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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>
468 lines
15 KiB
C
468 lines
15 KiB
C
/*
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* Copyright © 2017 Faith Ekstrand
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*
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* Permission is hereby granted, free of charge, to any person obtaining a
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* copy of this software and associated documentation files (the "Software"),
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* to deal in the Software without restriction, including without limitation
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* the rights to use, copy, modify, merge, publish, distribute, sublicense,
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* and/or sell copies of the Software, and to permit persons to whom the
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* Software is furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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* DEALINGS IN THE SOFTWARE.
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*/
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#ifndef RB_TREE_H
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#define RB_TREE_H
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#include <stdbool.h>
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#include <stddef.h>
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#include <stdint.h>
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#include <stdlib.h>
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#ifdef __cplusplus
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extern "C" {
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#endif
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/** A red-black tree node
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*
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* This struct represents a node in the red-black tree. This struct should
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* be embedded as a member in whatever structure you wish to put in the
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* tree.
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*/
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struct rb_node {
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/** Parent and color of this node
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*
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* The least significant bit represents the color and is set to 1 for
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* black and 0 for red. The other bits are the pointer to the parent
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* and that pointer can be retrieved by masking off the bottom bit and
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* casting to a pointer.
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*/
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uintptr_t parent;
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/** Left child of this node, null for a leaf */
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struct rb_node *left;
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/** Right child of this node, null for a leaf */
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struct rb_node *right;
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};
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/** Return the parent node of the given node or NULL if it is the root */
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static inline struct rb_node *
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rb_node_parent(struct rb_node *n)
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{
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return (struct rb_node *)(n->parent & ~(uintptr_t)1);
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}
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/** A red-black tree
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*
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* This struct represents the red-black tree itself. It is just a pointer
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* to the root node with no other metadata.
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*/
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struct rb_tree {
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struct rb_node *root;
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};
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/** Initialize a red-black tree */
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static inline void
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rb_tree_init(struct rb_tree *T)
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{
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T->root = NULL;
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}
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/** Returns true if the red-black tree is empty */
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static inline bool
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rb_tree_is_empty(const struct rb_tree *T)
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{
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return T->root == NULL;
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}
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/** Get the first (left-most) node in the tree or NULL */
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struct rb_node *rb_tree_first(struct rb_tree *T);
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/** Get the last (right-most) node in the tree or NULL */
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struct rb_node *rb_tree_last(struct rb_tree *T);
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/** Get the next node (to the right) in the tree or NULL */
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struct rb_node *rb_node_next(struct rb_node *node);
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/** Get the next previous (to the left) in the tree or NULL */
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struct rb_node *rb_node_prev(struct rb_node *node);
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#ifdef __cplusplus
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/* This macro will not work correctly if `t' uses virtual inheritance. */
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#define rb_tree_offsetof(t, f, p) \
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(((char *) &((t *) p)->f) - ((char *) p))
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#else
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#define rb_tree_offsetof(t, f, p) offsetof(t, f)
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#endif
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/** Retrieve the data structure containing a node
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*
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* \param type The type of the containing data structure
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*
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* \param node A pointer to a rb_node
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*
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* \param field The rb_node field in the containing data structure
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*/
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#define rb_node_data(type, node, field) \
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((type *)(((char *)(node)) - rb_tree_offsetof(type, field, node)))
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/** Insert a node into a possibly augmented tree at a particular location
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*
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* This function should probably not be used directly as it relies on the
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* caller to ensure that the parent node is correct. Use rb_tree_insert
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* instead.
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*
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* If \p update is non-NULL, it will be called for the node being inserted as
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* well as any nodes which have their children changed and all of their
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* ancestors. The intent is that each node may contain some augmented data
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* which is calculated recursively from the node itself and its children, and
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* \p update should recalculate that data. It's assumed that the function used
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* to calculate the node data is associative in order to avoid calling it
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* redundantly after rebalancing the tree.
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*
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* \param T The red-black tree into which to insert the new node
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*
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* \param parent The node in the tree that will be the parent of the
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* newly inserted node
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*
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* \param node The node to insert
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*
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* \param insert_left If true, the new node will be the left child of
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* \p parent, otherwise it will be the right child
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*
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* \param update The optional function used to calculate per-node data
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*/
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void rb_augmented_tree_insert_at(struct rb_tree *T, struct rb_node *parent,
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struct rb_node *node, bool insert_left,
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void (*update)(struct rb_node *));
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/** Insert a node into a tree at a particular location
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*
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* This function should probably not be used directly as it relies on the
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* caller to ensure that the parent node is correct. Use rb_tree_insert
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* instead.
