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# Prim's Algorithm Example

In computer science, Prim's algorithm is usually a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph.

## Prim’s Algorithm Example:

 Connected Graph

### Solution:

 Step 0: s=[a] v/s= [b,c,d,e,f,g] lightest edge=[a,b] Step 1.1: before S=[a] v/s=[b,c,d,e,f,g] a=[ ] lightest edge=[a,b] Step 1.1: after s=[a,b] v/s=[c,d,e,f,g] a=[[a,b]] lightest edge=[[b,d],[a,c]] Step 1.1: before s=[a,b] v/s=[c,d,e,f,g] a=[a,b] lightest edge=[[b,d],[a,c]] Step 1.2: after s=[a,b,d] v/s=[c,e,f,g] a=[[a,b],[b,d]] lightest edge=[d,c] Step 1.3: before s=[a,b,c] v/s=[c,e,f,g] a=[[a,b],[b,d]] lightest edge=[d,c] Step 1.3: after s=[a,b,c,d] v/s=[e,f,g] a=[[a,b],[b,d],[c,d]] lightest edge=[c,f] Step 1.4: before s=[a,b,c,d] v/s=[e,f,g] a=[[a,b],[b,d],[c,d]] lightest edge=[c,f] Step 1.4: after s=[a,b,c,d,f] v/s=[e,g] a=[[a,b],[b,d],[c,d],[c,f]] lightest edge=[c,f] Step 1.5: before s=[a,b,c,d,f] v/s=[e,g] a=[[a,b],[b,d],[c,d],[c,f]] lightest edge=[f,g] Step 1.5: after s=[a,b,c,d,f,g] v/s=[e] a=[[a,b],[b,d],[c,d],[c,f],[f,g]] lightest edge=[f,e] Step 1.6: before s=[a,b,c,d,f,g] v/s=[e] a=[[a,b],[b,d],[c,d],[c,f],[f,g]] lightest edge=[f,e] Step 1.6: after s=[a,b,c,d,f,g] v/s=[ ] a=[[a,b],[b,d],[c,d],[c,f],[f,g][f,e]] MST COMPLETED

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