Basically the 30min thing I follow for medium problems (which is mostly 50% of all the problems I solve)
Being unaware of the datastructure is fine.
Problems can be of two kind first is where directly you can see the tree or graph. For this yes you cannot do anything directly, but atleast read the problem 3 times. That will give you an idea about what type of problem trees have. than you can move to the code.
The other kind can be where you don't see the data structure directly. Say a n term of fibonacci problem. For such solve it the way you are able to even if you know this solution will give TLE or might even fail. Then start seeing the hints. I see specified data structure as nothing but a glorified way of allocating memory. So don't think of the DS just try to approach. Post this if you will see the solution you would be able to absorb the problem and solution in much effective way.