Subtree Queries with Euler Tour

With Euler tour, subtree operations become range operations:

Subtree sum of v: query range $[tin[v], tout[v]]$

Update node v: update position $tin[v]$

Add x to all nodes in subtree of v: range update $[tin[v], tout[v]]$

Build a segment tree on the tour array.

Each node's value is stored at its $tin$ position. Time: $O(n)$ for tour construction, $O(\log n)$ per query/update. Space: $O(n)$.