Asymptotic Notations- Big O

Duration: 9 min

This video lesson is available to enrolled students.

Return to /learn/UP-LT-GRADE-ASSISTANT-TEACHER-2025/cs-03-data-structures-and-algorithm/algorithm-analysis/asymptotic-notations/asset-asymptotic-notations-big-o after enrolling

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.

This lecture introduces asymptotic notations as an abstract method for describing algorithm behavior and determining the rate of growth of functions. It emphasizes that asymptotic analysis provides a measure of efficiency independent of machine-specific constants and implementation details, covering worst, average, and best cases. The core focus is Big O notation, defined as an upper bound of an algorithm that bounds a function only from above. The formal definition states: O(g(n)) = {f(n): there exist positive constants C and N₀ such that 0 ≤ f(n) ≤ C·g(n) for all n ≥ N₀}. A graph illustrates this by plotting f(n) and c·g(n), with a vertical dashed line at N₀ showing that f(n) remains below c·g(n) for all n ≥ N₀. Handwritten notes on the slide include examples such as f(n) ≤ n², f(n) ≤ n³, and g(n) ≥ 2ⁿ, reinforcing the upper-bound relationship. The lecture progresses from conceptual introduction to formal definition and graphical interpretation.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The slide titled 'Asymptotic Notations' presents two bullet points: the first defines asymptotic notations as an abstract notation for describing algorithm behavior and determining the rate of growth of a function; the second references asymptotic analysis, worst/average/best cases, and efficiency measures independent of machine-specific constants. The instructor gestures while explaining, and red underlines appear on key phrases. The final frame transitions to the Big O notation slide with its formal definition and a graph showing f(n) and c·g(n).

  2. 2:00 – 5:00 02:00-05:00

    The Big O notation slide displays the formal definition involving positive constants C and N₀, stating 0 ≤ f(n) ≤ C·g(n) for all n ≥ N₀. A graph on the left plots f(n) and c·g(n) with a vertical dashed line at N₀; the portion of f(n) to the right of N₀ is highlighted in red, showing it stays below c·g(n). Red handwritten notes build up on the right side, starting with 'g(n) < n' and adding lines such as 'f(n) ≤ n²', 'f(n) ≤ n³', and 'g(n) ≥ 2ⁿ'. A small red sketch showing '10' with an arrow is drawn near the n-axis beneath the graph.

  3. 5:00 – 9:11 05:00-09:11

    The graph continues to show two green curves, the higher labeled 'c g(n)' and the lower 'f(n)', with a dashed vertical line at n₀ and the caption 'f(n) = O(g(n))' beneath. Red handwritten notes build up on the right side, including a circled expression and an inequality reading 'f(n) ≤ g(n)', along with notations like 'n²' and '3³'. The instructor reinforces that Big O bounds a function from above, using the graph to demonstrate that f(n) remains below c·g(n) for all n ≥ N₀, solidifying the upper-bound concept.

The lecture systematically builds understanding of Big O notation from abstract definition to concrete graphical interpretation. It begins by establishing asymptotic notations as machine-independent efficiency measures, then introduces Big O as an upper bound with its formal mathematical definition. The graph serves as the central pedagogical tool, visually demonstrating that f(n) ≤ C·g(n) for all n ≥ N₀. Handwritten examples (f(n) ≤ n², f(n) ≤ n³, g(n) ≥ 2ⁿ) connect the abstract definition to specific function growth rates. The progression from conceptual introduction → formal definition → graphical illustration → worked examples creates a coherent learning arc suitable for exam revision on algorithm analysis.

Loading lesson…