1. Application of greedy method:
Prim’s Algorithm

2. Greedy Method ???
A greedy method is an method that follows
the problem solving technique of making the
locally optimal choice at each stage with the
hope of finding a global optimum.

3. Prim’s Algorithm
Prim's algorithm is a greedy algorithm that
finds a minimum spanning tree for
a connected weighted undirected graph. This
means it finds a subset of the edges that forms
a tree that includes every vertex, where the
total weight of all the edges in the tree is
minimized.

4. Spanning Tree ???
A spanning tree of a connected graph G can
be defined as a maximal set of edges of G that
contains no cycle, or as a minimal set of edges
that connect all vertices.

6. Minimum Spanning Tree ???
A minimum spanning tree is a subgraph of an
undirected weighted graph G, such that
• it is a tree (i.e., it is acyclic)
• it covers all the vertices V
– contains |V| - 1 edges
• the total cost associated with tree edges is the
minimum among all possible spanning trees
• not necessarily unique

8. Algorithm

11. Example 1

12. 5
A B
4 6 2
2 D 3
C
3 1 2
E F
4

13. 5
A B
4 6 2
2 D 3
C
3 1 2
E F
4

14. 5
A B
4 6 2
2 D 3
C
3 1 2
E F
4

15. 5
A B
4 6 2
2 D 3
C
3 1 2
E F
4

16. A B
2
2 D 3
C
3 1 2
E F
4

17. A B
2
2 D 3
C
3 1 2
E F

18. A B
2
2 D 3
C
3 1 2
E F

19. A B
2
2 D
C
3 1 2
E F

20. A B
2
2 D
C
3 1 2
E F

21. minimum- spanning tree
A B
2
2 D
C
3 1 2
E F

22. Example 2

23. Prim’s Algorithm
9 b
a 2 6
d
4 5
5 4
5 e
c

24. Prim’s algorithm
9 b
a 2 6
d
4 5
5 4
5 e
c
The MST initially consists of the vertex e

25. Prim’s algorithm
9 b
a 2 6
d
4 5
5 4
5 e
c

26. Prim’s algorithm
9 b
a 2 6
d
4 5
5 4
5 e
c

27. Prim’s algorithm
9 b
a 2 6
d
4 5
5 4
5 e
c

28. Prim’s algorithm
9 b
a 2 6
d
4 5
5 4
5 e
c
The final minimum spanning tree

29. Example 3

36. Weight (T) = 23 + 29 + 31 + 32 + 47 + 54 + 66 = 282

37. Problem: Laying Telephone
Wire
Central office

38. Wiring: Normal Approach
Central office
Expensive!

39. Wiring: Better Approach
Central office
Minimize the total length of wire connecting the customers

40. Thank You