UVa 10078 - The Art Gallery

Summary
A polygon without any critical points is a convex polygon. This problem reduce to finding out rather a polygon is convex or not.

Explanation
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.

Gotcha's

 * The order is not given, and needs to be figured out.

Input
4 0 0 3 0 3 3 0 3 4 0 0 3 0 1 1 0 3 0

Output
No Yes

Solutions

 * Code All the Problems