Node Structure

Full node structure for Link-Cut tree with path aggregates:

class Node:
    // Tree structure
    left, right: Node
    parent: Node

    // Value and aggregates
    value: int
    subtreeSum: int // or min, max, etc.
    subtreeSize: int

    // Lazy propagation
    lazy: int // pending add
    reversed: bool // pending reversal

    function isRoot()
        // Root of auxiliary tree: parent is null or parent doesn't point back
        return parent is null or (parent.left != this and parent.right != this)

The isRoot check is subtle: a node can have a parent (path-parent) but still be root of its auxiliary tree.