P6902 [ICPC 2014 WF] Surveillance

The International Corporation for Protection and Control (ICPC) develops efficient technology for, well, protection and control. Naturally, they are keen to have their own headquarters protected and controlled. Viewed from above, the headquarters building has the shape of a convex polygon. There are several suitable places around it where cameras can be installed to monitor the building. Each camera covers a certain range of the polygon sides (building walls), depending on its position. ICPC wants to minimize the number of cameras needed to cover the whole building.

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Time limit: 4000 ms, Memory limit: 1048576 kB. International Collegiate Programming Contest (ACM-ICPC) World Finals 2014