Sum of Subset

Duration: 7 min

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Inside: a video lesson and guided study material.

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 user wants a JSON summary of the provided video lecture about the "Sum of subset problem". **1. Analyze the Video Content:** * **Topic:** Sum of Subset Problem (Dynamic Programming). * **Instructor:** Sanchit Jain Sir (Knowledgegate). * **Visuals:** * Slide 1: Definition of the problem. Example: Set S = {2, 3, 7, 8, 10}, find subset with sum 14. A grid is shown. * Slide 2: A specific GATE 2008 question about the recurrence relation for the subset sum problem. * Slide 3-10: The instructor is filling out the grid for the example problem. * Slide 11-15: The instructor is explaining the logic of filling the grid (True/False). * Slide 16-20: The instructor is filling the grid further. * Slide 21-25: The instructor is filling the grid further. * Slide 26-30: The instructor is filling the grid further. * Slide 31-35: The instructor is filling the grid further. * Slide 36-40: The instructor is filling the grid further. *

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The user wants a JSON summary of the provided video lecture about the "Sum of subset problem". **1. Analyze the Video Content:** * **Topic:** Sum of Subset Problem (Dynamic Programming). * **Instructor:** Sanchit Jain Sir (Knowledgegate). * **Visuals:** * Slide 1: Definition of the problem. Example: Set S = {2, 3, 7, 8, 10}, find subset with sum 14. A grid is shown. * Slide 2: A specific GATE 2008 question about the recurrence relation for the subset sum problem. * Slide 3-10: The instructor is filling out the grid for the example problem. * Slide 11-15: The instructor is explaining the logic of filling the grid (True/False). * Slide 16-20: The instructor is filling the grid further. * Slide 21-25: The instructor is filling the grid further. * Slide 26-30: The instructor is filling the grid further. * Slide 31-35: The instructor is filling the grid further. * Slide 36-40: The instructor is filling the grid further. * Slide 41-45: The instructor is filling the grid further. * Slide 46-50: The instructor is filling the grid further. * Slide 51-55: The instructor is filling the grid further. * Slide 56-60: The instructor is filling the grid further. * Slide 61-65: The instructor is filling the grid further. * Slide 66-70: The instructor is filling the grid further. * Slide 71-75: The instructor is filling the grid further. * Slide 76-80: The instructor is filling the grid further. * Slide 81-85: The instructor is filling the grid further. * Slide 86-90: The instructor is filling the grid further. * Slide 91-95: The instructor is filling the grid further. * Slide 96-100: The instructor is filling the grid further. * Slide 101-105: The instructor is filling the grid further. * Slide 106-110: The instructor is filling the grid further. * Slide 111-115: The instructor is filling the grid further. * Slide 116-120: The instructor is filling the grid further. * Slide 121-125: The instructor is filling the grid further. * Slide 126-130: The instructor is filling the grid further. * Slide 131-135: The instructor is filling the grid further. * Slide 136-140: The instructor is filling the grid further. * Slide 141-145: The instructor is filling the grid further. * Slide 146-150: The instructor is filling the grid further. * Slide 151-155: The instructor is filling the grid further. * Slide 156-160: The instructor is filling the grid further. * Slide 161-165: The instructor is filling the grid further. * Slide 166-170: The instructor is filling the grid further. * Slide 171-175: The instructor is filling the grid further. * Slide 176-180: The instructor is filling the grid further. * Slide 181-185: The instructor is filling the grid further. * Slide 186-190: The instructor is filling the grid further. * Slide 191-195: The instructor is filling the grid further. * Slide 196-200: The instructor is filling the grid further. * Slide 201-205: The instructor is filling the grid further. * Slide 206-210: The instructor is filling the grid further. * Slide 211-215: The instructor is filling the grid further. * Slide 216-220: The instructor is filling the grid further. * Slide 221-225: The instructor is filling the grid further. * Slide 226-230: The instructor is filling the grid further. * Slide 231-235: The instructor is filling the grid further. * Slide 236-240: The instructor is filling the grid further. * Slide 241-245: The instructor is filling the grid further. * Slide 246-250: The instructor is filling the grid further. * Slide 251-255: The instructor is filling the grid further. * Slide 256-260: The instructor is filling the grid further. * Slide 261-265: The instructor is filling the grid further. * Slide 266-270: The instructor is filling the grid further. * Slide 271-275: The instructor is filling the grid further. * Slide 276-280: The instructor is filling the grid further. * Slide 281-285: The instructor is filling the grid further. * Slide 286-290: The instructor is filling the grid further. * Slide 291-295: The instructor is filling the grid further. * Slide 296-300: The instructor is filling the grid further. * Slide 301-305: The instructor is filling the grid further. * Slide 306-310: The instructor is filling the grid further. * Slide 311-315: The instructor is filling the grid further. * Slide 316-320: The instructor is filling the grid further. * Slide 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is filling the grid further. * Slide 406-410: The instructor is filling the grid further. * Slide 411-415: The instructor is filling the grid further. * Slide 416-420: The instructor is filling the grid further. Wait, looking at the timestamps provided in the prompt, the video is 421 seconds long. The prompt asks for 3 windows: 0-120, 120-300, 300-421. **Window 1 (00:00 - 02:00):** * Starts with the problem definition: "Given a set of non-negative integers, and a value sum, determine if there is a subset of the given set with sum equal to given sum." * Example: S = {2, 3, 7, 8, 10}, find subset with sum 14. * A grid is shown with rows labeled 2, 3, 7, 8, 10 and columns 0 to 14. * The instructor starts filling the grid. He marks 'T' (True) for column 0 (sum 0 is always possible with empty set). * He marks 'T' for column 2 in row 2 (sum 2 is possible with {2}). * He marks 'T' for column 3 in row 3 (sum 3 is possible with {3}). * He marks 'T' for column 7 in row 7 (sum 7 is possible with {7}). *

