Building Red-Black Tree from sorted array in linear time

Question

i know how to build it with n insertions ( each with O(log(n)) efficiency ) (n*log(n)) overall ,i also know that the equivalent structure of 2-3-4 tree can also be build wit

Answer 1

A complete binary tree of height H has 2^H-1 nodes.

To make a red black tree from a sorted list:

1. Remove every second item from the list until you have 2^H-1 items remaining for some H. Note that you will always have enough.
2. Build a complete tree out of the remaining items, all black.
3. Now attach all the items you removed to the tree. Each item will be a red node, attached to whichever of the black nodes around its proper position is a leaf.

The easiest way to do step (3) is just to do a pre-order traversal of the tree, attaching new red nodes to every black leaf until you run out of items.

NOTE: Sasha's algorithm also works, but this one obviously works.