K-ary Tree Practice Question 8

Duration: 2 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
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  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
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  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
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  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
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  19. Emerging Trends and AI: Emerging Tech Trends, Artificial Intelligence
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  24. Paper 1 - Full Mock Tests:
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  26. BCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video segment presents a practice problem on k-ary trees, specifically focusing on calculating the branching factor k given leaf and internal node counts. The instructor systematically guides students through identifying known variables, calculating total nodes, and applying a fundamental tree relationship formula to derive the solution. The problem statement is clearly displayed on screen, establishing that a full k-ary tree contains 67 leaf nodes and 33 internal nodes, with the objective being to find k. The instructional flow moves from variable identification to arithmetic calculation and finally algebraic manipulation using the edge-node relationship.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces a problem involving a full k-ary tree with 67 leaf nodes and 33 internal nodes, asking to find the value of k. He begins by defining variables for leaf nodes (L) and internal nodes (I), then calculates the total number of nodes (n) by summing L and I. On-screen text displays 'Q. A full k-ary tree contains 67 leaf nodes and 33 internal nodes. Find the value of k.' The instructor writes 'L = 67' and 'I = 33', then applies the formula 'n = L + I' resulting in '67 + 33'. Subsequently, the total nodes n is calculated as 100. The instructor then introduces the relationship formula 'kI = n - 1', substituting values to get 'k * 33 = 99'. This establishes the core algebraic equation needed to solve for k, demonstrating the standard method for determining branching factors in full trees using node counts.

  2. 2:00 – 2:02 02:00-02:02

    The final calculation step is shown where the instructor solves for k by dividing 99 by 33, resulting in 'k = 3 Ans'. The screen displays the completed solution with the final answer clearly marked. This concludes the problem-solving process, verifying that a full k-ary tree with 67 leaves and 33 internal nodes must have a branching factor of 3. The visual evidence confirms the mathematical derivation is complete and the answer is explicitly stated.

The video demonstrates a standard approach to solving k-ary tree problems by leveraging the relationship between internal nodes, total edges, and branching factor. The key formula kI = n - 1 connects the number of internal nodes (I) to total edges, which equals total nodes minus one. By calculating n = L + I first, students can substitute known values into the equation to isolate k. This method is universally applicable to full k-ary trees where every internal node has exactly k children. The problem illustrates how structural properties of trees allow algebraic solutions without needing to draw the entire tree structure.

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