1091 - Target Practice

Time Limit : 1 Second

Memory Limit : 128 MB

Submission: 17

Solved: 11

There are many forms of contests where the contestants (shooters) try to hit targets, either moving or
still. In this version there are a number of small balloons sitting on the tops of poles that are in turn
stuck in the ground at various points in a large field. These poles are not all the same height. The
shooter circles the field and fires at the balloons, the goal being to burst all the balloons with as few
shots as possible. Since the balloons offer almost no resistance to a bullet, the bullet will pass right
through and possibly hit one or more other balloons. So, by judiciously taking shots, the shooter might
need only a very few shots to hit all the targets (provided the shooter is a good marksman, which we
will assume is the case).
For example, the following field of 10 targets can be covered in only four shots, as shown. (The first
two numbers at each position indicate the position of the balloon, and the third number the height.)

Your job is to determine the fewest number of shots necessary to hit all the targets in a given field.
There will be multiple test cases. Each test case will consist of an integer n (<=50) indicating the number
of target positions to follow. A value of n = 0 indicates end of input. There will follow n integer triples,
x y h, indicating a balloon at position (x, y) in the field at height h. (There will be at most one balloon
at any position (x, y).) All integers are greater than 0 and no greater than 100. Furthermore assume
that the shooter can take shots from anywhere on the field at any height. For simplification, assume
here that the balloons are points and that the bullets can pass through the poles on which the balloons
are perched.
Each test case should produce one line of output of the form:
Target set k can be cleared using only s shots.
where k is the number of the test case, starting at 1, and the value of s is the minimum number of shots
needed to hit all the targets in the set.
sample input
5 15 4 10 60 52 17 27 4 33 20 10 33 85 31 42 52 4 70 70 22
78 88 4 85 40 58 100 75 7
5 15 4 10 60 52 17 27 4 33 20 10 33 85 31 42 52 4 70 70 22
78 88 4 100 75 7
sample output
Target set 1 can be cleared using only 4 shots.
Target set 2 can be cleared using only 3 shots.
The 2007 ACM East Central North America
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