Prim's algorithm is a greedy algorithm that finds a minimum spanning tree in a weighted graph. It works by iteratively adding the lowest weight edge that connects an isolated vertex to the growing spanning tree. The algorithm starts with a single vertex and adds the lowest cost edge that extends the tree until all vertices are connected. The document provides an example of applying Prim's algorithm to find the minimum spanning tree of a weighted graph.

1. PRIM’sSPANNINGTREEALGORITHM
Name : Anwar
Roll No : 44
MCS 3rd Open
TOPIC

2.  An algorithm is designed to achieve optimum solution for a given problem.
In greedy algorithm approach, decisions are made from the given solution
domain. As being greedy, the closest solution that seems to provide an
optimum solution is chosen.
 Greedy algorithms try to find a localized optimum solution, which may
eventually lead to globally optimized solutions. However, generally greedy
algorithms do not provide globally optimized solutions.
Greedy Algorithm Approach

3. s
 Most networking algorithms use the greedy approach. Here is a list of few of them −
 Travelling Salesman Problem
 Prim's Minimal Spanning Tree Algorithm
 Kruskal's Minimal Spanning Tree Algorithm
 Dijkstra's Minimal Spanning Tree Algorithm
 Graph - Map Coloring
 Graph - Vertex Cover
 Knapsack Problem
 Job Scheduling Problem
 There are lots of similar problems that uses the greedy approach to find an optimum solution.
Examples

4.  Example: Use Prim’s algorithm to find a minimum spanning tree in the following
weighted graph. Use alphabetical order to break ties.
B
A
2
Prim's Minimal Spanning Tree Algorithm

5.  Prim’s algorithm will proceed as follows. First we add edge {d, e} of weight1.
 Next, we add edge {c, e} of weight 2. Next, we add edge {d, z} of weight 2.
 Next, we add edge {b, e} of weight 3. And finally, we add edge {a, b} of
weight 2.
 This produces a minimum spanning tree of weight 10.
SOLUTION

6. minimumspanning tree is the following
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or

7. A minimumspanningtree
Tree
Vertices
 A(_,_)
 B(A,2)
 E(B,3)
 D(E,1)
 C(E,2)
 Z(D,2)
Remaining
Vertices
 B(A,2) C(A,3) D(_,_) E(_,_) Z(_,_)
 C(A,3) D(B,5) E(B,3) Z(_,_)
 C(E,2) D(E,1) Z(E,4)
 C(E,2) Z(D,2)
 Z(D,2)
ILLUSTRATION
minimum spanning tree

8. Add a Slide Title - 3
 Tree
Vertices
 A(_,_)
 B(A,2)
 C(A,3)
 E(C,2)
 D(E,1)
 Z(D,2)
 Remaining
Vertices
 B(A,2) C(A,3) D(_,_) E(_,_) Z(_,_)
 C(A,3) D(B,5) E(B,3) Z(_,_)
 D(B,5) E(C,2) Z(_,_)
 D(E,1) Z(E,4)
 Z(D,2)
ILLUSTRATION
minimum spanning tree