Every node in a red-black tree is colored either red or black.
They guarantee O(lg n) time per access by
adjusting tree structure so that the following properties
are always maintained.
They provide an efficient binary tree-based implementation of
2,3,4-trees. (I.e. like B-trees, for B=4.
This representation is available from the last menu below.)
Every node on the resulting tree is guaranteed to have a depth less than
2 lg n in the worst case. Moreover, the required overhead
is very small: there are never more than 2
rotations required for
an insertion, and never more than m "recoloring events" in
any sequence of m insertions - i.e. a constant amount
of extra work per operation (amortized) for all the required
bookkeeping and restructuring.
- The root is always black.
- Every path on the tree, from the root down to the exterior,
has the same number of black nodes.
- No red node has a red child.
This demo begins with a "worst case" sequence of 14 insertions,
and then turns over control to the user.
Note that deletion is not yet implemented!