A data-structure for 1:1 mappings in python?

I have a problem which requires a reversable 1:1 mapping of keys to values.

That means sometimes I want to find the value given a key, but at other times I want to find the key given the value. Both keys and values are guaranteed unique.

x = D[y]
y == D.inverse[x]

The obvious solution is to simply invert the dictionary every time I want a reverse-lookup: Inverting a dictionary is very easy, there's a recipe here but for a large dictionary it can be very slow.

The other alternative is to make a new class which unites two dictionaries, one for each kind of lookup. That would most likely be fast but would use up twice as much memory as a single dict.

So is there a better structure I can use?

• My application requires that this should be very fast and use as little as possible memory.
• The structure must be mutable, and it's strongly desirable that mutating the object should not cause it to be slower (e.g. to force a complete re-index)
• We can guarantee that either the key or the value (or both) will be an integer
• It's likely that the structure will be needed to store thousands or possibly millions of items.
• Keys & Valus are guaranteed to be unique, i.e. len(set(x)) == len(x) for for x in [D.keys(), D.valuies()]

class TwoWay:
    def __init__(self):
       self.d = {}
    def add(self, k, v):
       self.d[k] = v
       self.d[v] = k
    def remove(self, k):
       self.d.pop(self.d.pop(k))
    def get(self, k):
       return self.d[k]