An "augmented tree" is a tree with extra data attached which flows from
the leaves to the root. An "interval tree" is a datastructure of
(potentially-overlapping) intervals where, in addition to inserting and
removing intervals, we can quickly lookup all the intervals which
overlap a given interval.
After describing red-black trees, CLRS explains how it's possible to
implement an interval tree using an augmented red-black tree where the
nodes are ordered by interval start and each node also stores the
maximum interval end for its entire subtree.
Implement the interval tree extension described by CLRS. Iterating over
all overlapping intervals is actually an exercise, so we have to solve
the exercise. The recursive solution has been re-written to use the
parent pointers to avoid needing a stack, similarly to rb_tree_first()
and rb_node_next().
For now, we only implement unsigned intervals, but the core algorithms
are all abstracted to allow other types. There's still some boilerplate,
but it's the best that can be done in C.
Part-of: <https://gitlab.freedesktop.org/mesa/mesa/-/merge_requests/22071>
This is a simple, invasive, liberally licensed red-black tree
implementation. It's an invasive data structure similar to the
Linux kernel linked-list where the intention is that you embed a
rb_node struct the data structure you intend to put into the
tree.
The implementation is mostly based on the one in "Introduction to
Algorithms", third edition, by Cormen, Leiserson, Rivest, and
Stein. There were a few other key design points:
* It's an invasive data structure similar to the [Linux kernel
linked list].
* It uses NULL for leaves instead of a sentinel. This means a few
algorithms differ a small bit from the ones in "Introduction to
Algorithms".
* All search operations are inlined so that the compiler can
optimize away the function pointer call.
Reviewed-by: Lionel Landwerlin <lionel.g.landwerlin@intel.com>