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*
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* \param T The red-black tree into which to insert the new node
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*
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* \param parent The node in the tree that will be the parent of the
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* newly inserted node
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*
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* \param node The node to insert
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*
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* \param insert_left If true, the new node will be the left child of
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* \p parent, otherwise it will be the right child
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*/
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static inline void
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rb_tree_insert_at(struct rb_tree *T, struct rb_node *parent,
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struct rb_node *node, bool insert_left)
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{
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rb_augmented_tree_insert_at(T, parent, node, insert_left, NULL);
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}
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/** Insert a node into a possibly augmented tree
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*
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* \param T The red-black tree into which to insert the new node
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*
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* \param node The node to insert
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*
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* \param cmp A comparison function to use to order the nodes.
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*
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* \param update Same meaning as in rb_augmented_tree_insert_at()
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*/
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static inline void
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rb_augmented_tree_insert(struct rb_tree *T, struct rb_node *node,
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int (*cmp)(const struct rb_node *, const struct rb_node *),
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void (*update)(struct rb_node *))
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{
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/* This function is declared inline in the hopes that the compiler can
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* optimize away the comparison function pointer call.
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*/
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struct rb_node *y = NULL;
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struct rb_node *x = T->root;
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bool left = false;
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while (x != NULL) {
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y = x;
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left = cmp(x, node) < 0;
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if (left)
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x = x->left;
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else
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x = x->right;
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}
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rb_augmented_tree_insert_at(T, y, node, left, update);
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}
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/** Insert a node into a tree
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*
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* \param T The red-black tree into which to insert the new node
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*
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* \param node The node to insert
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*
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* \param cmp A comparison function to use to order the nodes.
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*/
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static inline void
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rb_tree_insert(struct rb_tree *T, struct rb_node *node,
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int (*cmp)(const struct rb_node *, const struct rb_node *))
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{
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rb_augmented_tree_insert(T, node, cmp, NULL);
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}
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/** Remove a node from a possibly augmented tree
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*
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* \param T The red-black tree from which to remove the node
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*
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* \param node The node to remove
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*
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* \param update Same meaning as in rb_agumented_tree_insert_at()
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*
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*/
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void rb_augmented_tree_remove(struct rb_tree *T, struct rb_node *z,
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void (*update)(struct rb_node *));
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/** Remove a node from a tree
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*
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* \param T The red-black tree from which to remove the node
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*
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* \param node The node to remove
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*/
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static inline void
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rb_tree_remove(struct rb_tree *T, struct rb_node *z)
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{
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rb_augmented_tree_remove(T, z, NULL);
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}
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/** Search the tree for a node
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*
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* If a node with a matching key exists, the first matching node found will
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* be returned. If no matching node exists, NULL is returned.
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*
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* \param T The red-black tree to search
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*
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* \param key The key to search for
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*
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* \param cmp A comparison function to use to order the nodes
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*/
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static inline struct rb_node *
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rb_tree_search(struct rb_tree *T, const void *key,
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int (*cmp)(const struct rb_node *, const void *))
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{
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/* This function is declared inline in the hopes that the compiler can
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* optimize away the comparison function pointer call.
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*/
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struct rb_node *x = T->root;
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while (x != NULL) {
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int c = cmp(x, key);
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if (c < 0) {
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x = x->left;
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} else if (c > 0) {
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x = x->right;
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} else {
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/* x is the first *encountered* node matching the key. There may
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* be other nodes in the left subtree that also match the key.
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*/
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while (true) {
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struct rb_node *prev = rb_node_prev(x);
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if (prev == NULL || cmp(prev, key) != 0)
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return x;
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x = prev;
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}
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}
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}
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return x;
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}
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/** Sloppily search the tree for a node
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*
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* This function searches the tree for a given node. If a node with a
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* matching key exists, that first encountered matching node found (there may
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* be other matching nodes in the left subtree) will be returned. If no node
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* with an exactly matching key exists, the node returned will be either the
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* right-most node comparing less than \p key or the right-most node comparing
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* greater than \p key. If the tree is empty, NULL is returned.
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*
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* \param T The red-black tree to search
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*
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* \param key The key to search for
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*
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* \param cmp A comparison function to use to order the nodes
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*/
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static inline struct rb_node *
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rb_tree_search_sloppy(struct rb_tree *T, const void *key,
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int (*cmp)(const struct rb_node *, const void *))
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{
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/* This function is declared inline in the hopes that the compiler can
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* optimize away the comparison function pointer call.
