Solvable Vs Unsolvable Problem Part-1

Duration: 10 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.

This educational video lecture provides a foundational overview of computational problem classification and introduces the historical Konigsberg Bridge Problem. The instructor begins by presenting a hierarchical flowchart that categorizes all problems into Solvable and Unsolvable types. He further breaks down Solvable problems into Decidable and Undecidable categories, and finally into P Type and NP Type complexity classes. The lecture then transitions to graph theory, using the Konigsberg Bridge Problem as a case study. The instructor illustrates the physical layout of the city with its river and bridges, labeling landmasses A, B, C, and D. He demonstrates how to abstract this physical map into a mathematical graph, explaining the concept of traversing edges (bridges) exactly once. This segment highlights the origins of graph theory and the distinction between solvable and unsolvable problems in a practical context.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the broad classification of problems using a flowchart diagram. The top node is labeled 'PROBLEM', which branches into 'SOLVABLE' and 'UNSOLVABLE'. The instructor points to the 'PROBLEM' box and then the 'SOLVABLE' box, establishing the primary dichotomy. He explains that every problem in computer science falls into one of these two main categories. The visual aid clearly shows the hierarchy, setting the stage for a deeper dive into computability theory.

  2. 2:00 – 5:00 02:00-05:00

    The lecture delves deeper into the 'SOLVABLE' branch of the flowchart. The instructor draws red arrows connecting 'PROBLEM' to 'SOLVABLE' and 'UNSOLVABLE' to emphasize the relationship. He explains that 'SOLVABLE' problems are further divided into 'DECIDABLE' and 'UNDECIDABLE'. He notes that 'DECIDABLE' problems are those for which an algorithm exists that always halts with a correct yes or no answer. The flowchart also shows 'DECIDABLE' branching into 'P TYPE' and 'NP TYPE', indicating complexity classes. The instructor uses hand gestures to trace the path from the root problem down to these specific types.

  3. 5:00 – 10:00 05:00-10:00

    The topic shifts to the 'Konigsberg Bridge Problem'. The slide displays a diagram of the city with a river and seven bridges connecting four landmasses labeled A, B, C, and D. The instructor explains the challenge: to find a path that crosses every bridge exactly once. He then converts this physical map into a graph representation, drawing nodes for the landmasses and edges for the bridges. He draws the graph on the right side of the screen, showing nodes A, B, C, D connected by lines. He discusses how this problem was historically significant and led to the birth of graph theory, illustrating the concept of Eulerian paths and circuits.

  4. 10:00 – 10:02 10:00-10:02

    The video concludes with the graph of the Konigsberg Bridge Problem fully displayed on the screen. The instructor is likely summarizing the key takeaway that this problem, while seemingly simple, was unsolvable in its original form, reinforcing the earlier discussion on unsolvable problems. The visual focus remains on the graph with nodes A, B, C, D and the connecting edges, serving as a final visual anchor for the lesson on graph theory and problem solvability.

The lecture effectively connects abstract computational theory with concrete historical examples. It starts by defining the landscape of problems (Solvable vs. Unsolvable) and their sub-categories (Decidable, P, NP). It then grounds these concepts in the Konigsberg Bridge Problem, showing how a real-world scenario can be modeled as a graph. This progression helps students understand not just the definitions of solvability, but also the historical context and practical application of graph theory in determining whether a problem can be solved.

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