Solvable Vs Unsolvable Problem Part-2

Duration: 9 min

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि और वर्ण, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, पद-भेद और रूप-विकार, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, शब्द-भंडार, अपठित बोध, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): رسم الخط، حروفِ تہجی اور املا / Script, Alphabet and Spelling, اسم، ضمیر اور صفت / Nouns, Pronouns and Adjectives, الفاظ، محاورے اور ضرب الامثال / Vocabulary, Idioms and Proverbs, تفہیمِ عبارت، انشا اور ترجمہ / Comprehension, Writing and Translation, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): শব্দার্থ, বাগধারা ও ভাষাশুদ্ধি / Meaning, Idioms and Correct Usage, বাক্য ও বাচ্য / Sentences and Voice, শব্দগঠন ও শব্দভান্ডার / Word Formation and Vocabulary, অনুবাদ, বোধপরীক্ষণ ও রচনা / Translation, Comprehension and Composition
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Verbs and Tenses, Pronoun, Verb, Adverb, Prepositions and Conjunctions, Parts of Speech, Determiner, Conjunction, Modals, Transformation of Sentences, Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Structure and Common Errors, Reading Comprehension, Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, अशाब्दिक तर्क / Non-Verbal Reasoning, प्रतिशत / Percentage, औसत / Average, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, समय और कार्य / Time and Work, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, Algebra, Probability, Trigonometry, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, Data Arrangement, Inequality, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, Chemistry, History, Geography, Indian Economy, Environment, समसामयिकी / Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, कंप्यूटर नेटवर्क / Computer Networks, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), Terms & Abbreviations, प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References, OOPS with Java
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video lecture introduces the classification of computational problems using a hierarchical flowchart, distinguishing between solvable and unsolvable problems. The instructor, Sanchit Jain, uses the Konigsberg Bridge Problem as a concrete example to illustrate unsolvability. He demonstrates how to model the physical problem as a graph, calculate vertex degrees, and apply Euler's criterion to prove that no solution exists. The lecture connects this historical problem back to the theoretical framework of decidable and undecidable problems.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a structured flowchart displayed on the screen, serving as the central visual aid for the lecture. The diagram is titled with the branding "KNOWLEDGE GATE EDUCATOR" and identifies the instructor as "Sanchit Jain Sir." The flowchart categorizes computational problems starting from the top node labeled "PROBLEM." This root node branches into two primary categories: "SOLVABLE" and "UNSOLVABLE." The "SOLVABLE" branch is further subdivided into "DECIDABLE" and "UNDECIDABLE," which then split into "P TYPE" and "NP TYPE" at the bottom level. The instructor uses this structure to introduce the theoretical framework of computability. He explains that not all problems can be solved by algorithms, setting the stage for distinguishing between solvable and unsolvable problems. The visual hierarchy helps students understand the relationship between these concepts, positioning "P TYPE" and "NP TYPE" as subsets of decidable problems, while "UNDECIDABLE" sits alongside "UNSOLVABLE" in the broader context of problem classification. The blue and white color scheme of the boxes helps distinguish the different levels of the hierarchy clearly. The instructor likely discusses the definitions of these terms, emphasizing that "Decidable" means a solution can be found in finite time, while "Undecidable" implies no algorithm exists. He gestures towards the diagram to guide the viewer's attention through the levels.

  2. 2:00 – 5:00 02:00-05:00

    The lecture transitions to a concrete historical example known as the "Konigsberg Bridge Problem." A diagram appears showing a river with two islands and two mainland sections, labeled A, B, C, and D. Seven bridges are depicted connecting these landmasses as white rectangles crossing blue river lines. The instructor begins the process of mathematical abstraction, converting the physical map into a graph theory model. He draws nodes to represent the landmasses and edges to represent the bridges. This transformation is critical because it allows the application of graph theory rules to determine solvability. He carefully sketches the connections, ensuring the graph mirrors the physical layout where landmass A is connected to the others via multiple bridges. The instructor emphasizes the importance of this modeling step, showing how real-world problems can be translated into mathematical structures to analyze their properties. The visual shift from the hierarchy to the map marks a transition from theory to application. He likely explains that the goal is to find a path that crosses every bridge exactly once without retracing steps. He uses a digital pen to draw the graph on the right side of the screen, creating a clear visual representation of the problem.

  3. 5:00 – 9:07 05:00-09:07

    The instructor analyzes the graph derived from the Konigsberg map to determine if a path exists that crosses every bridge exactly once. He calculates the degree of each vertex, which corresponds to the number of bridges connected to each landmass. He identifies that landmass A has a degree of 5, while landmasses B, C, and D each have a degree of 3. He explains Euler's criterion for an Eulerian path: a graph allows such a path if and only if it has zero or exactly two vertices with an odd degree. Since all four vertices in the Konigsberg graph have odd degrees (5, 3, 3, 3), he concludes that the problem is unsolvable. He then returns to the initial hierarchy diagram, circling "UNSOLVABLE" and "UNDECIDABLE" in red ink to categorize the Konigsberg problem within this framework. He writes "P -> S" and "P -> S?" to symbolize the search for a solution, reinforcing that for this specific problem, the answer is definitively "no solution." This connects the abstract hierarchy back to the concrete example, solidifying the concept of unsolvability. The use of red ink for annotations highlights the key conclusions drawn from the analysis. He likely emphasizes that this is a classic example of an unsolvable problem in the history of mathematics. He points to the specific nodes in the graph to illustrate the odd degrees.

The lecture effectively bridges theoretical computer science concepts with a classic mathematical puzzle. By starting with a hierarchy of problems, the instructor establishes a framework for understanding solvability. The Konigsberg Bridge Problem serves as a practical application, demonstrating how graph theory can be used to prove unsolvability. The visual transition from the abstract flowchart to the concrete map and back again reinforces the connection between theory and practice, helping students grasp the significance of undecidable problems.

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