I came up on a problem and got it to solving this one, but now I am stuck. Can someone help please?

How can we efficiently count the number of regular bracket sequences with length $$$2n$$$ that have first closing bracket on position $$$k + 1$$$ (any way faster than $$$O(nk)$$$ or $$$O(n^2))$$$?

If there will be 3 or 4 rounds before rating update on problems, we'll have full empty page. Is it like a challenge that codeforces is trying?

Hello. I've been trying to understand min cost max flow algorithm for several days and now I realised I don't understand why Jonhson's potentials work. We use them so that all edges have nonnegative weights. As I remember, Jonhson's algorithm works only if there aren't any cycles with negative weight. But isn't it the criteria for optimal MCMF, that there are no negative cycles in the residual network? So, until we actually find the optimal flow, we can't use potentials as there are negative cycles. Why can we use potentials then?

Hello. I've heard there is a way to store trees using like 3 integer arrays. How exactly is it done? And can it be extended on any graph?

After rounds problems appear in the problemset and somehow get their difficulties after some time. How is the difficulty selected for a problem and what's the time needed for rating to be determined?