Q:

What is the maximum attainable height of a red-black tree with black-height k and why?

What is attainable height in red-black tree? Is it the height of the tree? I have read the wiki of it but still have no clue. Thank you.

A:

Since a node of height h has black-height >= h/2, the answer should be 2k.
Black Height of a Red-Black Tree :
Black height is number of black nodes on a path from a node to a leaf. Leaf nodes are also counted black nodes. From above properties 3 and 4, we can derive, a node of height h has black-height >= h/2.

