Use Prims Algorithm:

A railway contractor has been employed to lay a railway network which connects a set or

of cities. The cost of connecting one city to another depends upon the distance between

them and the nature of the terrain. The constructor must ensure that it is possible to

travel from any city to any other using the network. The cities and the potential costs

of building track between any two cities are defined as nodes and edges of the weighted

$($undirected$)$ graph below.

$($Note: every integer in the range $1$dots$18$ appears as a weight on exactly two edges.$)$

Explain the number of nodes and Use Prim's algorithm to develop a solution and draw a picture of a connecting network which

may be built to minimise the total cost.