Internal Nodes vs External Nodes in Binary Tree
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Lecture 265:- Internal Nodes vs External Nodes in Binary Tree
In a binary tree, nodes can be categorized into two main types: internal nodes and external nodes (also known as leaf nodes). These categories are based on the number of child nodes each node has.
- Internal Nodes:
- An internal node is a node that has at least one child node (i.e., it has a left child and/or a right child).
- In other words, an internal node is any node that is not a leaf node (external node).
- Internal nodes are also called non-leaf nodes or branch nodes.
- Internal nodes are the nodes that form the structure of the binary tree, and they are used for branching and creating the hierarchy.
- External Nodes (Leaf Nodes):
- An external node (leaf node) is a node that has no child nodes (i.e., it has neither a left child nor a right child).
- Leaf nodes are the terminal nodes of the binary tree and do not have any descendants.
- Leaf nodes are located at the edges of the binary tree and are the endpoints of the tree's branches.
For example, consider the following binary tree:
markdownCopy code
10 / \ 5 15 / \ / \ 3 8 12 20In this binary tree, the internal nodes are: 10, 5, and 15. The external nodes (leaf nodes) are: 3, 8, 12, and 20.
Note that in a binary tree, the number of leaf nodes is always one more than the number of internal nodes, as each internal node branches into two child nodes (if present).
The distinction between internal nodes and external nodes is essential in various tree operations and algorithms. Internal nodes play a crucial role in traversing the tree and performing actions on the tree's structure, while external nodes (leaf nodes) typically hold the actual data in tree-based data structures and are the endpoints for searching and accessing data in the tree.
- 1. Arrays Basics
- 2. Practice Arrays Basics
- 3. Practice Structures
- 4. Practice Pointers
- 5. Reference in C++
- 6. Practice Reference
- 7. Pointer to Structure
- 8. Practice Pointer to Structure
- 9. Functions
- 10. Practice Functions
- 11. Parameter Passing Methods
- 12. Practice Parameter Passing Methods
- 13. Array as Parameter
- 14. Practice Array as Parameter
- 15. Practice Structure as Parameter
- 16. Converting a C program to a C++ class
- 17. Practice Monolithic Program
- 18. Practice Modular Program
- 19. Practice Structure and Functions
- 20. Practice Object-Oriented Program
- 21. Practice Cpp Class
- 22. Template classes
- 23. Practice Template Class
- 1. How Recursion Works ( Tracing )
- 2. Generalising Recursion
- 3. How Recursion uses Stack
- 4. Recurrence Relation - Time Complexity of Recursion
- 5. Lets Code Recursion
- 6. Static and Global Variables in Recursion
- 7. Let's Code Static and Global in Recursion
- 8. Tail Recursion
- 9. Head Recursion
- 10. Tree Recursion
- 11. Indirect Recursion
- 12. Let's Code Indirect Recursion
- 13. Nested Recursion
- 14. Let's Code Nested Recursion
- 15. Sum of Natural Number using Recursion
- 16. Let's Code Sum of N using Recursion
- 17. Factorial using Recursion
- 18. Let's Code Factorial using Recursion
- 19. Let's Code Power Recursion
- 20. Taylor Series using Recursion
- 21. Let's Code Taylor Series using Recursion
- 22. Taylor Series using Horner's Rule
- 23. Let's Code Taylor Series Horner's Rule-Recursion
- 24. Let's Code Fibonacci
- 25. nCr using Recursion
- 26. Let's Code nCr using Recursion
- 27. Tower of Hanoi Problem
- 28. Let's Code Tower of Hanoi
- 29. Quiz 1 Solutions
- 1. Introduction to Array
- 2. Declarations of Array
- 3. Demo - Array Declaration
- 4. Static vs Dynamic Arrays
- 5. Demo - Static vs Dynamic Array
- 6. How to Increase Array Size
- 7. Demo - Increasing Array Size
- 8. 2D Arrays
- 9. Array Representation by Compiler
- 10. Row Major Formula for 2D Arrays
- 11. Column Major Formula for 2D Arrays
- 12. Formulas for nD Arrays
- 13. Formulas for 3D Arrays
- 14. Solutions for Quiz 2
- 1. Introduction to Strings
- 2. Finding Length of a String
- 3. Changing Case of a String
- 4. Counting Words and Vowels in a String
- 5. Validating a String
- 6. Reversing a String
- 7. Comparing Strings and Checking Palindrome
- 8. Finding Duplicates in a String
- 9. Finding Duplicates in a String using Bitwise Operations
- 10. Checking if 2 Strings are Anagram distinct letters
- 1. Section Introduction
- 2. Let's Code Diagonal Matrix
- 3. C++ class for Diagonal Matrix
- 4. Let's Code C++ class for Diagonal matrix
- 5. Lower Triangular Matrix Row-Major Mapping
- 6. Lower Triangular Matrix Column-Major Mapping
- 7. Let's Code Lower Triangular Matrix in C
- 8. Upper Triangular Matrix Row-Major Mapping
- 9. Symmetric Matrix
- 10. Tri-Diagonal and Tri-Band Matrix
- 11. Toeplitz Matrix
- 12. Menu Driven Program for Matrices
- 13. Menu Driven Program for Matrices using Functions
- 1. Why we need Dynamic Data Structure Linked List
- 2. About Linked List
- 3. More About Linked List
- 4. Display Linked List
- 5. Let's Code Display for Linked List
