K-ary Tree Practice Question 3

Duration: 2 min

This video lesson is available to enrolled students.

Return to /learn/TPSC-ASSISTANT-TECHNICAL-OFFICER/data-structures-and-programming/tree/advanced-k-ary-trees/asset-k-ary-tree-practice-question-3 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Paper 2 | Computer Organization And Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Control Unit Design, Instr Formats & Modes, Programming the Basic Computer
  4. Paper 2 | Analog And Digital Communication: Introduction to Communication Systems & Random Signals, Analog Communication Systems, Information Theory & Digital Communication Fundamentals, Digital Modulation & Detection Techniques, Error Control, Synchronization & Multiple Access Techniques
  5. Paper 2 | Programming in C: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. Paper 2 | Data Structures And Programming: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  7. Paper 2 | Algorithms: Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  8. Paper 2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  9. Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS
  10. Paper 2 | Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  11. Paper 2 | Information Systems and Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Paper 2 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware Basics
  13. Paper 2 | Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, CSS, XML, HTML5
  14. Paper 2 | Cyber Security And Emerging Technologies: Emerging Tech Trends
  15. Paper 2 | Cloud Technology: Cloud Computing
  16. Paper 2 | Probability and statistics: Probability, Statistics
  17. Paper-1 English: Vocabulary, Preposition, Articles, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage), Sentence Construction
  18. Paper 1 General Mental Ability & Logical reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Arithmetic, Speed Mathematics and Basic Mathematics, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Venn Diagram, Analogy
  19. Paper-1 General Knowledge & Current Affairs: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge
  20. Full Length Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video segment presents a practice problem involving the calculation of internal nodes within a full k-ary tree. The instructor begins by defining the problem parameters: a total node count of n=85 and an arity of k=4. The core teaching objective is to apply the mathematical relationship between total nodes, internal nodes, and edges in a k-ary tree structure. By establishing that the number of total edges equals n minus 1, the instructor derives a formula where k times the internal nodes (I) equals the total edges. This leads to the calculation 4I = 84, resulting in 21 internal nodes. The lesson concludes by determining the number of leaf nodes through subtraction, reinforcing the structural properties of full k-ary trees.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces a problem statement visible on screen: 'Q. A full 4-ary tree contains 85 nodes. Find the number of internal nodes.' He explicitly writes down the given variables n=85 and k=4 to classify the structure as a 4-ary Tree. The instructor then calculates the total edges using the property that edges equal n minus 1, resulting in a value of 84. He introduces the fundamental formula for k-ary trees, writing '4I = n - 1' on the board to relate internal nodes (I) to the total edge count. This section establishes the theoretical framework required for solving the specific numerical problem presented.

  2. 2:00 – 2:14 02:00-02:14

    In the final segment, the instructor executes the algebraic solution derived in the previous window. He substitutes the calculated edge count into the formula, writing '4I = 84' and solving for I to find that there are exactly 21 internal nodes. The instructor then verifies the result by calculating the number of leaf nodes (L) using the relationship L = n - I, which yields 64 leaves. The visible text 'I = (84/4)' confirms the arithmetic step, and the final answer is presented as a complete solution to the practice question regarding full 4-ary tree properties.

The video demonstrates a systematic approach to solving k-ary tree problems by first identifying given parameters (n and k) and then applying structural properties. The key concept is the relationship between internal nodes and edges, expressed as kI = n - 1. This formula allows for the direct calculation of internal nodes without needing to draw the entire tree structure. The method relies on the fact that in a full k-ary tree, every internal node contributes exactly k edges to the total count. The instructor's progression from problem statement to variable identification, formula application, and final arithmetic verification provides a clear pedagogical model for students tackling similar graph theory questions.

Loading lesson…