Practice Question

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.

The video presents a detailed solution for the recurrence relation T(n) = 9T(n/3) + n using the Master Theorem. The instructor clearly writes the general form T(n) = a * T(n/b) + f(n) and maps the specific values a=9, b=3, and f(n)=n. He calculates the term n^(log_b a), simplifying n^(log_3 9) to n^2. Comparing f(n)=n with n^2, he establishes that f(n) is polynomially smaller, satisfying f(n) = O(n^(2-epsilon)) for epsilon > 0. This confirms Case 1 applies. He concludes the complexity is determined by the recursive part, writing T(n) = Theta(n^(log_b a)), and simplifies the result to Theta(n^2).

Chapters

  1. 0:00 – 1:39 00:00-01:39

    The lecture starts with the recurrence T(n) = 9T(n/3) + n. The instructor writes the standard form T(n) = a * T(n/b) + f(n) on the whiteboard. He identifies the parameters a=9 and b=3. He calculates the critical exponent log_b a as log_3 9, which equals 2, resulting in the term n^2. He compares f(n)=n against n^2, noting that f(n) is smaller by a polynomial factor, satisfying f(n) = O(n^(2-epsilon)). This identifies the scenario as Case 1 of the Master Theorem. He writes the general solution T(n) = Theta(n^(log_b a)) and substitutes the values to get Theta(n^(log_3 9)). Finally, he underlines the simplified answer Theta(n^2).

This lesson demonstrates the Master Theorem for divide-and-conquer algorithms. By identifying parameters a, b, f(n) and comparing growth rates, the instructor shows how to bypass complex expansions. The visual derivation reinforces calculating the critical exponent log_b a to determine the applicable case, leading to a very concise asymptotic bound for the specific recurrence.

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