⚔🛠 Binary Tree 🛠⚔

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🌳 What is a Binary Tree?

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

📌 Think of a binary tree like a family tree where each person (node) can have up to two children (left and right).

📂 Structure of a Node in Python

class Node: def __init__(self, data): self.data = data self.left = None # Left child self.right = None # Right child

🧠 Terminology in Binary Tree

Term	Explanation
Root	The topmost node in the tree
Leaf	A node with no children
Parent	A node that has children
Child	A node that has a parent
Subtree	A tree formed from a node and its descendants
Height	Length of the longest path from the node to a leaf
Depth	Length of the path from the root to a given node
Level	The number of edges from the root to the node

Representation of Binary Tree

Each node in a Binary Tree has three parts:-

• Data
• Pointer to the left child
• Pointer to the right child

🏷️ Types of Binary Trees

Type	Description
Full Binary Tree	Every node has 0 or 2 children
Perfect Binary Tree	All internal nodes have 2 children & all leaves are at the same level
Complete Binary Tree	All levels are completely filled except possibly the last, which is filled from left to right
Balanced Binary Tree	For every node, the difference in height of left and right subtree is at most 1
Degenerate / Skewed Tree	Each parent has only one child, either left or right (like a linked list)

⚙️ Basic Operations on Binary Tree

Operation	Description
Insertion	Add new nodes at the appropriate position  👈 Click Here
Traversal	Visit each node in a specific order 👈 Click Here
Search	Find whether a node exists in the tree 👈 Click Here
Deletion	Remove a node and rearrange the tree 👈 Click Here

🌱 Insertion

• New nodes are added in level-order (left to right).

• Use a queue to find the first empty spot.

🔄 Traversal

Visiting all nodes in a specific order:

• Inorder: Left → Root → Right

• Preorder: Root → Left → Right

• Postorder: Left → Right → Root

• Level Order: Level by Level (BFS using Queue)

🔍 Searching

• Binary Tree: Use DFS or BFS.

• Binary Search Tree (BST): Use sorted rule — left < root < right.

🗑️ Deletion

• Replace the target node with the deepest rightmost node, then delete the deepest one.

🧠 Summary Table

Operation	Key Point	Time Complexity
Insertion	Insert at first empty place (level-order)	O(n)
Traversal	Visit all nodes (DFS or BFS)	O(n)
Searching	Check each node (BT) or use BST property	O(n) or O(log n)
Deletion	Replace with deepest node, delete it	O(n)

✅ Advantages of Binary Tree

1. Hierarchical Structure: Represents data with a natural hierarchy (like file systems).

2. Efficient Searching: Especially in Binary Search Tree (BST) – average time is O(log n).

3. Faster Insertion/Deletion: Compared to arrays or linked lists (especially in BSTs).

4. Memory Efficient: Doesn’t require contiguous memory like arrays.

5. Scalable: Easily expanded or reduced without affecting the structure.

❌ Disadvantages of Binary Tree

1. Unbalanced Trees Perform Poorly: If not balanced, worst-case time complexity becomes O(n).

2. Overhead of Pointers: Each node stores two additional pointers (left & right).

3. Difficult to Implement: More complex logic than linear data structures.

4. Complex Deletion: Deleting nodes while maintaining structure is tricky.

🧾 Key Notes for Revision

• Binary tree = At most 2 children per node.

• Types: Full, Perfect, Complete, Balanced, Skewed.

• Traversals: Inorder, Preorder, Postorder, Level Order.

• Used in: Expression trees, Huffman coding, hierarchical data, file systems, BSTs, Heaps.

• Balanced trees are optimal in performance.

• Represented using linked structure, not arrays.

📌 Real-Life Analogy

Think of a company hierarchy:

• CEO is the root

• Managers are internal nodes

• Interns or employees without subordinates are leaves