DIjakstra algorithim and bellaman ford Practice questions

Duration: 4 min

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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
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AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video addresses a conceptual question regarding shortest paths in weighted graphs. The central problem asks whether doubling the weight of every edge in a graph preserves the identity of the shortest path from a source to any destination, altering only the total weight. The instructor analyzes this by first reading the problem statement and underlining critical conditions. He then constructs a specific directed graph with four vertices (A, B, C, D) and assigns positive integer weights to the edges. Through step-by-step calculation, he compares the total weights of different paths before and after the modification to verify if the minimum weight path remains unchanged.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem statement: "Given a graph, suppose we have calculated shortest path from a source to all other vertices. If we modify the graph such that weights of all edges is becomes double of the original weight, then the shortest path remains same only the total weight of path changes." He underlines phrases like "shortest path from a source to all other vertices" and "weights of all edges is becomes double" to focus attention. To test the validity of this statement, he begins drawing a graph on the whiteboard. He sketches four nodes labeled A, B, C, and D. He draws directed edges from A to B with weight 2, A to C with weight 3, B to D with weight 5, and C to D with weight 7. This visual setup serves as a concrete test case for the question.

  2. 2:00 – 4:14 02:00-04:14

    The instructor proceeds to calculate the shortest paths for the drawn graph. Initially, he computes the path from A to D. He identifies two possible paths: A->B->D with total weight 2+5=7, and A->C->D with total weight 3+7=10. Since 7 is less than 10, the shortest path is A->B->D. Next, he applies the modification: doubling all edge weights. The new weights become 4, 6, 10, and 14. He recalculates the path sums: A->B->D becomes 4+10=14, and A->C->D becomes 6+14=20. He observes that 14 is still less than 20, meaning the shortest path A->B->D remains the same. He generalizes this observation by writing inequalities showing that if w1 <= w2, then 2w1 <= 2w2. Consequently, he concludes the statement is valid and selects option (A) True.

The lecture demonstrates a fundamental property of shortest path algorithms: scaling all edge weights by a positive constant factor does not change the shortest path structure. By using a concrete example where path weights are compared before and after doubling, the instructor proves that the relative order of path costs is preserved. This confirms that the shortest path remains the same, validating the statement. The mathematical generalization provided at the end solidifies the understanding that scalar multiplication maintains inequality relationships between path sums.

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