UVa 216 getting in: Full Arrangement & Enumeration

216-getting in line

Time limit:3.000 seconds

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=152

Computer networking requires the computers in the network to be linked.

This problem considers a ' linear ' network in which the computers are, chained, so, each are together to connected Y two others except for the two computers on the ends of the chain which the are of connected. A picture is shown below. Here's the computers are the black dots and their locations in the network are identified by planar coordinates (relative to A coordinate system not shown to the picture.

Distances between linked computers in the network are, shown in feet.

For various reasons it are desirable to minimize the length of cable used.

Your problem is to determine how the computers should be connected into such a chain to minimize the total amount of cable Needed. In the installation being constructed, the cabling would run beneath the floor, so the amount of cable used to join 2 Adjac ENT computers on the network is equal to the distance between the computers plus additional feet of cable to Conne CT from the floor to the computers and provide some slack for ease of installation.

The picture below shows the optimal way of connecting to computers shown, and the total length of above cable fo R This configuration is (4+16) + (5+16) + (5.83+16) + (11.18+16) = 90.01 feet.

Input

The input file would consist of a series of data sets. Each data set would begin with a line consisting of a single number indicating the number of computers in a network. Each network has in least 2 and at most 8 computers. A value of 0 for the number of computers indicates the end of input.

After the initial line in a data set specifying the number of computers in a network, each additional line in the data set Would give the coordinates of a computer in the network. These coordinates is integers in the range 0 to 150. No two computers are at identical locations and each computer'll be listed once.

Output

The output for each network should include a line which tells the number of the network (as determined to its position in The input data), and one line for each length of cable to is cut to connect each adjacent pair of computers in the network . The final line should is a sentence indicating the total amount of cable used.

In listing the lengths of the cable of is cut, traverse the network from one to the other. (It makes no difference at which end/start.) Use a format similar to the "one shown in" sample output, with a line of asterisks separating output for different netwo Rks and with distances in feet printed to 2 decimal places.

Sample Input

6
5 (
116
5
)------BA (95)
3
132
0

Sample Output

Network #1 Cable requirement to connect (5,19) to (55,28) is 6
6.80 feet.
Cable requirement to connect (55,28) to (28,62) is 59.42 feet.
Cable requirement to connect (28,62) to (38,101) is 56.26 feet.
Cable requirement to connect (38,101) to (43,116) is 31.81 feet.
Cable requirement to connect (43,116) to (111,84) is 91.15 feet.
Number of feet of cable required is 305.45. Network #2 Cable requirement to connect (11,27) to (88,30) is
93.06 feet.
Cable requirement to connect (88,30) to (95,38) is 26.63 feet.
Cable requirement to connect (95,38) to (84,99) is 77.98 feet.
Cable requirement to connect (84,99) to (142,81) is 76.73 feet.
Number of feet of cable required is 274.40. Network #3 Cable requirement to connect (132,73) to (72,111)
is 87.02 feet.
Cable requirement to connect (72,111) to (49,86) is 49.97 feet.Number of feet of cable required is 136.99. 

Water problem.