ENG  RUSTimus Online Judge
Online Judge
Online contests
About Online Judge
Frequently asked questions
Site news
Problem set
Submit solution
Judge status
Update your info
Authors ranklist
Current contest
Scheduled contests
Past contests

USU Open Personal Contest 2009

About     Problems     Submit solution     Judge status     Standings
Contest is over

G. Photovoltaic Spaceship

Time limit: 0.5 second
Memory limit: 64 MB
The Empire is not safe. Because of the lingering economic crisis, people's discontent is growing in central sectors. On the outskirts of the Galaxy, the Rebels' activity has sharply increased. The Imperial Fleet has to repel attacks on strategically important stellar systems almost every day. The hostilities have led to the drastic increase in fuel consumption. The situation is aggravated by the fact that local facilities for helium-3 production are scarce and fuel has to be brought from the center of the Galaxy. The Rebels are well-informed about that and regularly carry out raids upon main logistics hubs, which leads to the permanent fuel shortage.
Darth Vader charged Commander of the Fleet with the task of improving this situation as soon as possible. A group of officers proposed a plan based on the constant change of supply routes with a simultaneous increase in the number of patrols. But Head of Advanced Defense Technology Department came forth with a more radical proposal. He suggested decreasing the dependence of the Fleet on the fuel supply by using alternative energy sources. In his opinion, the most promising technology was the use of photovoltaic cells. He proposed to cover all spaceships with solar panels which would absorb the energy of stars.
The officers were shocked by this plan, because any competent specialist understands that even if every square meter of the surface of a spaceship were covered with solar batteries their power would be insufficient for the supply of the hyperdrive. The worst of it was that Commander of the Fleet liked the idea. In the course of the ensuing bureaucratic struggle it turned out that the owner of the largest supplier of solar panels was the son of Head of Advanced Defense Technology Department. In order to discredit the proposal still further, the officers asked you to calculate the power provided by solar panels for a typical spaceship in that sector of the Galaxy.
As you were working on this task, an unknown man dressed in all black came into your cabin. He was quite friendly and offered his assistance. He promised you a rapid career advancement if you inflated the result twofold. And if you refused, he wouldn't be able to guarantee your family's safety. After some thought, you agreed.


A typical spaceship is a tetrahedron. In the first four lines you are given the coordinates of its vertices. These are integers with absolute values not exceeding 100; the unit of measure is meter. In the following line you are given the number n of stars (1 ≤ n ≤ 10). Each of the following n lines contains three integers, which are the coordinates of the vector directed to the star. The length of this vector is the light intensity of the star in watts per square meter. This is a positive number not exceeding 2500 W/m2, because typical spaceships don't fly near stars. It is guaranteed that the directions to all stars are different.


Find the total power of the solar panels of the spaceship taking into account the man in black's wish. Output this power in watts accurate to 10−5. The power of a solar panel with an area of 1 m2 illuminated by light of intensity 1 W/m2 is the cosine of the incidence angle of the light beams.


0 -1 0
0 1 0
0 0 2
1 0 0
0 0 -1358
21 0 0
Problem Author: Pavel Atnashev
Problem Source: USU Open Personal Contest 2009 (February 28, 2009)
To submit the solution for this problem go to the Problem set: 1686. Photovoltaic Spaceship