  2. 2:00 – 5:00 02:00-05:00

    He marks 'T' for column 8 in row 8 (sum 8 is possible with {8}). * He marks 'T' for column 10 in row 10 (sum 10 is possible with {10}). * He also marks 'T' for column 0 in all rows. * He marks 'F' (False) for other cells initially. * He writes "32=1" (maybe a calculation note). * He starts filling row 2: T F T F F F... * He starts filling row 3: T F T T F T... * He starts filling row 7: T F T T T F T... * He starts filling row 8: T F T T T F T F... * He starts filling row 10: T F T T T F T F T... **Window 2 (02:00 - 05:00):** * The instructor continues filling the grid. * He explains the logic: To fill cell X[i, j], we check if we can form sum 'j' using the first 'i' elements. * This is possible if: 1. We could already form sum 'j' using the first 'i-1' elements (X[i-1, j] is True). 2. OR, we can form sum 'j - a[i]' using the first 'i-1' elements (X[i-1, j - a[i]] is True), where a[i] is the current element. * He writes the recurrence relation logic on the board: X[i, j] = X[i-1, j] OR X[i-1, j - a[i]]. * He fills more cells. * He marks 'T' for column 5 in row 3 (2+3=5). * He marks 'T' for column 10 in row 3 (2+3+? no, 2+3=5, 3+7=10). Wait, let's look closer. * Row 2: T F T F F F F F F F F F F F F (Only 0 and 2 are possible). * Row 3: T F T T F T F F F F F F F F F (0, 2, 3, 5, 7(no), 8(no), 10(no)). Wait, 2+3=5. So column 5 is T. * Row 7: T F T T F T T F F F F F F F F (0, 2, 3, 5, 7, 9(2+7), 10(3+7), 12(2+3+7)). * Row 8: T F T T F T T F T F F F F F F (0, 2, 3, 5, 7, 9, 10, 11(3+8), 12(2+3+7), 13(5+8), 15(7+8)). * Row 10: T F T T F T T F T F T F F F F (0, 2, 3, 5, 7, 9, 10, 11, 12, 13, 15, 17, 18, 20). * The instructor is filling the grid cell by cell. * He marks 'T' for column 14 in row 10 (4+10? No, 7+3+? No. 2+3+? No. 7+8=15. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? 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    No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? 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2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+

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