Download presentation
Presentation is loading. Please wait.
Published byWilliam Warner Modified over 9 years ago
1
MCA 202: Discrete Structures Instructor Neelima Gupta ngupta@cs.du.ac.in
2
Table of Contents Prim’s MST Algorithm Kruskal MST Algorithm
3
Minimum Spanning Tree
4
THANKS Saumya Agarwal (Roll No 35) & Saurabh Garg(Roll No 36) (MCA 2012)
5
Prim’s Algorithm for Minimum Spanning Tree THANKS Saumya Agarwal (Roll No 35) & Saurabh Garg(Roll No 36) (MCA 2012)
6
Example a b c d ef h g 2 8 6 2 4 3 7 5 2 3 THANKS Saumya Agarwal (Roll No 35) & Saurabh Garg(Roll No 36) (MCA 2012) T Edges from T to V-T Selected edge
7
Idea of Correctness THANKS Saumya Agarwal (Roll No 35) & Saurabh Garg(Roll No 36) (MCA 2012)
8
Cut A cut is defined as a collection of edges which separates one collection of vertices from another. THANKS Saumya Agarwal (Roll No 35) & Saurabh Garg(Roll No 36) (MCA 2012) T V-T
9
Thanks: Shammi-37 and Shivangi-38 (MCA 202) Step 1: Sort the edges in the increasing order of weights. Step 2: Pick the minimum weighted edge and include it in your partial constructed forest if it does not form a cycle. Step 3: Repeat step 2 until you include all the vertices (n) or exactly (n-1) edges. Kruskal’s algorithm
10
Thanks: Shammi-37 and Shivangi-38 (MCA 202) a b c d h e g f 2 4 2 6 1 3 8 3 7 5 Minimum Spanning Tree Traversing edges: be df ah ef, de The edge ‘de’ is traversed but not included because it forms cycle. fg cd, bc Similarly, ‘bc’ is traversed but not included. gh, ab The edge ‘ab’ is not traversed at all as we have included n-1 edges. a b c h e g f Now we have completed the tree, with minimized weights. d
11
Thanks: Shammi-37 and Shivangi-38 (MCA 202) How to check cycle: If both the vertices are of same component it will form cycle. Data structure used: Linked list. How much time to check for cycles? How much time to merge two components? Only constant amount of time is needed to perform step 2, as edges are already sorted before step 1.
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.