Reading trees and strings fast

A tree with q queries on paths = LCA family. If values never change, root-distance prefixes + LCA finish it; updates push you to HLD or Euler + BIT on subtrees. "For every node" output = one postorder DFS; if the answer for a child's parent depends on the child, it is tree DP.

A string asking "what repeats" = borders and failure functions. The KMP failure array answers period, borders, and occurrence counting in one preprocessing pass. If the question is "how many distinct", expect suffix structures or hashing instead.