Updating BST, AVL tree, splay tree height member

[proven solar]

Hey I'm thinking through a project for my data structures class and I've run into a roadblock. For this project I'm implementing a BST which can also be converted to an AVL tree or splay tree so we need to update the height member of each node on insertion, but I'm not allowed to add an additional parent node pointer to the nodes. I'm wondering how I would go about updating the height member of each affected node after insertion when I'm not able to recurse back up the tree.

[shut wharf]

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[proven solar]

Updating BST, AVL tree, splay tree height member