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Farmer John's N cows (1 <= N <= 2000) are all standing at various positions along the straight path from the barn to the pasture, which we can think of as a one-dimensional number line. Since his cows like to stay in email contact with each-other, FJ wants to install Wifi base stations at various positions so that all of the cows have wireless coverage.
After shopping around, FJ learns that the cost of a Wifi base station depends on distance it can transmit: a base station of power r costs A + B*r, where A is a fixed cost for installing the base station and B is a cost per unit of transmission distance. If FJ installs such a device at position x, then it can transmit data to any cow located in the range x-r ... x+r. A base station with transmission power of r=0 is allowed, but this only provides coverage to a cow located at the same position as the transmitter.
Given the values of A and B, as well as the locations of FJ's cows, please determine the least expensive way FJ can provide wireless coverage for all his cows.
3 20 5 7 0 100
There are 3 cows at positions 7, 0, and 100. Installation of a base station of power r costs 20 + 5*r.
The optimal solution is to build a base station at position 3.5 (with power 3.5) and another at position 100 (with power 0). The first base station covers cows 1 and 2, and the second covers cow 3.