Stack Practice questions

Duration: 10 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. CS | 01 | Digital Logic and Circuits and Discrete Mathematical Structures: Digital Systems & Boolean Basics, Number System, Number Representation, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Permutation and Combination
  3. CS | 02 | Computer Organization and Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Multiprocessors
  4. CS | 03 | Data Structures and Algorithm: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Complexity Theory, Advanced Algorithms
  5. CS | 04 | Problem Solving through C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. CS | 05 | Object Oriented Techniques: Object Oriented Technology, Java
  7. CS | 06 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Unix OS
  8. CS | 07 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Query Processing & Optimization, File Organization & Indexing
  9. CS | 08 | Computer Networks: 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
  10. CS | 09 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  11. CS | 10 | Internet Technology, Web Design and Web Technology: Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, JavaScript-Basics, HTML Basics
  12. CS | 11 | System Analysis And Design: Fundamentals of Systems and Information Systems, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance
  13. CS | 12 | Information Security and Cyber Laws: Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security
  14. CS | 13 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  15. GS Paper | 01 | Indian and World Geography: Geography
  16. GS Paper | 02 | History: History
  17. GS Paper | 03 | Indian Economy & Social Development: Indian Economy
  18. GS Paper | 04 | General Science: Biology, Chemistry, Physics
  19. GS Paper | 05 | Elementary Maths: Number System, Divisibility Rules, HCF LCM, Percentage, Profit and Loss, Simple Interest and Compound Interest, Ratio and Proportion (Ratios), Average, Time and Work, Speed Time and Distance, Algebra, Mensuration and Geometry, Data Interpretation, Arithmetic, Statistics, Probability, Sequence and Series (Series), Mixture and Alligation, Calculus, Trigonometry, Vectors
  20. GS Paper | 06 | Indian Polity and Governance: Polity
  21. GS Paper | 07 | Current Events: GK- Current Affairs
  22. UPLT Live Classes Notes: UPLT Live Classes
  23. UPLT Full Mock Tests Tier 1:
  24. UPLT Full Mock Tests Tier 2:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video lecture analyzes two C functions, `fun` and `fun2`, to determine the mathematical operation performed by `fun2`. The instructor first identifies that `fun(x, y)` implements multiplication (`x * y`). He then traces the execution of `fun2(a, b)` using specific inputs (a=2, b=3) to find the output. By expanding the recursive calls, he calculates the result as 8. Finally, he generalizes the recursive structure of `fun2` to show that it computes `a` raised to the power of `b` (exponentiation), confirming option (C) as the correct answer.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem by displaying two C functions on the screen: `fun(int x, int y)` and `fun2(int a, int b)`. He begins by analyzing `fun`, noting that it recursively adds `x` to itself `y` times, effectively implementing multiplication (`x * y`). He then sets up a trace for `fun2` using the specific input values `a=2` and `b=3`. He writes down the initial recursive expansion on the whiteboard: `fun2(2, 3)` calls `fun(2, fun2(2, 2))`. He continues to expand the inner call, writing `fun(2, fun(2, fun2(2, 1)))` and then `fun(2, fun(2, fun(2, fun2(2, 0))))`. This establishes the recursive structure needed to evaluate the function.

  2. 2:00 – 5:00 02:00-05:00

    The instructor proceeds to evaluate the nested function calls starting from the base case. He identifies that `fun2(2, 0)` returns `1` based on the base condition `if (b == 0) return 1;`. Substituting this back, the expression becomes `fun(2, fun(2, fun(2, 1)))`. He evaluates the innermost `fun(2, 1)` as `2 * 1 = 2`. The expression simplifies to `fun(2, fun(2, 2))`. Next, he evaluates `fun(2, 2)` as `2 * 2 = 4`. The expression further simplifies to `fun(2, 4)`. Finally, he calculates `fun(2, 4)` as `2 * 4 = 8`. He writes `2^3 = 8` on the board, noting that the result matches the power operation.

  3. 5:00 – 9:52 05:00-09:52

    To confirm the general behavior, the instructor analyzes the recursive step of `fun2` algebraically. He observes that `fun2(a, b)` returns `fun(a, fun2(a, b-1))`. Since `fun(x, y)` is multiplication, this translates to `a * fun2(a, b-1)`. This recurrence relation, `f(a, b) = a * f(a, b-1)` with base case `f(a, 0) = 1`, is the standard definition of exponentiation `a^b`. He compares this with the given options: (A) `a*b`, (B) `a+a*b`, (C) `a^b`, and (D) `b^a`. Although option (B) also yields 8 for inputs (2,3), the recursive structure `a * fun2(...)` clearly matches exponentiation, not addition. He circles option (C) `a^b` as the correct answer, concluding that `fun2` computes `a` raised to the power of `b`.

The lecture demonstrates a method for analyzing recursive C functions by first simplifying helper functions and then tracing specific examples to find a pattern. By identifying `fun` as multiplication and tracing `fun2(2, 3)` to get 8, the instructor establishes a numerical pattern. He then generalizes the recursive step `fun(a, fun2(a, b-1))` into the algebraic form `a * fun2(a, b-1)`, which definitively proves that `fun2` implements exponentiation `a^b`.

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