Can a red black tree be augmented with a field that gives the height o a node in

Question

Can a red black tree be augmented with a field that gives the height o a node in the tree without adversely affecting the lg(n) run time of insertiona nd deletion? Recall that insertion and deletion may require rotations which change the height of the node in the tree.

What about depth?

Could someone please answer these questios and possibly give me a diagram explaining why? I'm not very familiar with red black trees and this isn't a homework question. It's just review and I want to understand it.

Thank you so much for your time.

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Can a red black tree be augmented with a field that gives the height o a node in

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