Longest commom Subsequence Part-1

Duration: 14 min

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Module outline

  1. About Course: UPPSC Course Overview
  2. Interview Preparation & Guidance: Interview Preparation
  3. Paper 1 | General Hindi: भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, वर्णमाला, समास, संधि, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), शब्द-भंडार, वर्ण-विचार, हिन्दी की ध्वनि और स्वनिम व्यवस्था, प्राचीन और मध्यकालीन भारतीय आर्यभाषाएँ, काव्य के लक्षण, हेतु और प्रयोजन, अशुद्धि-शोधन, शब्द-रचना, शब्द-भेद, हिन्दी की रूप रचना, रूप-रचना, हिन्दी शब्द रचना, हिन्दी साहित्येतिहास दर्शन, भक्तिकालीन काव्यधाराएँ, भारतीय काव्यशास्त्र की परंपरा, भारतीय नवजागरण और स्वाधीनता आंदोलन, अन्य गद्य विधाएँ एवं प्रवासी साहित्य, निर्धारित उपन्यासों का तुलनात्मक अध्ययन, गोदान, हिन्दी कहानी का विकास, स्वातंत्र्योत्तर और नयी कहानी, हिन्दी निबंध का विकास, शुक्लोत्तर निबंध, द्विवेदी और शुक्ल युग के निबंध, हिन्दी की संवैधानिक स्थिति, आधुनिक भारतीय आर्यभाषाएँ और हिन्दी का उद्भव, हिन्दी भाषा प्रयोग के विविध रूप, रीतिकाल, जीवनी, द्विवेदी युग और छायावाद, रीति, वक्रोक्ति और औचित्य सिद्धान्त, शब्दशक्ति और ध्वनि सिद्धान्त, रस सिद्धान्त और साधारणीकरण, उत्तर आधुनिकतावाद, लोहिया दर्शन, हिन्दी उपन्यास का विकास, हिन्दी नवजागरण, अंबेडकर दर्शन, आदिकाल, प्रयोगवाद और नयी कविता, छायावादी काव्य: प्रसाद और निराला, प्रगतिवाद से समकालीन कविता, निर्गुण भक्ति काव्य, द्विवेदीयुगीन काव्य, रीतिकालीन काव्य, आरंभिक हिन्दी उपन्यास, स्वातंत्र्योत्तर उपन्यास, आत्मकथा, स्वाधीनता-पूर्व प्रेमचंदोत्तर उपन्यास, निर्धारित कहानियों का तुलनात्मक अध्ययन, साठोत्तरी नाटक, प्रसाद और प्रसादोत्तर युग के नाटक, भारतेन्दु युगीन नाटक, स्वातंत्र्योत्तर नाटक, भारतेन्दु युगीन निबंध, संस्मरण और रेखाचित्र, व्यंग्य, एक साहित्यिक की डायरी, संस्कृति के चार अध्याय, सगुण भक्ति काव्य, हिन्दी नाटक, एकांकी और रंगमंच, आधुनिक गद्य और हिन्दी नवजागरण, अलंकार सिद्धान्त, हिन्दी आलोचना का विकास, भक्ति आंदोलन, कल्पना, बिम्ब, प्रतीक, मिथक और फंतासी, नयी कविता का विस्तार और साठोत्तरी कविता, उत्तर-छायावादी और प्रगतिवादी काव्य, काव्यगुण और काव्यदोष, प्लेटो, अरस्तू और पाश्चात्य परंपरा, मार्क्सवाद, स्वच्छन्दतावादी काव्यशास्त्र, आधुनिक पाश्चात्य आलोचना, भाषा और भाषा परिवार, देवनागरी लिपि
  4. Paper 2 | General Studies: State Wise GK, Polity, Geography, History, GK- Current Affairs
  5. Paper 1 | Programming Language: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++
  6. Paper 1 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, ORDBMS, NoSQL
  7. Paper 1 | Cyber Security: Society, Law & Ethics, 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, Ethical Hacking
  8. Paper 1 | Computer Organization and Architecture: Basics of COA, Programming the Basic Computer, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design
  9. Paper 1 | 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, Network Security
  10. Paper 1 | Design and Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  11. Paper 1 | Data Structures: Introduction to DS, Array, Linked List, Stack, Queue, Tree, Graphs, Hashing
  12. Paper 1 | Discrete Structures and Theory of Logic: Permutation and Combination, Set Theory, Relations, Functions, Propositional and Predicate Logic, Graph Theory, Group Theory
  13. Paper 1 | Software Project Management: Software Project Management
  14. Paper 2 | Operating Systems: 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, Security
  15. 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, Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Pushdown Automata & CFG, Complexity Theory
  16. Paper 2 | Artificial Intelligence & High Performance Computing: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Natural Language Processing, Emerging Tech Trends
  17. Paper 2 | Image Processing: Digital Image Fundamentals, Image Enhancement, Image Restoration, Color Image Processing, Image Compression
  18. Paper 2 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  19. Paper 2 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  20. Paper 2 | Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, Java
  21. Paper 2 | Soft Computing: Fuzzy Sets, Artificial Neural Networks, Genetic Algorithms
  22. Paper 2 | Distributed System: Distributed Systems
  23. UPPSC Live Class Recordings: UPPSC Polytechnic Lecturer 2025 (CS)
  24. Previous Year Papers:
  25. Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The lecture introduces the Longest Common Subsequence (LCS) problem, defining it as finding the longest subsequence common to a set of sequences, typically two. It highlights applications in bioinformatics (DNA comparison), computational linguistics, and version control systems like Git. The instructor then transitions to a concrete example involving two strings, X and Y, demonstrating the dynamic programming approach to solve the problem by constructing a matrix and tracing back the optimal path to identify the subsequence. The visual progression from abstract definitions to a biological diagram, and finally to a filled matrix, helps students understand both the 'why' and the 'how' of solving the LCS problem. The instructor meticulously fills the table, showing the recurrence relation in action. He uses red ink to highlight the values and arrows, ensuring clarity for the students.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a slide titled 'Longest common subsequence.' The text defines the LCS problem as finding the longest subsequence common to all sequences in a set, noting that it often involves just two sequences. The slide describes it as a classic computer science problem that forms the basis for data comparison programs like the `diff` utility. It further lists applications in computational linguistics and bioinformatics. Additionally, the text highlights its widespread use in revision control systems such as Git for reconciling multiple changes made to a revision-controlled collection of files. The instructor introduces the topic by reading these points, establishing the foundational context for the algorithm. He emphasizes that while the problem can involve a set of sequences, the most common case is comparing just two.

