f(x) = f(y)+f(x-y)+2y (1<=y<=x/2) f(1)=1

i know that f is about xlogx when y is x/2

but i cant prove xlogx is maximum

can someone help me? why cant it be bigger?

Can i determine whether the size of minimum vertex cover of general graph is less than 3 or not within 2 seconds where V,E <= 5* 10^4 ??

Thank you

here's example problems.

https://www.codechef.com/START21B/problems/MSUB121

https://atcoder.jp/contests/abc219/tasks/abc219_g

is there any tag or name for n*sqrt(n) problems? or are they just ad-hoc? i can't even approach to these type of problems during the contest. i wanna practice but i don't know what to search.

Q : is there any tag or category for type of problems above? or any tutorial blogs for those

There is simple undirected graph with n vertices and m edges. ( N<=10 , m<=n*(n-1)/2 ) At most how many edges can we pick so that in graph with n vertices and edges we picked, degree of every vertices is equal or less than P. ( P <= n-1 )

I know this problem is about bitmask dp but i cant figure out dp-state.

Is there any hint or similar problem in codeforces or atcoder?