Hi everyone, I was studying how to solve query problems on trees using Euler Tour. I was wondering how to solve path query problems on trees. We can solve problems which can be solved by maintaining a prefix array (for e.g. sum of nodes in path from a to b), but how to solve say, node with maximum value in path from a to b. Can anyone guide me on this?

More specifically, sum(a, b) = sum(root, a) + sum(root, b) — 2*sum(root, lca(a, b)) + val(lca). I was using this to solve these problems using Euler Tour. But I cannot find maximum using this (CSES Path Queries 2).

Q1. Can we apply segment trees on Euler Tour array? Q2. How to solve problems like CSES Path Queries 2?