Kruskal Algo Part-1

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
  16. Full Mock Test:
  17. Previous Year Papers:
  18. GATE 2026 Counselling: Counselling and Guidance Sessions
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive introduction to Kruskal's Algorithm, a greedy method for finding the Minimum Spanning Tree (MST) in a weighted graph. The lecture begins by honoring the algorithm's creator, Joseph Bernard Kruskal, Jr., detailing his multifaceted career as a mathematician, statistician, and computer scientist. The instructor then transitions to the technical implementation, presenting the standard pseudocode that relies on the Disjoint Set Union (DSU) data structure. Through a live demonstration on a sample graph, the instructor visually walks through the edge selection process, highlighting how edges are added to the MST without forming cycles, ensuring the total weight is minimized.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for "Kruskal Algorithm" underlined in red, alongside a bullet point introducing Joseph Bernard Kruskal, Jr. The text explicitly lists his professions: "American mathematician, statistician, computer scientist and psychometrician." The instructor, identified as Sanchit Jain Sir from Knowledgegate, appears in the bottom right corner, setting the stage for the lecture. A "KG" logo is visible in the top right.

  2. 2:00 – 4:07 02:00-04:07

    The slide changes to display the pseudocode for "Minimum_Spanning_Tree (G, w)". The code outlines initializing a set A, creating sets for each vertex using Make_Set, and sorting edges by weight. The instructor demonstrates this on a graph with vertices labeled 'a' through 'g'. He uses red digital ink to scribble over edges, indicating the selection of the minimum weight edges, and circles vertices to show the merging of disjoint sets as the algorithm progresses. The condition if (Find_Set(u) != Find_Set(v)) is central to the logic shown. Specific edges like the weight 2 edge between 'b' and 'e' are highlighted first, followed by weight 3 edges, illustrating the non-decreasing order sorting requirement.

The lecture successfully contextualizes the algorithm by first introducing its creator before moving to the rigorous mathematical steps. The visual demonstration is crucial, as it translates the abstract pseudocode—specifically the Find_Set and UNION operations—into a tangible process of connecting graph vertices. This progression from biography to code to visual application ensures students grasp both the history and the mechanics of Kruskal's Algorithm, emphasizing the importance of sorting edges by weight to achieve the minimum total cost. The use of the Disjoint Set Union data structure is highlighted as the key mechanism for efficiently checking for cycles during the edge selection process.

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