What does it mean for two binary trees to be isomorphic?

Question

What does it mean for two binary trees to be isomorphic? I\'ve been looking online and I can\'t seem to find a clear explanation.

As far as I understand, two trees

Answer 1

I think your understanding is pretty much correct. If you ignore the values and just look at the structure, then for every node in the first tree there must be a corresponding node in the other tree and vice versa.

Naturally, both trees would have the same number of nodes. In addition, you could write a (super-naive) algorithm to confirm this isomorphism by attempting all possible mapping functions, and ensuring that for every node in the first tree that gets mapped to a node in the other, the corresponding mapping happens with the parent and with the two children. There are obviously efficient algorithms to check for this.

You may benefit from reading about graph isomorphism first; trees are a special (and easier to solve) case since they do not have cycles.