I talked to @admin regarding that. I dont think it will help much, since the polygons in that TC arent “small”. Example, one of the cases where many solutions failed was-
Basic idea is, huge change in x axis with very small change in y axis. Your code passed this TC though, but quite many failed at it (esp those who took mid points)
We can create a square, which is convex, with corners at (\pm 1, \pm 1). The only internal integer point is at (0,0), but doesn’t have the form (x \pm 1, y) or (x, y \pm 1).
A more general counter-example follows from multiplying the points in the sample data by some matrix like \left( \begin{matrix} 1000 & 999999 \\ 1 & 1000 \end{matrix}\right). The result is a long narrow convex polygon. The internal integer points are not close to the vertices.
If the original points form a convex polygon, then so do the transformed points. Internal grid points of the original polygon will transform 1-to-1 onto the internal grid points of the transformed polygon.
See also the comment by @alexthelemon. There he takes a possibly long thin triangle and transforms it to a nicer shape where it is easy to find the internal grid points.