  2. 2:00 – 5:00 02:00-05:00

    The presentation transitions to a diagram labeled 'Fig. 2. The double helical structure of DNA.' The instructor uses this biological example to explain the relevance of LCS in bioinformatics. He points out the sugar-phosphate backbone and the bases (A, T, C, G) that make up the DNA sequence. He draws a simplified linear representation of a DNA strand and writes a sequence like 'ATCG' to illustrate how biological data is encoded as strings. This visual aid helps students connect the abstract algorithm to real-world data processing tasks involving genetic sequences. He emphasizes that comparing these long strings of characters is exactly what the LCS algorithm is designed to handle efficiently. The diagram shows the helical structure with labeled components like Phosphorus, Carbon, Hydrogen, and Oxygen, providing a detailed scientific context.

  3. 5:00 – 10:00 05:00-10:00

    The lecture returns to the text slide, specifically underlining the phrase 'often just two sequences.' A new problem statement appears: 'Consider two strings X = 'A, B, C, B, D, A, B' and Y = 'B, D, C, A, B, A'. Find the longest common subsequence?' The instructor sets up a dynamic programming table (matrix) with rows labeled 0 to 7 and columns labeled 0 to 6. He initializes the first row and column with zeros. He begins filling the table, explaining the logic: if the characters at the current row and column match, the value is the diagonal value plus one; if they do not match, it is the maximum of the top or left cell. He fills the first row where 'A' matches the last column, resulting in values like 0, 0, 0, 0, 1, 1, 1. In the second row for 'B', he finds a match at the first column, setting the value to 1, and propagates the maximums across the row. He methodically calculates values for each cell, showing how the length of the common subsequence grows as he moves through the grid. He writes the numbers in red ink, making them stand out against the grid lines.

  4. 10:00 – 13:47 10:00-13:47

    The instructor continues to fill the matrix, completing the dynamic programming table. He demonstrates the backtracking process to find the actual subsequence. He draws arrows indicating the path from the bottom-right cell back to the top-left. By following the diagonal moves where characters matched, he identifies the sequence 'B, C, B, A'. He circles the corresponding characters in string Y and writes the number '4' at the top right, indicating the length of the longest common subsequence. This final step solidifies the method for extracting the solution from the computed table. He specifically traces the path through cells (2,1), (3,3), (4,5), and (6,6) to confirm the characters. The final result is clearly displayed, showing both the length and the specific sequence. The table is fully populated with values like 1, 2, 3, and 4, culminating in the final answer. He circles the final answer '4' to emphasize the result.

The lesson effectively bridges theoretical definition with practical application and algorithmic implementation. It starts by contextualizing LCS within computer science and biology, then moves to a step-by-step walkthrough of the dynamic programming algorithm. The visual progression from abstract definitions to a biological diagram, and finally to a filled matrix, helps students understand both the 'why' and the 'how' of solving the LCS problem. The instructor's methodical filling of the table and subsequent backtracking provide a clear template for solving similar problems in exams. The specific example of DNA sequences reinforces the real-world importance of the algorithm. The use of a grid and arrows makes the abstract concept of dynamic programming concrete and easy to follow.

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