I've written a short blog discussing the applications of tracking time while performing DFS. It also discusses the (partial) solution to problem E: Happy Life in University from Good Bye 2023. To help you solidify the concepts discussed, I've created 4 + 1 practice problems.You can access them here: https://codeforces.com/group/7Dn3ObOpau/contest/496216

If you're familiar with DFS, but don't know what Euler Tour and Tree Flattening mean, this tutorial is for you.

https://cfstep.com/training/tutorials/trees/timer-on-trees/