K-ary Tree Practice Question 8

Duration: 2 min

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Module outline

  1. Quantitative Aptitude: Number System, Divisibility Rules, HCF LCM, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Mixture and Alligation, Partnership, Age Problems, Time and Work, Pipe and Cistern, Speed Time and Distance, Algebra, Arithmetic, Data Interpretation, Sequence and Series (Series), Logarithm, Powers and Exponents (Surds and Indices), Permutation and Combination, Probability, Speed Mathematics and Basic Mathematics, Trigonometry
  2. Logical Reasoning: Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Seating Arrangements, Puzzle Solving (Puzzles), Data Arrangement, Syllogisms, Inequality, Data Sufficiency, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Venn Diagram, Logical Sequence Of Words, Calendar, Clock, Cubes & Dices, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning)
  3. Verbal Ability: Noun, Pronoun, Adjectives, Verb, Adverb, Tenses, Subject Verb Agreement (Verb Noun Agreement), Articles, Preposition, Conjunction, Modals, Determiner, Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Construction
  4. Data Structures (Domain Test): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  5. Algorithms (Domain Test): Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms
  6. OOPs (Domain Test): Object Oriented Programming (OOPS)
  7. DBMS (Domain Test): 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
  8. SQL (Domain Test): SQL
  9. Operating Systems (Domain Test): 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
  10. Computer Networks (Domain Test): 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
  11. Coding: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir
  12. Written English Test: English Writing Ability
  13. Psychometric Test: Behavioral Assessment (Behavioral Competency Profiling) (Psychometric Test)
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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