Czech ACM Student Chapter
Czech Technical University in Prague
Charles University in Prague
Technical University of Ostrava
acm
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Slovak University of Technology
Pavol Jozef Safarik University in Koˇice
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cz
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University of Zilina
Masaryk University
Matej Bel University in Bansk´ Bystrica
a
University of West Bohemia
CTU Open Contest 2012 -- Practice Session
Charlie the Cockchafer
cockchaf.c, cockchaf.cpp, Cockchaf.java
Charlie knows how to fly. Despite this, whenever Charlie wants to move from one point to
another, it becomes a tedious task for him. The main trouble is that Charlie is a cockchafer.
And it is a well-known fact that all cockchafers (do not confuse them with cockroaches) are
clumsy and slow. Not only they need some time to fly along a straight line, they also spend
more time making turns. Knowing their limitations, will you help Charlie to find the quickest
route?
Input Specification
The input consists of several instances. The first line of each instance contains integers S and
T (1 ≤ S, T ≤ 1000), where S is Charlie's speed in meters per second, and T is the speed of
him turning in degrees per second. The second line contains four integers (0 ≤ Xf , Yf , Xt , Yt ≤
10000) indicating the starting point (Xf , Yf ) and the destination (Xt, Yt). All coordinates are
given in meters.
Output Specification
For each input instance, print a single line containing one real number R, giving the shortest time
Charlie needs to get from the initial to the final point. At the beginning, Charlie is facing north,
which is the positive direction of Y-axis. So, he first needs to turn by D degrees (0 ≤ D ≤ 180)
to an appropriate direction, then he can fly over a straight path to the final point. If the length
of the straight flight is L, the total time will be R = L/S + D/T seconds.
The answer will be accepted as correct if the difference between R and the answer computed by
the judges is at most 0.001.
Sample Input
3
10
0
0 0 10
3
10
0
0 10 10
Output for Sample Input
3.3333
9.2140
