Can you please write a c or c$++$ code for this prim algorithm$($minimum prim algorithm$).$ Example $11\mathrm{.}7$ Describe the action of Prim's algorithm for the graph shown in Figure $14$ using

the Minneapolis vertex as a starting point

Solution:

Note that the tree obtained is the same as that obtained by Kruskal's algorithm, but the edges are

added in a different order. It is not hard to see that when a connected graph is input to Prim's

algorithm, the result is a spanning tree. What is not so clear is that this spanning tree is a

minimum.

Theorem $11\mathrm{.}8($Correctness of Prim's Algorithm$)$ When a connected, weighted graph $G$ is input

to Prim's algorithm, the output is a minimum spanning tree for $G.$

Theorem $11\mathrm{.}9$ Prim's algorithm yields the shortest spanning tree of the graph $G$ under

consideration.