Problem B: WiFi
One day, the residents of Main Street got together and decided that
they would install wireless internet on their street, with coverage
for every house. Now they need your help to decide where they should
place the wireless access points. They would like to have as strong
a signal as possible in every house, but they have only a limited
budget for purchasing access points.
They would like to place
the available access points so that the maximum distance between any house
and the access point closest to it is as small as possible.
Main Street is a perfectly straight road. The street number of each
house is the number of metres from the end of the street to the house.
For example, the house at address 123 Main Street is exactly 123 metres
from the end of the street.
Input Specification
The first line of input contains an integer specifying the number
of test cases to follow.
The first line of each test case contains two positive integers n,
the number of access points that the residents can buy,
and m, the number of houses on Main Street.
The following m lines contain the house numbers of the
houses on Main Street, one house number on each line.
There will be no more than 100 000 houses on Main Street,
and the house numbers will be no larger than one million.
Sample Input
1
2 3
1
3
10
Output Specification
For each test case, output a line containing one number,
the maximum distance between any house
and the access point nearest to it.
Round the number to the nearest tenth of a metre, and output it
with exactly one digit after the decimal point.
Output for Sample Input
1.0
Ondřej Lhoták
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