Codeforces Round 930 (Div. 1) |
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Finished |
You are given $$$n$$$ circles on the plane. The $$$i$$$-th of these circles is given by a tuple of integers $$$(x_i, y_i, r_i)$$$, where $$$(x_i, y_i)$$$ are the coordinates of its center, and $$$r_i$$$ is the radius of the circle.
Please find a circle $$$C$$$ which meets the following conditions:
Let the largest suitable circle have the radius of $$$a$$$.
Your output $$$C$$$, described as $$$(x,y,r)$$$, will be accepted if it meets the following conditions:
The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the number of circles.
The $$$i$$$-th of the following $$$n$$$ lines contains three integers $$$x_i$$$, $$$y_i$$$, $$$r_i$$$ ($$$-10^6 \le x_i,y_i \le 10^6$$$, $$$1 \le r_i \le 2 \cdot 10^6$$$).
It is guaranteed that there is a circle with a radius of at least $$$10^{-6}$$$ which is contained inside all $$$n$$$ circles.
Output three real values, $$$x$$$, $$$y$$$, and $$$r$$$ — the coordinates of the center and the radius of the circle.
4 1 1 3 -1 1 3 1 -1 2 -1 -1 2
0.0000000000000000 -0.7637626158259733 0.9724747683480533
4 41580 -23621 95642 -41580 -23621 95642 0 47821 95642 0 0 109750
0.0000000000000000 0.0000000000000000 47821.0000000000000000
A two-dimensional plot depicting the first test case is given below. The output circle $$$C$$$ is dashed with blue lines.
A two-dimensional plot depicting the second test case is given below. The output circle $$$C$$$ is dashed with blue lines.
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