must be as small
as possible. Write a program that computes the position ot the k depots, such
that the total distance sum is minimized.
| Program | FASTFOOD.C, FASTFOOD.CPP, FASTFOOD.PAS |
The fastfood chain McBurger owns several restaurants along a highway. Recently, they have decided to build several depots along the highway, each one located at a restaurent and supplying several Of the restaurants with the needed ingredients. Naturally, these depots should be placed so that the average distance between a restaurant and its assigned depot is minimized. You are to write a program that computes the optimal positions and assignments of the depots.
To make this more precise, the management of McBurger has issued the following specification:
You will be given the positions of n restaurants along the highway as n integers d1 < d2 < … <dn (these are the distances measured from the company's headquarter, which happens to be at the same highway). Furthermore, a number k (k £ n) will be given, the number of depots to be built.
The k depots will be built at the locations of k different restaurants. Each
restaurant will be assigned to the closest depot, from which it will then receive
its supplies. To minimize shipping costs, the total distance sum, defined as
must be as small
as possible. Write a program that computes the position ot the k depots, such
that the total distance sum is minimized.
The input file will end with a case starting with n = k = 0. This case should not be processed.
If there is more than one optimal solution, output any of them. After the depot descriptions output a line containing the total distance sum, as defined in the problem text.
Output a blank line after each test case.
Sample Input
6 3
5
6
12
19
20
27
0 0
Sample Output
Chain 1
Depot 1 at restaurant 2 serves restaurants 1 to 3
Depot 2 at restaurant 4 serves restaurants 4 to 5
Depot 3 at restaurant 6 serves restaurant 6
Total distance sum = 8