single source shortest path practice question

Duration: 4 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Paper 2 | Computer Organization And Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Control Unit Design, Instr Formats & Modes, Programming the Basic Computer
  4. Paper 2 | Analog And Digital Communication: Introduction to Communication Systems & Random Signals, Analog Communication Systems, Information Theory & Digital Communication Fundamentals, Digital Modulation & Detection Techniques, Error Control, Synchronization & Multiple Access Techniques
  5. Paper 2 | Programming in C: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. Paper 2 | Data Structures And Programming: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  7. Paper 2 | Algorithms: Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  8. Paper 2 | 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
  9. Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS
  10. Paper 2 | Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  11. Paper 2 | Information Systems and Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Paper 2 | Computer Networks: Introduction to CN, Data Communication, 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
  13. Paper 2 | Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, CSS, XML, HTML5
  14. Paper 2 | Cyber Security And Emerging Technologies: Emerging Tech Trends
  15. Paper 2 | Cloud Technology: Cloud Computing
  16. Paper 2 | Probability and statistics: Probability, Statistics
  17. Paper-1 English: Vocabulary, Preposition, Articles, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage), Sentence Construction
  18. Paper 1 General Mental Ability & Logical reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, 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, Average, Powers and Exponents (Surds and Indices), Algebra, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Arithmetic, Speed Mathematics and Basic Mathematics, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Venn Diagram, Analogy
  19. Paper-1 General Knowledge & Current Affairs: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge
  20. Full Length Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video addresses a theoretical question in graph theory concerning the stability of shortest paths under uniform weight modification. The instructor begins by presenting the problem statement displayed on the screen: "If we increase weight of every edge by 1, the shortest path always remains same." He asks if this statement is true or false. To investigate this, he constructs a counterexample on the whiteboard. He writes "ex." and draws a graph with a source node 'S' on the left and a destination node 't' on the right. He creates two distinct paths between them. The first path, S -> A -> B -> C -> D -> t, consists of 5 edges with weights 2, 4, 5, 6, and 7 respectively, drawn in the upper section. The second path, S -> E -> t, consists of 2 edges with weights 10 and 15, drawn in the lower section.

Initially, the total weight of the first path is calculated as 2 + 4 + 5 + 6 + 7 = 24. The total weight of the second path is 10 + 15 = 25. Since 24 is less than 25, the first path is the shortest path. The instructor then applies the condition of the problem: increasing every edge weight by 1. The new weights for the first path become 3, 5, 6, 7, and 8, summing to 29. The new weights for the second path become 11 and 16, summing to 27. Comparing the new totals, 27 is now less than 29. This demonstrates that the shortest path has shifted from the first path to the second path. Consequently, the instructor concludes that the statement is false, marking "No" as the correct answer. He circles the "No" option to emphasize the conclusion.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem statement regarding shortest paths and edge weight modification. He begins drawing a graph with source 'S' and destination 't', creating a multi-edge path S->A->B->C->D->t and a two-edge path S->E->t. He writes down the initial weights for each edge: 2, 4, 5, 6, 7 for the first path and 10, 15 for the second.

  2. 2:00 – 4:21 02:00-04:21

    The instructor calculates the initial total weights (24 vs 25) to establish the baseline shortest path. He then applies the transformation of adding 1 to every edge weight. He writes the new weights (3, 5, 6, 7, 8 and 11, 16) and calculates the new totals (29 vs 27). He demonstrates that the path with fewer edges becomes shorter, proving the statement false and selecting option (B) No.

The lesson demonstrates a critical property of shortest path algorithms: they are sensitive to uniform weight shifts if paths have different numbers of edges. By adding a constant to every edge, paths with more edges accumulate a larger total increase than paths with fewer edges. This example highlights that shortest paths are not invariant under such transformations, a key concept for understanding algorithm behavior in weighted graphs.

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