Geometry Special 2018
A. Sledding down the mountain
time limit per test
12 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputSee PDF statement in attachment.
Examples
Input
1
0 0 0
1 -1 -1
1 1 1
Output
0.707106781187
Input
3
1 2 1
0 2 2
1 1 1
1 1 1
2 2 2
1 2 1
0 0 -1
1 1 1
0 2 2
Output
1.247219128925
Input
2
1 0 1
0 0 0
1 -1 -1
1 -1 -1
0 0 0
0 -1 1
Output
1.837117307087
B. Pen spinning accident
time limit per test
1 secondmemory limit per test
256 megabytesinput
standard inputoutput
standard outputSee PDF statement in attachment.
Examples
Input
1 0 0
0 0 1
1 0 0
0 1 0
0 1 0
0 0 1
Output
0.785398163397
Input
1 0 0
0 0 1
1 0 0
0 1 0
0 1 0
0 0 -1
Output
never
Input
0 0 0
1 0 0
0 1 0
0 0 1
0 1 0
-1 0 0
Output
never
Input
1 0 0
-1 0 -1
-1 0 1
0 1 0
0 1 0
0 0 1
Output
0.392699081699
Input
0 0 1
0 -1 1
0 1 1
-1 0 -1
-1 0 0
0 -1 0
Output
0.511669644114
Input
0 -1 0
-1 0 0
0 0 -1
1 0 0
0 0 -1
0 1 0
Output
0.785398163397
C. Polar map
time limit per test
8 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputSee PDF statement in attachment.
Examples
Input
3
45 0
-45 0
0 90
Output
0.269064434316
Input
6
0 90
0 180
0 -90
80 -90
80 180
80 90
Output
0.389591701512
Input
3
-85 0
-85 179
0 90
Output
0.207400294880
D. Gold paint optimization
time limit per test
10 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputSee PDF statement in attachment.
Examples
Input
2 1
2 0 0
0 2 0
Output
0.50000000
0.50000000
Input
2 2
2 0 0
10 10 10
Output
1.00000000
1.00000000
Input
2 2
2 0 0
0 1 1
Output
0.98985430
1.01014568