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. HPSC Interview Preparation: Interview Preparation
  2. Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  3. Data Structure & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Sorting Algorithms, Minimum Spanning Trees, Time Complexity Analysis, Graph Theory, Shortest Path Algos
  4. Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security
  5. Computer System & Organisation: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  6. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Transaction Management, Concurrency Control
  7. Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling
  8. Digital Logic & Circuits: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  9. Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Pushdown Automata & CFG, Turing Machines, Moore & Mealy Machines
  10. 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
  11. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Data Warehousing & Mining
  12. Introduction to Emerging Trends: Emerging Tech Trends, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, कंप्यूटर नेटवर्क / Computer Networks
  13. Digital Society & Cyber Law: Society, Law & Ethics, साइबर सुरक्षा / Cyber Safety and Security
  14. HPSC PGT Previous Year Paper:
  15. HPSC Assistant Professor Previous Year Paper:
  16. Live Sessions: HPSC Live Sessions, EMRS TGT/PGT Live Class
  17. Full Mock Test:
  18. HPSC PGT - MOCK Test Series:
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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