given a polygon P, i want to calculate the area of the polygon.
my solution: find a triangulation, and sum all the area of the triangles.
Total time complexity: o(nlogn).
Does there exist a better solution?
You don't need to explicitly decompose, use the shoelace formula. It is easy and O(n).
https://en.wikipedia.org/wiki/Shoelace_formula
The method generalizes to the computation of geometric moments
https://en.wikipedia.org/wiki/Second_moment_of_area#Any_polygon