Practice Question

Duration: 3 min

This video lesson is available to enrolled students.

Return to /learn/AMCAT-PREPARATION/algorithms/time-complexity-analysis/master-theorem/asset-practice-question-4697 after enrolling

Inside: a video lesson and guided study material.

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.

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.

Loading lesson…