(root.left)
        print(root.data, end=" ")
        inorder(root.right)

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### 7. Build a Simple Binary Tree and Traverse It

# Tree Structure:
#      1
#     / \
#    2   3
#   / \
#  4   5

root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)

print("Inorder Traversal:")
inorder(root)  # Output: 4 2 5 1 3

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### 8. Applications of Binary Trees

• Expression evaluation
• Search algorithms (Binary Search Trees)
• Priority queues (Heaps)
• Huffman encoding trees (data compression)
• Syntax trees in compilers

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### 9. Key Characteristics

• Recursive nature makes tree problems suitable for recursion
• Not sequential – can't be represented with only arrays or lists
• Memory-efficient using pointers in linked structure

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### 10. Summary

• Trees are hierarchical and non-linear
• Binary trees limit nodes to max 2 children
• Various types of binary trees serve different use cases
• Tree traversal is fundamental for solving tree problems

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### Exercise

Create a class-based binary tree and implement:
• Inorder, Preorder, and Postorder traversals
• Function to count total nodes and leaf nodes

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#DSA #BinaryTree #DataStructures #Python #TreeTraversal

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