I was reading about tree isomorphism and came across this paper. It explains an amazing algorithm developed by Aho, Hopcroft and Ullman which finds out if two rooted trees are isomorphic in linear time. I have searched for this problem on several online judges in order to test my implementation, but have had no success. If anyone has seen a problem that requires this algorithm could he/she be so kind to share the link?

Any help is appreciated :)

Something like that? Problem

Thank you for sharing. However, that is not exactly what I am looking for. That problem requires checking if two

binarytrees are isomorphic. I have actually already tested this algorithm on that problem XD. But now I want to test if my implementation works on any type of rooted tree, not only binary.I think it could help so Any type tree Problem

That is a great example too. However, in that problem, the tree is not rooted.

No, it doesn’t really matter. Can you see why?

SpoilerSimply root by centroid. If there is two choice of centroid, then just brute force for 2*2 cases.

Sorry for the possible necroposting, but there is a possible (but somewhat trivial) constant-optimization that can be done.

If the numbers of centroids do not match, the trees are not isomorphic.

If both have one centroid, it suffices to check after rooting by that centroid.

If both have two centroids, then fix one centroid in one tree and check both centroids in the other tree.

This gives a speed-up of about 2x in the worst-case :)

Hey, If there are two centroids, then aren't they adjacent and rooting them at any would result in 2 isomorphic rooted trees. So isn't it meaningless to check for each when we can choose any from the first and same for the second tree?

For example take $$$P_4$$$ and attach two vertices to one of the leaves. Centroids have different degrees so they can't result in two isomorphic rooted trees. We can get another example if we use $$$P_6$$$ instead of $$$P_4$$$. In this case rooted trees have different heights.

Hey, thank you for taking the time and helping me. I am sorry if this may sound dumb but can you please explain what $$${P_4}$$$ and $$${P_6}$$$ are.

$$$P_n$$$ stands for path of size $$$n$$$. check this (3 and 4 are centroids).

Hi, I am extremely thankful to you for taking the time again. I had wrongly read somewhere that the two centroids are similar and assumed that they should form isomorphic rooted trees. Thanks to you I understand my mistake now :))

This appeared in the Indian online regional — https://www.codechef.com/problems/TWOTREES

763D

https://cses.fi/problemset/task/1700

https://community.topcoder.com/stat?c=problem_statement&pm=13841&rd=16500

Hey,

This one isn't rooted, but by using the technique ko_osaga mentioned above, it should be reducible into it anyway. It's from a recent ICPC Regional.

Hope it helps!

Thankss ! I have long searched for something like this