UVa 361 - Cops and Robbers

Summary
Cops, Robbers and Civilians are placed within a world. Given the coordinates of each entity, determine the status of each civilian; it is safe if it is contained within a triangle of three cops, robbed if it is not safe and within a triangle of three robbers, and neither if otherwise.

Explanation
A citizen is safe if it is in the convex Hull formed by all cops. Cops inside that hull are irrelevant to this problem.

The convex hull formed by all robbers is also relevant. Robbers inside that hull are irrelevant to this problem.

Gotchas
What if a citizen is exactly on the line of the convex hull?

Implementations
Notes/Hints on actual implementation here.

Optimizations
Optimizations here.

Input
3 3 2 0 0 10 0 0 10 20 20 20 0 0 20 5 5 15 15 3 3 1 0 0 10 0 0 10 20 20 20 0 0 20 40 40 0 0 0

Output
Data set 1: Citizen at (5,5) is safe. Citizen at (15,15) is robbed.

Data set 2: Citizen at (40,40) is neither.