- 6. Recursive Display of Linked List
- 7. Let's Code Recursive Display for Linked List
- 8. Sum of All Elements in a Linked List
- 9. Let's Code Count and Sum
- 10. Maximum Element in a Linked List
- 11. Searching in a Linked List
- 12. Improve Searching in Linked List
- 13. Let's Code Searching in Linked List
- 14. Inserting in a Linked List
- 15. Let's Code Insert for Linked List
- 16. Creating a Linked List using Insert
- 17. Creating a Linked List by Inserting at List
- 18. Inserting in a Sorted Linked List
- 19. Let's Code Insert in Sorted Linked List
- 20. Deleting from Linked List
- 21. Let's Code Delete on Linked List
- 22. Check if a Linked List is Sorted
- 23. Let's Code to check if Linked List is Sorted
- 24. Remove Duplicates from Sorted Link List
- 25. Let's Code to Remove Duplicates from Sorted Linked List
- 26. Let's Code Reversing a Linked List
- 27. Concatenating 2 Linked Lists
- 28. Merging 2 Linked Lists
- 29. Let's Code to Concatenate and Merge Linked Lists
- 30. Check for LOOP in Linked List
- 31. Let's Code to Check LOOP
- 32. Circular Linked List
- 33. Let’s Code Circular Linked List
- 34. Inserting in a Circular Linked List
- 35. Let's Code Insert for a Circular Linked List
- 36. Insert In A Doubly Linked List
- 37. Let's Code Insert for Doubly Linked List
- 38. Deleting from Doubly Linked List
- 39. Let's Code Delete for Doubly Linked List
- 40. Reverse a Doubly Linked List
- 41. Let's Code Reverse for Doubly Linked List
- 42. Circular Doubly Linked List
- 43. Comparison of Linked List
- 44. Comparison of Array with Linked List
- 45. Student Challenge Finding Middle Element of a Linked List
- 46. Student Challenge Finding Intersecting point of two Linked List
- 1. Stack using Array
- 2. Let's Code Stack using Array
- 3. Stack using Linked List
- 4. Stack Operations using Linked List
- 5. Let's Code Stack using Linked List
- 6. Let's Code C++ class for Stack using Linked List
- 7. Parenthesis Matching
- 8. Program for Parenthesis Matching
- 9. Let's Code Parenthesis Matching
- 10. Infix to Postfix Conversion
- 11. Associativity and Unary Operators
- 12. Infix to Postfix using Stack Method
- 13. Let's Code Infix to Postfix Conversion
- 14. Student Challenge Infix to Postfix with Associativity and Parenthesis
- 15. Evaluation of Postfix Expression
- 16. Program for Evaluation of Postfix
- 1. Queue Adt
- 2. Queue using Two Pointers
- 3. Implementing Queue using Array
- 4. Let's Code Queue using Array
- 5. Let's Code Queue in C++
- 6. Circular Queue
- 7. Let's Code Circular Queue
- 8. Queue using Linked List
- 9. Let's Code Queue using Linked List
- 10. Double Ended Queue DEQUEUE
- 11. Queue using 2 Stacks
- 1. Trees Terminology
- 2. Number of Binary Trees using N Nodes
- 3. Height vs Nodes in Binary Tree
- 4. Internal Nodes vs External Nodes in Binary Tree
- 5. Strict Binary Tree
- 6. Height vs Node of Strict Binary Tree
- 7. Internal vs External Nodes of Strict Binary Tree
- 8. n-ary Trees
- 9. Analysis of n-Ary Trees
- 10. Representation of Binary Tree
- 11. Linked Representation of Binary Tree
- 12. Full vs Complete Binary Tree
- 13. Strict vs Complete Binary Tree
- 14. Binary Tree Traversals
- 15. Binary Tree Traversal Easy Method 2
- 16. Binary Tree Traversal Easy Method 3
- 17. Creating Binary Tree
- 18. Program to Create Binary Tree
- 19. Let's Code Creating Binary Tree
- 20. Let's Code Creating Binary Tree in C++
- 21. Preorder Tree Traversal
- 22. Iterative Preorder
- 23. Iterative Inorder
- 24. Let's Code Iterative Traversals
- 25. Level Order Traversal
- 26. Let's Code Level Order Traversal
- 27. Can we Generate Tree from Traversals
- 28. Generating Tree from Traversals
- 29. Height and Count of Binary Tree
- 30. Let's Code Height and Count
- 31. Student Challenge Count Leaf Nodes Of Binary Tree
- 1. Criteria used for Analysing Sorts
- 2. Bubble Sort
- 3. Let's Code Bubble Sort
- 4. Insertion Sort
- 5. Program for Insertion Sort
- 6. Analysis of Insertion Sort
- 7. Let's Code Insertion Sort
- 8. Comparing Bubble and Insertion Sort
- 9. Selection Sort
- 10. Program for Selection Sort
- 11. Analysis of Selection Sort
- 12. Let's Code Selection Sort
- 13. Idea behind Quick Sort
- 14. Quick Sort
- 15. Analysis of Quick Sort
- 16. Analysis of Quick Sort Continued
- 17. Let's Code Quick Sort
- 18. Merging
- 19. Iterative Merge Sort
- 20. Let's Code Iterative Merge Sort
- 21. Recursive Merge Sort
- 22. Let's Code Recursive Merge Sort
- 23. Count Sort
- 24. Let's Code Count Sort
- 25. Radix Sort
- 26. Bin Bucket Sort
- 27. Shell Sort
- 1. Introduction to Graphs
- 2. Representation of Undirected Graph
- 3. Representation of Directed Graphs
- 4. Breadth First Search
- 5. Program for BFS
- 6. Depth First Search
- 7. Program for DFS
- 8. Let's Code BFS & DFS
- 9. Prim's Minimum Cost Spanning Tree
- 10. Prim's Program
- 11. Let's Code Prim's using
- 12. Kruskal's Minimum Cost Spanning Tree
- 13. Disjoint Subsets
- 14. Kruskal's Program
- 15. Let's Code Kruskla's Program
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