Practice Question - 2

Duration: 6 min

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Module outline

  1. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  2. DataBase Management System/DBMS: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  6. C Language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. Computer Networks: Introduction to CN, 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
  10. Theory Of Computation/Automata Theory: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  11. 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
  12. Engineering Mathematics: Permutation and Combination, Linear Algebra, Calculus, Probability, Statistics
  13. General Aptitude: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, 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, Mensuration and Geometry, Mental Ability, Arithmetic, Profit and Loss, Powers and Exponents (Surds and Indices), Average, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Syllogisms, Venn Diagram, Seating Arrangements, Blood Relations, Directions (Direction Test), Analogy, Algebra, Time and Work, Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Cubes & Dices, Ranking, Order and Sequence, Mixture and Alligation, Age Problems, Clock, Selection Decision Table (Decision Making), Data Arrangement
  14. English (Verbal Aptitude): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Preposition, Direct and Indirect Speech, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Correction (Error Correction), Verbal Analogy (Word Based Analogy), Conjunction, Interjection, Verb, Articles, Adverb, Modals, Sentence Construction
  15. Live Classes Recordings(Earlier Batch): GATE 2026 Live Class
  16. Full Mock Test:
  17. Previous Year Papers:
  18. GATE 2026 Counselling: Counselling and Guidance Sessions
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture segment demonstrates the solution of a recurrence relation problem using variable substitution and the Master Theorem. The instructor begins by presenting the initial recurrence T(n) = 8T(⁸√n) + log₈ n and introduces the substitution method to simplify the logarithmic terms. By setting n = 8^m, the recurrence is transformed into a linear form S(m) = 8S(m/8) + m. The instructor then applies the Master Theorem parameters a=8, b=8, and g(m)=m to determine the asymptotic complexity. The derivation concludes with a final time complexity of Θ(log n log log n) after substituting m back to log₈ n. The visual evidence includes handwritten equations on the board, step-by-step algebraic simplifications, and explicit identification of Master Theorem parameters.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem by writing the recurrence relation T(n) = 8T(⁸√n) + log₈ n on the board. He explains that standard Master Theorem application is difficult due to the root term, so he proposes a substitution method. He writes n = 8^m on the board to transform the variable, aiming to convert the root into a linear exponent. The visual evidence shows the initial question text and the first step of substitution where n is replaced by 8^m to simplify the logarithmic base.

  2. 2:00 – 5:00 02:00-05:00

    The instructor proceeds to transform the recurrence into terms of m. He writes T(8^m) = 8T(8^(m/8)) + log₈(8^m), simplifying the logarithmic term to m. This results in a new recurrence S(m) = 8S(m/8) + m, which fits the standard Master Theorem form. He identifies parameters a=8, b=8, and g(m)=m. The board displays the calculation of log_b a = 1, leading to the comparison between g(m) and m^(log_8 8). The instructor writes Theta(m log m) as the intermediate complexity in terms of m.

  3. 5:00 – 5:42 05:00-05:42

    In the final segment, the instructor completes the derivation by substituting m back to log₈ n. He points to the board where he writes Theta(log_8 n log log_8 n) as the final time complexity. The visual evidence includes the step-by-step reduction from S(m) to Theta(m log m) and then to the final expression in terms of n. The instructor emphasizes the logarithmic growth rate by pointing to specific terms in the equation, confirming the solution involves nested logarithms.

The lecture provides a clear pedagogical example of handling non-standard recurrence relations. The key takeaway is the substitution technique where n = 8^m linearizes the recursive structure, allowing standard Master Theorem application. The instructor methodically transitions from T(n) to S(m), solves for m, and reverts to n. This process highlights the importance of variable transformation in algorithm analysis when direct application of standard rules is not feasible. The final result Θ(log n log log n) demonstrates how nested logarithms arise from such transformations.

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