An apple has the shape of a perfect sphere with the radius equal to 1. There is
a worm located at some point A on the surface of the apple. The worm wants to
move to the point B, also located on the surface of the apple. The worm may move
in two fashions:
- to crawl along the surface of the apple with the constant speed v0;
- to gnaw a wormhole in the shape of a straight line segment from point A to
point B.
The inside of the apple consists of a core surrounded by the pulp. The core of
the apple is also a perfect sphere, with the radius equal to P , and the center in the
center of the whole apple. The worm can gnaw through the core with the speed v 1
and through the pulp with the speed v 2.
Determine the minimal time the worm needs to get from the point A to the
point B. The size of the worm can be neglected.
each testcase consists of three lines. The first line contains
the values of P (0 < P < 1, the value is given with up to 3 decimal places), v0, v1,
and v2 (integers in the range from 1 to 100). The second and the third line give the
points A and B, respectively, as two angles in the spherical coordinate system. The
first angle, the azimuth φ (0 ≤ φ < 360°), gives the angle between the X axis and
the projection on the XY plane of the segment connecting the origin to the
corresponding point. The second angle, the polar θ (0 ≤ θ ≤ 180°), gives the angle
between the Z axis and the segment connecting the origin to the corresponding
point. The values φ and θ are integers and given in degrees. In all test cases where
θ = 0 or θ = 180, φ is given as 0.
for each case should contain
the minimal time of travel, accurate to 10-9.
0.5 10 15 20 0 0 0 180 0.5 20 5 2 0 0 0 180
0.116666667 0.157079633
Migrated from old NTUJ.
icpc2008, neerc west
| No. | Testdata Range | Score |
|---|