Dual look-up on keys?

[castironpi at gmail.com]

On Mar 6, 2:37 am, Bryan Olson <fakeaddr... at nowhere.org> wrote:
> Grant Edwards wrote:
> > It may be  obvious that he has a question.  It's not the least
> > bit obvious what that question is.
>
> How can we efficiently implement an abstract data type, call it
> 'DoubleDict', where the state of a DoubleDict is a binary
> relation, that is, a set of pairs (x, y); and the operations on
> a DoubleDict are those on a Python set, plus:
>
>      find_by_first(self, x):  return [y where (x, y) in DoubleDict]
>
>      find_by_second(self, y):  return [x where (x, y) in DoubleDict]
>
> Python can implement this ADT directly as specified, but the
> find_by_ operations would run in time len(self).  We want an
> implementation where the find_by's run in O(1 + k) where k is
> the length of the returned sequence.
>
> --
> --Bryan

It gets hairier if you have an element that isn't a first or second
necessarily.

      find_by_other(self, x): return [y where (x, y) in DoubleDict or
(y, x) in DoubleDict]