Path Queries - Implementation

Here's the structure:

function solve(tree, values, queries)
    // Build HLD
    buildHLD(root)

    // Initialize segment tree with node values
    arr := array of size n
    for each node v
        arr[pos[v]] := values[v]
    buildSegmentTree(arr)

    for each query
        if query is update(u, newVal) then
            segmentTreeUpdate(pos[u], newVal)
        else // query is pathMax(u, v)
            print pathMax(u, v)

The segment tree stores values at their HLD positions. Updates modify a single position. Queries combine multiple ranges.