2019(2)

Duration: 3 min

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Inside: a video lesson and guided study material.

Module outline

  1. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  2. DataBase Management System/DBMS: 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
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  6. C Language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. 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
  10. Theory Of Computation/Automata Theory: 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
  11. 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
  12. Engineering Mathematics: Permutation and Combination, Linear Algebra, Calculus, Probability, Statistics
  13. General Aptitude: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Mensuration and Geometry, Mental Ability, Arithmetic, Profit and Loss, Powers and Exponents (Surds and Indices), Average, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Syllogisms, Venn Diagram, Seating Arrangements, Blood Relations, Directions (Direction Test), Analogy, Algebra, Time and Work, Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Cubes & Dices, Ranking, Order and Sequence, Mixture and Alligation, Age Problems, Clock, Selection Decision Table (Decision Making), Data Arrangement
  14. English (Verbal Aptitude): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Preposition, Direct and Indirect Speech, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Correction (Error Correction), Verbal Analogy (Word Based Analogy), Conjunction, Interjection, Verb, Articles, Adverb, Modals, Sentence Construction
  15. Live Classes Recordings(Earlier Batch): GATE 2026 Live Class
  16. Full Mock Test:
  17. Previous Year Papers:
  18. GATE 2026 Counselling: Counselling and Guidance Sessions
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video presents a multiple-choice question from the GATE 2019 exam about Dijkstra's algorithm. The instructor analyzes each of the four options to determine which statement is not true. He confirms that options (A), (B), and (D) are true: Dijkstra's algorithm can find the shortest path within the same graph data structure, it always selects the node with the smallest known distance, and it requires non-negative edge weights. He then focuses on option (C), which states that the shortest path always passes through the least number of vertices. To disprove this, he draws a graph with vertices S, A, B, C, and D, and demonstrates that the shortest path from S to D (S->A->B->D with a total cost of 8) is not the path with the fewest vertices (S->C->D with a cost of 9). This counterexample shows that the shortest path is based on minimizing total weight, not the number of vertices, making (C) the correct answer to the question.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins with a question displayed on screen: 'When using Dijkstra's algorithm to find shortest path in a graph, which of the following statement is not true? (NET 2019 DEC)'. The four options are listed: (A) It can find shortest path within the same graph data structure, (B) Every time a new node is visited, we choose the node with smallest known distance/cost to visit first, (C) Shortest path always passes through least number of vertices, and (D) The graph needs to have a non-negative weight on every edge. The instructor, visible in the bottom right, begins to analyze the options. He marks (A) as true, explaining that the algorithm operates on the graph itself. He marks (B) as true, stating that the core of Dijkstra's algorithm is to always pick the node with the minimum distance. He then marks (D) as true, noting that negative weights can cause the algorithm to fail. He then focuses on option (C), which he identifies as the incorrect statement, and begins to explain why.

  2. 2:00 – 2:38 02:00-02:38

    The instructor draws a graph on the screen to provide a counterexample for option (C). The graph has vertices S, A, B, C, and D. The edges are S->A (weight 1), A->B (weight 1), B->D (weight 6), S->C (weight 2), and C->D (weight 7). He calculates the cost of the path S->A->B->D as 1+1+6=8. He calculates the cost of the path S->C->D as 2+7=9. He concludes that the shortest path from S to D is S->A->B->D, which has 3 vertices (A, B, D). The path S->C->D has only 2 vertices (C, D), which is fewer. Since the shortest path does not pass through the least number of vertices, the statement in (C) is false. He marks (C) as 'false' and confirms it is the correct answer to the question.

The video systematically evaluates four statements about Dijkstra's algorithm. It confirms that the algorithm operates on the same graph, always selects the node with the minimum known distance, and requires non-negative edge weights. The key insight is that the algorithm's goal is to minimize the total path weight, not the number of vertices. The instructor uses a clear counterexample to demonstrate that a path with a lower total weight can have more vertices than a path with a higher total weight, thereby proving that the shortest path does not necessarily pass through the least number of vertices. This logical disproof identifies (C) as the only false statement.

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