Dijakstra and bellaman ford algorithim

Duration: 5 min

This video lesson is available to enrolled students.

Return to /learn/AMCAT-PREPARATION/algorithms/shortest-path-algos/bellman-ford-algo/asset-dijakstra-and-bellaman-ford-algorithim after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Quantitative Ability: Percentage, Profit and Loss, Ratio and Proportion (Ratios), Average, Time and Work, Speed Time and Distance, Simple Interest and Compound Interest, Age Problems, Number System, Divisibility Rules, HCF LCM, Algebra, Permutation and Combination, Probability, Data Interpretation, Logarithm, Sequence and Series (Series), Powers and Exponents (Surds and Indices), Speed Mathematics and Basic Mathematics
  2. Logical Reasoning: Seating Arrangements, Puzzle Solving (Puzzles), Data Arrangement, Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Data Sufficiency, Venn Diagram, Inequality, Series (Number and Letter Series) (Numerical Relations and Reasoning), Logical Sequence Of Words, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning)
  3. Verbal Ability: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Subject Verb Agreement (Verb Noun Agreement), Tenses, Articles, Preposition, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Vocabulary, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Completion (Fill in the blanks), Sentence Correction (Error Correction), Cloze Test (Cloze Passage), Facts, Inference and Judgements
  4. Programming Fundamentals (Technical): C Fundamentals
  5. Data Structures (Technical): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  6. Algorithms (Technical): Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis, Advanced Algorithms
  7. OOPs (Technical): Object Oriented Programming (OOPS)
  8. DBMS (Technical): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  9. SQL (Technical): SQL
  10. Operating Systems (Technical): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  11. Computer Networks (Technical): 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, Network Security, Mobile Technology, Cloud Computing and IoT, Cyber and Info Security
  12. Software Engineering (Technical): Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Coding/Automata Round: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir, Pseudo Codes
  14. Personality / Behavioral Assessment: Behavioral Assessment (Behavioral Competency Profiling) (Psychometric Test)
  15. Writing Assessment: English Writing Ability
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video presents a True/False question regarding the behavior of Dijkstra's and Bellman-Ford algorithms on graphs with positive edge weights. The statement posits that while the specific shortest paths generated by these algorithms might differ, the total path weight will always be identical. The instructor analyzes this claim by breaking down the question's components and then constructing a specific graph example to demonstrate the concept in action.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem statement displayed on the screen. He reads the text: 'Given a graph where all edges have positive weights, the shortest paths produced by Dijkstra and Bellman Ford algorithm may be different but path weight would always be same.' He uses a digital pen to underline critical phrases to guide the analysis. He circles 'positive weights' to emphasize the graph constraint. He underlines 'shortest paths produced by Dijkstra and Bellman Ford algorithm' to identify the two methods being compared. Finally, he underlines the core claim 'may be different but path weight would always be same' to focus on the relationship between path variability and weight consistency.

  2. 2:00 – 5:00 02:00-05:00

    To verify the statement, the instructor draws a directed graph with four nodes labeled A, B, C, and D. He sets node A as the source. He draws an edge from A to B with weight 2 and an edge from A to C with weight 3. He then draws edges from B to D with weight 5 and from C to D with weight 4. He calculates the shortest path from A to D. He identifies two distinct paths: Path 1 is A -> B -> D with a total weight of 2 + 5 = 7. Path 2 is A -> C -> D with a total weight of 3 + 4 = 7. He explains that Dijkstra's algorithm might select the path through B, while Bellman-Ford might select the path through C, or vice versa, depending on implementation. However, he highlights that both paths result in the same minimum weight of 7. He writes 'A->D = 7' to confirm the invariant weight.

  3. 5:00 – 5:02 05:00-05:02

    The instructor concludes the explanation by confirming that the statement is True. He reiterates that the uniqueness of the shortest path weight is a fundamental property of the graph, whereas the specific path taken is not unique if multiple paths share the same minimum weight. This confirms that different algorithms can produce different paths but must agree on the optimal cost.

The lecture demonstrates that the shortest path weight is a unique value determined by the graph's structure and edge weights, regardless of the algorithm used. While Dijkstra's and Bellman-Ford algorithms may traverse different sequences of nodes to reach the destination due to tie-breaking or processing order, they will always converge on the same minimum total weight. This distinction between the path (sequence of nodes) and the path weight (sum of edge costs) is the key takeaway.

Loading lesson…