Step 1. Given n points in the plane, create an algorithm that constructs any simply polygon having those points as vertices. Prove that your resulting polygon is simple (no self intersections), and uses all points. Our strategy is to make a plan where we are sure that the polygon includes all points, and that we can find an order to connect them where none of the lines intersect.
Step 2. Repeat the step 1 for different set of points and compare these polygons in memory and return the left over polygons
PS: I am looking for solution to the above algorithm.