# Voronoi diagram implementation using Delaunay Triangulation

I am trying to implement Voronoi diagram using Delaunay Triangulation as the dual of Delaunay Triangulation is Voronoi diagram. I have a little bit confusion about the time complexity of it considering two different approach. One is, if I insert the points in Delaunay triangulation at a random sorted order and if not. Does the random ordering of input before inserting into triangulation ensures a better $O(n\log n)$ running time all the times? what is the main difference between these two approaches?

It depends on the details of your implementation. The easiest methods have a worst case complexity of $O(n^2)$, but average $O(n \log n)$.
It is worth noting that it is possible to write a fully deterministic version of the algorithm with $O(n\log n)$ worst case runtime. But that makes the code quite a bit more complex, so it might well not be worth the trouble.