What sequence of broken line’s vertexes  should print my program? Give me some hints or tests.

Just find a convex octagon of minimal area which satisfyes the following conditions:

- all the points given are inside it or lay on it's borders
- it's 2 sides are parallel to oX (-)
- it's 2 sides are parallel to oY (|)
- it's 2 sides are 45 degrees to oX (/)
- it's 2 sides are -45 degrees to oX (\)

And then output all the vertices of this figure. There could be 8 vertices, but some of them might be the same (some sides has zero length), so output them only once. So your output is from 1 till 8 vertices.

Very easy statistical solution is O(N) time, O(1) memory.

P.S. I will answer any your question - just mail me.

I can only understand the problem statement after reading this thread...

Thanks so much!

Area should not be minimal, the number of points inside convex polygon should be minimal, in other words, try so that more points lie on the boundary rather than inside the polygon.