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*/
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struct rb_node *y = NULL;
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struct rb_node *x = T->root;
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while (x != NULL) {
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y = x;
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int c = cmp(x, key);
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if (c < 0)
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x = x->left;
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else if (c > 0)
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x = x->right;
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else
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return x;
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}
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return y;
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}
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#define rb_node_next_or_null(n) ((n) == NULL ? NULL : rb_node_next(n))
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#define rb_node_prev_or_null(n) ((n) == NULL ? NULL : rb_node_prev(n))
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/** Iterate over the nodes in the tree
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*
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* \param type The type of the containing data structure
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*
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* \param node The variable name for current node in the iteration;
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* this will be declared as a pointer to \p type
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*
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* \param T The red-black tree
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*
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* \param field The rb_node field in containing data structure
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*/
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#define rb_tree_foreach(type, iter, T, field) \
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for (type *iter, *__node = (type *)rb_tree_first(T); \
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__node != NULL && \
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(iter = rb_node_data(type, (struct rb_node *)__node, field), true); \
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__node = (type *)rb_node_next((struct rb_node *)__node))
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/** Iterate over the nodes in the tree, allowing the current node to be freed
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*
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* \param type The type of the containing data structure
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*
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* \param node The variable name for current node in the iteration;
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* this will be declared as a pointer to \p type
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*
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* \param T The red-black tree
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*
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* \param field The rb_node field in containing data structure
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*/
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#define rb_tree_foreach_safe(type, iter, T, field) \
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for (type *iter, \
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*__node = (type *)rb_tree_first(T), \
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*__next = (type *)rb_node_next_or_null((struct rb_node *)__node); \
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__node != NULL && \
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(iter = rb_node_data(type, (struct rb_node *)__node, field), true); \
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__node = __next, \
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__next = (type *)rb_node_next_or_null((struct rb_node *)__node))
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/** Iterate over the nodes in the tree in reverse
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*
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* \param type The type of the containing data structure
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*
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* \param node The variable name for current node in the iteration;
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* this will be declared as a pointer to \p type
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*
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* \param T The red-black tree
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*
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* \param field The rb_node field in containing data structure
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*/
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#define rb_tree_foreach_rev(type, iter, T, field) \
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for (type *iter, *__node = (type *)rb_tree_last(T); \
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__node != NULL && \
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(iter = rb_node_data(type, (struct rb_node *)__node, field), true); \
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__node = (type *)rb_node_prev((struct rb_node *)__node))
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/** Iterate over the nodes in the tree in reverse, allowing the current node to be freed
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*
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* \param type The type of the containing data structure
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*
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* \param node The variable name for current node in the iteration;
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* this will be declared as a pointer to \p type
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*
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* \param T The red-black tree
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*
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* \param field The rb_node field in containing data structure
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*/
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#define rb_tree_foreach_rev_safe(type, iter, T, field) \
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for (type *iter, \
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*__node = (type *)rb_tree_last(T), \
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*__prev = (type *)rb_node_prev_or_null((struct rb_node *)__node); \
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__node != NULL && \
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(iter = rb_node_data(type, (struct rb_node *)__node, field), true); \
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__node = __prev, \
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__prev = (type *)rb_node_prev_or_null((struct rb_node *)__node))
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/** Unsigned interval
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*
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* Intervals are closed by convention.
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*/
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struct uinterval {
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unsigned start, end;
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};
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struct uinterval_node {
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struct rb_node node;
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/* Must be filled in before inserting */
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struct uinterval interval;
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/* Managed internally by the tree */
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unsigned max_end;
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};
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/** Insert a node into an unsigned interval tree. */
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void uinterval_tree_insert(struct rb_tree *tree, struct uinterval_node *node);
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/** Remove a node from an unsigned interval tree. */
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void uinterval_tree_remove(struct rb_tree *tree, struct uinterval_node *node);
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/** Get the first node intersecting the given interval. */
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struct uinterval_node *uinterval_tree_first(struct rb_tree *tree,
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struct uinterval interval);
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/** Get the next node after \p node intersecting the given interval. */
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struct uinterval_node *uinterval_node_next(struct uinterval_node *node,
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struct uinterval interval);
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/** Iterate over the nodes in the tree intersecting the given interval
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*
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* The iteration itself should take O(k log n) time, where k is the number of
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* iterations of the loop and n is the size of the tree.
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*
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* \param type The type of the containing data structure
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*
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* \param node The variable name for current node in the iteration;
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* this will be declared as a pointer to \p type
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*
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* \param interval The interval to be tested against.
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*
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* \param T The red-black tree
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*
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* \param field The uinterval_node field in containing data structure
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*/
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#define uinterval_tree_foreach(type, iter, interval, T, field) \
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for (type *iter, *__node = (type *)uinterval_tree_first(T, interval); \
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__node != NULL && \
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(iter = rb_node_data(type, (struct uinterval_node *)__node, field), true); \
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__node = (type *)uinterval_node_next((struct uinterval_node *)__node, interval))
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/** Validate a red-black tree
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*
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* This function walks the tree and validates that this is a valid red-
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* black tree. If anything is wrong, it will assert-fail.
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*/
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void rb_tree_validate(struct rb_tree *T);
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#ifdef __cplusplus
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} /* extern C */
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#endif
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#endif /* RB_TREE_H */
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