You learned Heavy-Light Decomposition, a technique that splits a tree into chains. By choosing heavy edges based on subtree size, you guarantee that any path crosses at most chains. You combined HLD with segment trees to answer path queries in and updates in .
You handled both vertex and edge queries by storing edge weights at child nodes. You solved CSES Path Queries II (path maximum) and SPOJ QTREE (edge updates and queries). This technique works for any associative operation: sum, min, max, GCD, XOR. Next: more tree techniques.