I would like to seek help about the following problem because I find it helpful in many problems in CP:
You are given a circle and a function which takes a point on the circumference of that circle and returns a real number, you know that there's one point A on that circle which gives minimum returned value of that function and one point B which gives maximum returned value of that function, and you know that the function is increasing on the paths from point A to point B (from both direction).
You don't know where are points A and B, but you know they exist. you can call the function on whichever point you want and get the value of it, one call cost O(1) time complexity, you should find points A and B within a fixed allowed small error EPS in best complexity possible (perhaps O(log(accuracy)) ?? )
assume you don't know the exact formula of that function, and it's preferable that you don't compare the value of two points which are at distance EPS from each other because in practice sometimes it's hard to choose correct EPS.
as I mentioned before this problem can exist in many problems in CP so it's useful to know how to solve it.