Using red black trees for sorting

Question

The worst-case running time of insertion on a red-black tree is O(lg n) and if I perform a in-order walk on the tree, I essentially vi

Answer 1

Big-O time complexity measures do not usually take into account scalar factors, e.g., O(2n) and O(4n) are usually just reduced to O(n). Time complexity analysis is based on operational steps at an algorithmic level, not at a strict programming level, i.e., no source code or native machine instruction considerations.

Quicksort is generally faster than tree-based sorting since (1) the methods have the same algorithmic average time complexity, and (2) lookup and swapping operations require fewer program commands and data accesses when working with simple arrays than with red-black trees, even if the tree uses an underlying array-based implementation. Maintenance of the red-black tree constraints requires additional operational steps, data field value storage/access (node colors), etc than the simple array partition-exchange steps of a quicksort.

The net result is that red-black trees have higher scalar coefficients than quicksort does that are being obscured by the standard O(n log n) average time complexity analysis result.

Some other practical considerations related to machine architectures are briefly discussed in the Quicksort article on Wikipedia