Longest common Subsequence Part-2

Duration: 7 min

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Module outline

  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
  2. General Awareness: Physics, Chemistry, Biology, History, Geography, Polity, Indian Economy, Environment, Static General Knowledge, GK- Current Affairs, Artificial Intelligence, MS Office Applications, Terms & Abbreviations, Keyboard Shortcuts, Evolution of Indian Banking (Banking & Financial Awareness), Emerging Tech Trends
  3. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: 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, Database Recovery, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  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. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Security, Windows OS, Distributed Systems, Unix OS, Linux OS
  12. Computer Networks: Introduction to CN, 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, Data Communication, Website, Browser & Services, Web Design & Development, Network Security, Cyber Threats and Malware Attacks, Cyber Safety and Security
  13. Full Length Mock Tests:
  14. Sectional Tests:
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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