K-ary Tree Practice Question 8

Duration: 2 min

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Module outline

  1. Quantitative Ability: Percentage, Profit and Loss, Ratio and Proportion (Ratios), Average, Time and Work, Speed Time and Distance, Simple Interest and Compound Interest, Age Problems, Number System, Divisibility Rules, HCF LCM, Algebra, Permutation and Combination, Probability, Data Interpretation, Logarithm, Sequence and Series (Series), Powers and Exponents (Surds and Indices), Speed Mathematics and Basic Mathematics
  2. Logical Reasoning: Seating Arrangements, Puzzle Solving (Puzzles), Data Arrangement, Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Data Sufficiency, Venn Diagram, Inequality, Series (Number and Letter Series) (Numerical Relations and Reasoning), Logical Sequence Of Words, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning)
  3. Verbal Ability: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Subject Verb Agreement (Verb Noun Agreement), Tenses, Articles, Preposition, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Vocabulary, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Completion (Fill in the blanks), Sentence Correction (Error Correction), Cloze Test (Cloze Passage), Facts, Inference and Judgements
  4. Programming Fundamentals (Technical): C Fundamentals
  5. Data Structures (Technical): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  6. Algorithms (Technical): Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis, Advanced Algorithms
  7. OOPs (Technical): Object Oriented Programming (OOPS)
  8. DBMS (Technical): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  9. SQL (Technical): SQL
  10. Operating Systems (Technical): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  11. Computer Networks (Technical): 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, Network Security, Mobile Technology, Cloud Computing and IoT, Cyber and Info Security
  12. Software Engineering (Technical): Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Coding/Automata Round: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir, Pseudo Codes
  14. Personality / Behavioral Assessment: Behavioral Assessment (Behavioral Competency Profiling) (Psychometric Test)
  15. Writing Assessment: English Writing Ability
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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