K-ary Tree Practice Question 6

Duration: 3 min

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Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Mensuration and Geometry, Age Problems, Arithmetic, Statistics, Probability, Profit and Loss, Simple Interest and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, Powers and Exponents (Surds and Indices), Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy
  3. Paper-1 & 2 | Data Interpretation: Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Analogy, Ranking, Order and Sequence, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Data Arrangement, Logical Sequence Of Words, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: Selection Decision Table (Decision Making)
  7. Paper-1 | General Science: Physics, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: State Wise GK, GK- Current Affairs
  9. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits
  10. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Calculus, Relational Algebra, SQL, NoSQL
  11. Paper-2 | Data Structures & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Algorithm Analysis, Sorting Algorithms, Intro to Compilers, Hashing
  12. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, Data Link Layer - Ethernet, DLL: Error Control, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Application Layer, Hardware basics, Network Security, Ethical Hacking
  13. Paper-2 | Operating Systems: Introduction to OS, Process Management, Memory Management, File Management, Deadlock
  14. Paper-2 | Computer Organization and Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer, Number System, Number Representation
  15. Paper 2 | System Analysis and Design: Fundamentals of Systems and Information Systems, Fundamentals of Software Engineering, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance, Software Testing
  16. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Paper 2 | OOPS , C++ , JAVA: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  18. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  19. Emerging Trends and AI: Emerging Tech Trends, Artificial Intelligence
  20. Paper-2 | Data Processing (Ms-Office): MS Office Applications
  21. Paper-2 | Internet and Web Technologies: HTML Basics, CSS, XML, JavaScript-Basics, Internet Fundamentals, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, Terms & Abbreviations, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर नेटवर्क / Computer Networks
  22. Paper 2 | Pedagogy: Child Development, Theories, Concept of Pedagogy, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Psychology, Curriculum Framework & Reforms, National Education Policy (NEP) 2020
  23. Live Classes: RSSB Live Sessions
  24. Paper 1 - Full Mock Tests:
  25. Paper 2 - Full Mock Tests:
  26. BCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture segment addresses a practice problem involving the calculation of leaf nodes in a full k-ary tree. The instructor begins by defining the problem parameters: a full 5-ary tree containing exactly 26 internal nodes. The core of the lesson focuses on deriving and applying specific formulas that relate the number of internal nodes, leaf nodes, and total edges within a k-ary tree structure. The instructor systematically establishes the relationship between total nodes (n) and internal nodes (I) using the formula n = kI + 1, where k represents the arity of the tree. By substituting the given values (k=5 and I=26), the total number of nodes is calculated as 131. The final step involves isolating the leaf nodes (L) by subtracting the internal nodes from the total node count, yielding a final answer of 105 leaf nodes.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces a problem involving a full 5-ary tree with 26 internal nodes and asks to determine the number of leaf nodes. He begins by listing the given values for internal nodes (I) and leaf nodes (L), then writes down a general formula relating total edges to the number of nodes (n-1). The instructor establishes the relationship between total edges and internal nodes, deriving the formula n = kI + 1 to calculate the total number of nodes. The process involves substituting the given values (k=5, I=26) into the derived equation. On-screen text displays 'Q. A full 5-ary tree contains 26 internal nodes' and the instructor writes 'Total edges = n - 1' followed by 'kI = n - 1'. The derivation leads to the equation 'n = kI + 1' with substitution shown as 'n = 5 * 26 + 1'. This section covers the initial setup and formula derivation.

  2. 2:00 – 2:56 02:00-02:56

    The instructor completes the calculation for total nodes using n = kI + 1, resulting in 131 total nodes. He then uses the relation n = L + I to solve for leaf nodes by subtracting internal nodes from the total. The final calculation shows L = 105. On-screen text confirms 'n = L + I' and the final result 'L = 105'. The instructor demonstrates how to isolate L by rearranging the equation to L = n - I, substituting 131 for n and 26 for I. This section covers the final arithmetic steps and the solution verification.

The lecture effectively demonstrates a standard algorithmic approach for solving k-ary tree problems. The key takeaway is the formula n = kI + 1, which allows students to find total nodes directly from internal nodes without counting edges individually. This formula is derived from the property that every internal node contributes k edges, and total edges equal n-1. The method is robust for any full k-ary tree where internal nodes are known. Students should memorize the relationship n = L + I to easily transition between total, internal, and leaf node counts. The example of a 5-ary tree with 26 internal nodes serves as a concrete application, showing that 131 total nodes minus 26 internal nodes equals 105 leaf nodes. This reinforces the concept that in a full k-ary tree, leaf nodes are significantly more numerous than internal nodes when k > 1.

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