next up previous
Next: Up: Previous:

Solution:

Use Augmented Red-Black Trees.

Define an order statistic tree as a Red-Black tree with an added size(x) field that contains the number of internal nodes in the subtree rooted at node x, where

size(x) = \(\left\{ \begin{array}{ll} 0 & {\rm if} \; x=NIL \\ 1 \;+\; size(left(x)) \;+\; size(right(x)) & {\rm otherwise} \end{array} \right.\)

next up previous
Next: Up: Previous: