Longest common Subsequence Part-2

Duration: 7 min

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Module outline

  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Paper 2 | Computer Organization And Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Control Unit Design, Instr Formats & Modes, Programming the Basic Computer
  4. Paper 2 | Analog And Digital Communication: Introduction to Communication Systems & Random Signals, Analog Communication Systems, Information Theory & Digital Communication Fundamentals, Digital Modulation & Detection Techniques, Error Control, Synchronization & Multiple Access Techniques
  5. Paper 2 | Programming in C: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. Paper 2 | Data Structures And Programming: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  7. Paper 2 | Algorithms: Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  8. Paper 2 | 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
  9. Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS
  10. Paper 2 | Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  11. Paper 2 | Information Systems and Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Paper 2 | 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
  13. Paper 2 | Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, CSS, XML, HTML5
  14. Paper 2 | Cyber Security And Emerging Technologies: Emerging Tech Trends
  15. Paper 2 | Cloud Technology: Cloud Computing
  16. Paper 2 | Probability and statistics: Probability, Statistics
  17. Paper-1 English: Vocabulary, Preposition, Articles, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage), Sentence Construction
  18. Paper 1 General Mental Ability & Logical reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Arithmetic, Speed Mathematics and Basic Mathematics, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Venn Diagram, Analogy
  19. Paper-1 General Knowledge & Current Affairs: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge
  20. Full Length Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video provides a comprehensive lecture on the Longest Common Subsequence (LCS) problem using dynamic programming. It begins with a concrete example involving two strings, X and Y, demonstrating the construction of a DP table to find the LCS length. It then transitions to the theoretical foundation, defining the problem formally with sequence notation. The lecture details the "Optimal Substructure" property, explaining how the solution depends on smaller subproblems based on character matches. Finally, it presents the recursive solution formula and the corresponding pseudocode algorithm for computing the LCS length and reconstructing the sequence. This structured approach moves from practical application to theoretical understanding and finally to algorithmic implementation.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins with a concrete problem statement: "Consider two strings X = 'A, B, C, B, D, A, B' and Y = 'B, D, C, A, B, A'. Find the longest common subsequence." He displays a large dynamic programming grid with rows labeled 0 to 7 and columns 0 to 6. The grid is filled with red numbers and arrows. He circles the characters in the strings at the top and left. He traces a path through the table using blue arrows, indicating the backtracking process to reconstruct the subsequence. The number "4" is written at the top right, representing the final length of the LCS. This section serves as a practical demonstration of the algorithm's output before diving into the theory.

  2. 2:00 – 5:00 02:00-05:00

    The lecture transitions to the theoretical foundation with a slide titled "Longest common subsequence." It defines two sequences $X_m = \{x_1, x_2, ..., x_m\}$ and $Y_n = \{y_1, y_2, ..., y_n\}$ and states the goal is to find the maximum length common sequence $Z = \{z_1, z_2, ..., z_k\}$. The instructor underlines the sequence notation and circles the variables X and Y. He then introduces "STEP 1: Optimal Substructure," which breaks down the problem into three cases. The first case states if $x_m = y_n$, then $z_k = x_m = y_n$ and $Z_{k-1}$ is an LCS of $X_{m-1}$ and $Y_{n-1}$. The other cases handle when characters do not match. He draws diagrams on the right to visualize these relationships, circling $X_{m-1}$ and $Y_n$ to show how the subproblem shrinks.

  3. 5:00 – 7:03 05:00-07:03

    The final section covers "STEP 2: Recursive Solution" and "STEP 3: Computing the length of L.C.S". The slide defines $C[i, j]$ as the length of the LCS of $X_i$ and $Y_j$. It presents the recursive formula: $C[i, j] = 0$ if $i=0$ or $j=0$; $C[i, j] = C[i-1, j-1] + 1$ if $x_i = y_j$; and $C[i, j] = \max(C[i, j-1], C[i-1, j])$ if $x_i eq y_j$. The instructor draws a small grid to explain the indices $i, j$ and their neighbors. The last slide shows pseudocode for `LCS-Length(x, y)`, detailing the initialization of $m$ and $n$, the loops to set the first row/column to 0, and the nested loop logic. It specifies updating `c[i, j]` and `b[i, j]` with edge directions like 'D_edge', 'V_edge', and 'H_edge'. The video ends by showing the filled table again.

The video effectively bridges the gap between a concrete example and abstract algorithmic theory. It starts by showing the "what" (the result on a specific grid), moves to the "why" (optimal substructure and mathematical definitions), and finishes with the "how" (recursive formulas and pseudocode). This progression helps students understand not just how to apply the algorithm, but the underlying logic that makes it work. The visual aids, such as the filled grid and the drawn diagrams, are crucial for understanding the index dependencies and the backtracking process required to find the actual subsequence, not just its length.

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