Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E 
Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. What is the minimum number of paths (in tens of yards) that must be built to connect each facility? 1) 54 C 2) 56 3) 60 4) 65

Answer: Option (1) - 54

Step 1: Arbitrarily begin at any node and connect it to the closest node. The two nodes are referred to as connected nodes, and the remaining nodes are referred to as unconnected nodes.

Step 2: Identify the unconnected node that is closest to one of the connected nodes (break ties arbitrarily). Add this new node to the set of connected nodes. Repeat this step until all nodes have been connected.

Note: A problem with n nodes to be connected will require n - 1 iterations of the above steps.

Using minimum spanning tree technique, the shortest distance to cover all the nodes is

??????BG + GE + ED + EF + FC + CA = 8+10+8+9+10+9 = 54

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