Common Board @ Timus Online Judge

Does anybody here wants to buy solution for TRIATHLON?

Posted by I.J. Matrix 8 Jun 2002 22:49

I can trade the solution for one of the most difficult problems on
TIMUS. I need any long arithmetic routines. Write an answer on this
webboard.

I can give you the solution of any problem I have solved without any trading :) (+)

Posted by Michael_Rybak 9 Jun 2002 00:12

I just want it to be useful for you... Maybe you would prefer an
idea, not a solution... Anyway, ask me. I'll help if I can.

GL

RM, can you give hint about problem Triathlon?

Posted by raxtinhac 10 Jun 2002 15:03

> I just want it to be useful for you... Maybe you would prefer an
> idea, not a solution... Anyway, ask me. I'll help if I can.
>
> GL

Here you are (+)

Posted by Michael_Rybak 10 Jun 2002 16:03

First, we may say that the length of first distance is 1 anyway
Now let's consider two other lengths to be x and y
Then we have:

A1x+B1y+C1>=0
A2x+B2y+C2>=0
...
Akx+Bky+Ck>=0

Which is the same as

x>=Q1y+P1,
...
x>=Qty+Pt,
x<=U1y+V1
...
x<=Uly+Vl

All you have to do is to determine whether there are such positive x
and y that all this inequivalences are hold.

I suppose that's enough for you to find the solution