Practice Question

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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.

The video presents a detailed walkthrough of solving the recurrence relation T(n) = T(2n/3) + 1 using the Master Theorem. The instructor begins by writing the general form of the theorem, T(n) = a * T(n/b) + f(n), on the whiteboard. He systematically identifies the coefficients for the given problem: a=1 and b=3/2, noting that n/b corresponds to 2n/3. He then calculates the critical exponent log_b a, which evaluates to log_{3/2} 1 = 0. This results in the term n^{log_b a} becoming n^0 = 1. By comparing this with the non-recursive part f(n) = 1, he establishes that f(n) = Theta(n^{log_b a}). This equality signifies that the problem falls under Case 2 of the Master Theorem.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the recurrence T(n) = T(2n/3) + 1 and writes the standard Master Theorem form T(n) = a * T(n/b) + f(n). He identifies a=1 and derives b=3/2 from the recursive term 2n/3. He calculates n^{log_b a} which simplifies to n^0 = 1. He compares this with f(n)=1 and notes the equality 1=1, indicating Case 2. He explicitly writes f(n) = Theta(n^{log_b a}) and 1 = Theta(1) on the board.

  2. 2:00 – 3:20 02:00-03:20

    The instructor finalizes the solution by applying the Case 2 formula T(n) = Theta(n^{log_b a} (log n)^{k+1}). Since k=0 (implied by the equality), the result simplifies to Theta(1 * log n), which is Theta(log n). He writes the final answer clearly on the board as Theta(log n). He also writes T(n) = Theta(n^{log_{3/2} 1} (log n)^{0+1}) to show the substitution steps.

The lecture demonstrates a step-by-step application of the Master Theorem to a specific recurrence relation. By correctly identifying the parameters a and b and comparing the non-recursive part f(n) with the critical exponent term, the instructor successfully determines the time complexity. The key takeaway is recognizing Case 2 where the work done at each level is constant, leading to a logarithmic total complexity. The visual progression from identifying parameters to calculating the exponent and finally applying the case formula provides a clear method for solving similar recurrence relations in algorithm analysis.

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