Kruskal Algo Part-2

Duration: 6 min

This video lesson is available to enrolled students.

Return to /learn/GATE-GUIDANCE-BY-SANCHIT-SIR/algorithms/minimum-spanning-trees/mst-kruskals-algo/asset-kruskal-algo-part-2 after enrolling

Inside: a video lesson and guided study material.

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.

The video provides a detailed lecture on Kruskal's algorithm for finding the Minimum Spanning Tree (MST) of a graph. The instructor begins by presenting the pseudocode, explaining the initialization of disjoint sets for each vertex and the sorting of edges by weight. He then demonstrates the algorithm step-by-step on a sample graph, visually adding edges in increasing order of weight while using the Union-Find data structure to avoid cycles. The lecture concludes with a summary of the greedy nature of the algorithm and the final return statement.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video starts with the pseudocode for Minimum_Spanning_Tree (G, w). The instructor explains the initialization phase where the set A is initialized to empty (A <- phi). He then explains the loop For each vertex v in V(G) do Make_Set(v), emphasizing that initially, every vertex is in its own disjoint set. He underlines the sorting step: Sort the edges of E into non-decreasing order by weight w. He also underlines for each edge (u, v) in E, indicating the iteration over sorted edges. The instructor uses a red pen to underline key phrases on the screen to draw attention to the algorithm's structure.

  2. 2:00 – 5:00 02:00-05:00

    The instructor moves to the core logic of the algorithm. He underlines the condition if (Find_Set(u) != Find_Set(v)). He explains that if the two vertices of an edge belong to different sets, the edge is added to the MST (A <- A U {(u, v)}) and the sets are merged (UNION (u, v)). He then demonstrates this on the graph shown on the right. He starts by identifying the edge with the minimum weight, which is (b, e) with weight 2, and draws a red zig-zag line on it. Next, he considers edges with weight 3, adding (a, c) and (e, f) with red zig-zags. He proceeds to weight 4, adding (b, c) and (f, g). He crosses out edges that would form cycles, such as (a, b) with weight 5, because 'a' and 'b' are already connected. He continues this process, crossing out edges with weight 5 like (e, g) if they form cycles, but actually adds (c, d) with weight 5 to connect vertex 'd'. He crosses out edges with weight 6 like (b, d), (c, f), (d, e), and (d, f) as they would create cycles. The visual demonstration clearly shows the construction of the MST step-by-step.

  3. 5:00 – 5:43 05:00-05:43

    The instructor concludes the lecture by pointing to the final line of the pseudocode, Return A. He explains that the algorithm returns the set of edges A which constitutes the Minimum Spanning Tree. He summarizes that Kruskal's algorithm is a greedy algorithm that builds the MST by adding the cheapest edge that doesn't form a cycle. He reiterates the importance of the Union-Find data structure in efficiently checking for cycles. The video ends with the instructor looking at the camera, having completed the explanation of the algorithm.

The lecture systematically breaks down Kruskal's algorithm, starting with the theoretical pseudocode and moving to a practical visual demonstration. The instructor emphasizes the greedy strategy of selecting edges by weight and using Union-Find to prevent cycles. The visual aids, including red zig-zags for added edges and crosses for rejected edges, effectively illustrate the algorithm's execution on a sample graph, culminating in the final Minimum Spanning Tree.

Loading lesson…