Knap Sack Problem

Duration: 13 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 introduction to the Knapsack Problem, a classic problem in combinatorial optimization. It begins by defining the problem: given a set of items, each with a weight and a value, the goal is to determine the number of each item to include in a collection such that the total weight is less than or equal to a given limit, while maximizing the total value. The lecture uses visual aids, including images of a gold bar, diamond, ruby, and coin, to illustrate items with varying weights and values against a backpack with a maximum weight capacity. The instructor then delves into the historical context, referencing early works from 1897 and mathematician Tobias Dantzig. The core of the lecture transitions to a specific numerical example involving three objects (O1, O2, O3) with defined weights and profits. The instructor demonstrates how to solve this problem using different greedy strategies, specifically analyzing selection based on total profit, total weight, and profit-to-weight ratio. He performs calculations on the screen to show how items can be selected, including fractional inclusion, to achieve the maximum possible profit within the knapsack's capacity limit. This structured approach helps students understand both the theoretical underpinnings and the practical calculation methods required for this algorithmic challenge.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lecture opens with a slide titled "Knap Sack Problem" and a bullet point defining it as a problem in combinatorial optimization. The text explains that given a set of items, each with a weight and a value, one must determine the number of each item to include so the total weight is within a limit and total value is maximized. Below the text, four items are displayed: a gold bar (Wt. = 5, Value = 10), a diamond (Wt. = 3, Value = 20), a ruby (Wt. = 8, Value = 25), and a coin (Wt. = 4, Value = 8). A graphic of a green and brown backpack is shown with an arrow pointing to "Maximum wt. = 13". The instructor uses these visuals to set the stage for understanding the constraints and objectives of the problem, explaining that the goal is to fill the backpack with the most valuable items possible without exceeding the weight limit.

  2. 2:00 – 5:00 02:00-05:00

    The slide changes to provide historical context. Text on the left states that the knapsack problem has been studied for more than a century, with early works dating as far back as 1897. It specifically mentions that the name "knapsack problem" dates back to the early works of mathematician Tobias Dantzig (1884–1956). To the right, there is a black and white photograph of a bearded man in a suit, presumably Tobias Dantzig. The instructor discusses this history, emphasizing the longevity and significance of the problem in the field of mathematics and computer science, noting that it has been a subject of study for over a hundred years.

  3. 5:00 – 10:00 05:00-10:00

    A new slide appears with the question: "Consider the weights and values of items listed below. Note that there is only one unit of each item." A table lists three objects: O1 (Weight 18, Profit 25), O2 (Weight 15, Profit 24), and O3 (Weight 10, Profit 15). The instructor writes "M = 20" in a red box, indicating the knapsack capacity. He begins to explore different solution strategies. He writes "1 -> Profit" and attempts a calculation involving `1*25 + 2/3*24`. He then writes "2 -> Weight" and calculates `0*18 + 1/2*15 + 1*15`. Finally, he writes "3 -> %" and calculates ratios like `25/18`, `24/15`, and `15/10` to determine the efficiency of each item. This section sets up the comparison of different greedy approaches, showing how different criteria lead to different selection orders. He is demonstrating how to prioritize items based on different metrics to find the optimal solution.

  4. 10:00 – 13:12 10:00-13:12

    The instructor continues the calculation for the third strategy, the percentage or ratio method. He writes out the equation `0*18 + 1*24 + 5/10*15`. This calculation implies selecting object O2 fully (weight 15, profit 24) and half of object O3 (weight 5, profit 7.5) to fill the capacity of 20. He sums the profits to get a total value of `31.5`, which he circles in red. This demonstrates the solution for a fractional knapsack problem where items can be broken, showing how to achieve the maximum profit of 31.5 within the weight limit of 20. The instructor concludes this segment by highlighting the final calculated value, reinforcing the result of the greedy algorithm based on profit-to-weight ratio.

The video effectively bridges the gap between theoretical definition and practical application. It starts with a clear definition and visual examples to ground the concept, moves to historical context to establish credibility, and then applies the theory to a concrete numerical problem. By walking through multiple strategies (profit, weight, ratio) and performing the actual arithmetic, the instructor demonstrates the decision-making process required to solve optimization problems. The final calculation of 31.5 serves as a concrete answer derived from the fractional knapsack logic, providing a clear takeaway for students learning about this algorithm.

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