10078 - The Art Gallery
It's easy to see (and prove) that a convex polygon satisfy the condition. An easy way to test if a polygon is convex or not is by walking the perimeter. If a polygon is a convex polygon, you can walk around the perimeter, and you will either keep turning left (counterclockwise) or turning right (clockwise). If a polygon does both, then there must be a reflex vertex, and thus not convex.
- The order is not given, and needs to be figured out.
4 0 0 3 0 3 3 0 3 4 0 0 3 0 1 1 0 3 0