A topic that I have come up with, which I personally think is quite interesting, but its feasibility is unknown.

First Of All,If the solution provider can provide ideas and code and can verify the correctness (of course, I will try my best to hack your solution, of course, I will give you the corresponding data range according to your practice, and such polygon points should exceed a certain number, perhaps more than 10 points, with a certain adaptability), if you are a Codeforces Coder in Chinese Mainland, I will contact you and give you rand (100-300) RMB to thank you for your contribution. (Although this is not a high sum of money, it contains my persistence in this problem. I will give a certain amount of money based on the superiority of the solution)

Question description:

Here is an arbitrary polygon, with each corner size ranging from 0 to 360 degrees. I hope you can find a strictly convex polygon that is completely contained within this polygon, so that the area of this convex polygon is maximized. You only need to calculate the value of this area.

Of course, since I don't have any effective methods, and I can't determine which interval corresponds to the correct method for the number of points in this polygon. But I'll give you some pictures to understand the meaning of this question.

If the two polygons given in this figure are assumed to be the same, then both extraction schemes for convex polygons may be optimal. Is there a universal construction algorithm or other technology that can solve this problem?

As shown in the figure, the definition of a convex hull is that for a polygon, the degree of each interior angle is between 0 and 180 degrees.

Here are some other examples as well：

Perhaps my computational geometry is not profound enough, and I hardly believe that there is a solution to this problem.If you don't like this question, please don't Downvote. Thank you~