(1) Normal Search
(2) Number of Elements less than a particular value
(3) Number of Elements greater than a particular value
(1) Persistent
(1) Dinic
(2) PushRelabel
(1) to be added ...
(2) to be added ...
Some Important Links for the same
https://www.hackerearth.com/problem/algorithm/tree-and-coprime-queries/editorial/
https://discuss.codechef.com/t/how-would-you-solve-distnum3/13989
You could check your favourites for the codeforces blog.
The implementations have been added, but require more practice to check th implementation of the codes.
There are many tricks when it comes to HLD, you should look them up here https://assets.hkoi.org/training2019/hld.pdf
Another Trick is that when there is no Update Query one can store the chain results in the form of prefix starting with the chain head. It will help slash the complexity by O (log N).
Some Important Links
https://www.quora.com/q/threadsiiithyderabad/Centroid-Decomposition-of-a-Tree