Subtract and Conquer

Duration: 2 min

This video lesson is available to enrolled students.

Return to /learn/HPSC-PGT-COMPUTER-SCIENCE/data-structure-algorithms/time-complexity-analysis/master-theorem/asset-subtract-and-conquer after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. HPSC Interview Preparation: Interview Preparation
  2. Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  3. Data Structure & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Sorting Algorithms, Minimum Spanning Trees, Time Complexity Analysis, Graph Theory, Shortest Path Algos
  4. Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security
  5. Computer System & Organisation: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  6. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Transaction Management, Concurrency Control
  7. Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling
  8. Digital Logic & Circuits: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  9. Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Pushdown Automata & CFG, Turing Machines, Moore & Mealy Machines
  10. 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
  11. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Data Warehousing & Mining
  12. Introduction to Emerging Trends: Emerging Tech Trends
  13. Digital Society & Cyber Law: Society, Law & Ethics
  14. HPSC PGT Previous Year Paper:
  15. HPSC Assistant Professor Previous Year Paper:
  16. Live Sessions: HPSC Live Sessions, EMRS TGT/PGT Live Class
  17. Full Mock Test:
  18. HPSC PGT - MOCK Test Series:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video focuses on analyzing the time complexity of a specific recurrence relation commonly found in divide-and-conquer algorithms. The instructor presents the inequality T(n) <= c if n <= 1, and aT(n-b) + f(n) if n > 1. He explains that a represents the number of subproblems, b is the reduction in problem size, and f(n) is the cost of dividing and combining. The core of the lesson involves determining the Big-O complexity of T(n) given that f(n) is O(n^k). The instructor systematically breaks down the solution into three distinct scenarios based on the value of a.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by writing the recurrence relation on the screen. He then draws a rough tree diagram to illustrate the recursive structure, labeling the root as T(n) and the branches as T(n-b). He explicitly writes the condition 'If f(n) is O(n^k)' to set the context for the complexity analysis. Following this, he lists three numbered cases on the left side of the screen. Case 1 states that if a < 1, then T(n) = O(n^k). Case 2 states that if a = 1, then T(n) = O(n^{k+1}). Case 3 states that if a > 1, then T(n) = O(n^k a^{n/b}). As he discusses each case, he draws a blue checkmark next to it to indicate validity or completion of the point. He also circles the assumption f(n) = O(n^k) to emphasize its importance.

  2. 2:00 – 2:04 02:00-02:04

    The video ends with the instructor having completed the list of cases. The screen displays the full recurrence relation at the top and the three solved cases at the bottom, providing a complete reference for this specific type of recurrence.

The lecture provides a concise summary of the solution for a linear recurrence relation where the problem size decreases by a constant b at each step. It categorizes the complexity based on whether the number of subproblems (a) is less than, equal to, or greater than 1, assuming the non-recursive work is polynomial.

Loading lesson…