how to do a dictionary reverse lookup

Question

I have a dictionary of type and for a particular case, I need to do a reverse lookup. So for instance suppose I have this entry <\"S

Answer 1

1) Keys are unique, values are not. For a given value you have a set of keys.

2) Lookup by key is O(log n). Iterating with foreach or LINQ is O(n).

So,
Option A: Iterate with LINQ, spend O(n) per request, no additional memory.
Option B: Maintain Dictionary>, spend O(log n) per request, use O(n) additional memory. (There are two suboptions: build this dictionary before a series of look-ups; maintain it all the time)