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>
Previously rb_tree_search would return the first node encountered, but
that may not be the first node that would be encoutnered by, say,
rb_tree_foreach.
Two test cases are added.
v2: Add more curly braces. Suggested by Faith.
Reviewed-by: Faith Ekstrand <faith.ekstrand@collabora.com>
Part-of: <https://gitlab.freedesktop.org/mesa/mesa/-/merge_requests/24856>
