# UVa 10078

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## 10078 - The Art Gallery[edit]

## Summary[edit]

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

## Explanation[edit]

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[edit]

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

## Input[edit]

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

## Output[edit]

No Yes