I think the correct output for the example should be:
YES
YES
YES
NO
NO
NO
NO       //not YES
NO
YES

if  I am wrong plz tell me why


this is the way i thought of solving the problem

STEP 1:
--sort the contestants in descending order:
  after v     |        after W    |     after u
10 2 6        |        1 8 7      |      5 6 7
10 7 3        |        10 7 3     |     3 2 7
10 4 2        |        5 6 7      |     3 5 7
8 4 6         |        3 5 7      |     1 8 7
6 2 6         |        8 4 6      |     10 2 6
5 6 7         |        10 4 2     |     6 2 6
3 2 7         |        10 2 6     |     8 4 6
3 5 7         |        3 2 7      |     10 7 3
1 8 7         |        6 2 6      |     10 4 2

STEP 2:
--only the first of each sort might be winners
=>
after v  |   after w    |   after u
10 2 6   |   1 8 7      |  5 6 7
10 7 3   |              |  3 2 7
10 4 2   |              |  3 5 7
         |              |  1 8 7

STEP 3:
--I sort the three columns after the other 2 speeds
column 1 --after w and than u
         --after u and than w
column 2 ...

STEP 4:
-- the first of  every sort is surely a winner

in conclusion i sort the competitors after:
vwu
vuw
wvu
wuv
uvw
uwv
and the first of every sort is a winner


hope you cold understand me :)

PS:
-if you have a nother idea post it plz
-if the example is ok than plz tell me why


Edited by author 20.02.2005 18:51

STEP 2 is wrong. Try this:

4
100 100 1
100 1 100
1 100 100
50 50 50

The answer should be:
YES
YES
YES
YES!!!

A my idea.
We should find answer for the first contestant.
a[i] b[i] c[i] - is the speeds.
x y z - the lengths.
Write inequation describing that first contestant will win over i-th:
(1/a[1] - 1/a[i])x + (1/b[1] - 1/b[i])y + (1/c[1] - 1/c[i])z < 0
Then, we should answer: are exist such x, y and z, that satisfy this inequations for each i > 1?

Edited by author 30.03.2005 19:31

Ok, and which algo can answer on this question?