Do This
This program creates a variable counter and then uses the counter pattern to make it count up. When you run the program what do you think you'll see on the screen?
Read the program and make a prediction of what the output will be.
Run the program to check your prediction.
Discuss with a neighbor. Can you explain what you observed?

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In many applications, only a small percentage of the points in a given set p of n points are extreme. in such a case, the convex hull of p has less than n vertices. this can actually make our algorithm convexhull run faster than θ(nlogn). assume, for instance, that the expected number of extreme points in a random sample of p of size r is o(rα ), for some constant α < 1. (this is true when the set p has been created by picking points uniformly at random in a ball.) prove that under this condition, the running time of the algorithm is o(n).