DIjakstra algorithim and bellaman ford Practice questions

Duration: 4 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. English Language: Vocabulary, Noun, Adjectives, Tenses, Pronoun, Adverb, Preposition, Conjunction, Active Passive Voice (Voice), Articles, Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage)
  3. Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Puzzle Solving (Puzzles), Seating Arrangements, Blood Relations, Syllogisms, Inequality, Directions (Direction Test), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Clock, Calendar, Analytical Reasoning (Counting Figures Reasoning), Selection Decision Table (Decision Making), Cubes & Dices, Machine Input-Output
  4. Quantitative Aptitude: Ratio and Proportion (Ratios), Data Interpretation, Mixture and Alligation, Permutation and Combination, Number System, Sequence and Series (Series), Speed Time and Distance, Algebra, Speed Mathematics and Basic Mathematics, Percentage, Average, Time and Work, Simple Interest and Compound Interest, Profit and Loss, Age Problems, Partnership, Mensuration and Geometry, Probability, IBPS Specific Videos
  5. Data Structures - Professional Knowledge: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  6. Algorithms- Professional Knowledge: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  7. Python- Professional Knowledge: Python for Placements by Yash Sir, Python Basics
  8. Operating System- Professional Knowledge: Introduction to OS, Process Management, CPU Scheduling, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management
  9. DBMS + SQL- Professional Knowledge: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), File Organization & Indexing, SQL, Transaction Management, Concurrency Control
  10. Computer Networks- Professional Knowledge: Introduction to CN, Data Communication, Net Layer: IP Addressing, Net Layer: IPv4 & Proto, Application Layer, Hardware basics, Network Security
  11. Software Engineering- Professional Knowledge: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Computer Organization & Microprocessor- Professional Knowledge: Basics of COA, Cache Memory Organization, Programming the Basic Computer
  13. Digital Logic Design- Professional Knowledge: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  14. Theory of Computation- Professional Knowledge: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Regular Language Properties, Pushdown Automata & CFG, Turing Machines
  15. Compiler Design- Professional Knowledge: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Intermediate Code Gen, Code Optimization
  16. Programming Languages- Professional Knowledge: C Programming by Yash Sir, Object Oriented Programming (OOPS), Programming in C++, Java, C Language Core
  17. Emerging Tech- Professional Knowledge: Emerging Tech Trends
  18. Artificial Intelligence: Artificial Intelligence
  19. Unit Test - Professional Knowledge:
  20. Full Length Mock Test:
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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