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e8b3006bfd
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>
368 lines
12 KiB
C++
368 lines
12 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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#undef NDEBUG
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#include "rb_tree.h"
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#include <assert.h>
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#include <gtest/gtest.h>
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#include <limits.h>
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#include "macros.h"
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/* A list of 100 random numbers from 1 to 100. The number 30 is explicitly
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* missing from this list.
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*/
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int test_numbers[] = {
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26, 12, 35, 15, 48, 11, 39, 23, 40, 18,
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39, 15, 40, 11, 42, 2, 5, 2, 28, 8,
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10, 22, 23, 38, 47, 12, 31, 22, 26, 39,
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9, 42, 32, 18, 36, 8, 32, 29, 9, 3,
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32, 49, 23, 11, 43, 41, 22, 42, 6, 35,
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38, 48, 5, 35, 39, 44, 22, 16, 16, 32,
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31, 50, 48, 5, 50, 8, 2, 32, 27, 34,
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42, 48, 22, 47, 10, 48, 39, 36, 28, 40,
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32, 33, 21, 17, 14, 38, 27, 6, 25, 18,
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32, 38, 19, 22, 20, 47, 50, 41, 29, 50,
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};
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#define NON_EXISTANT_NUMBER 30
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struct rb_test_node {
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int key;
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struct rb_node node;
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};
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static int
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rb_test_node_cmp_void(const struct rb_node *n, const void *v)
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{
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struct rb_test_node *tn = rb_node_data(struct rb_test_node, n, node);
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return *(int *)v - tn->key;
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}
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static int
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rb_test_node_cmp(const struct rb_node *a, const struct rb_node *b)
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{
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struct rb_test_node *ta = rb_node_data(struct rb_test_node, a, node);
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struct rb_test_node *tb = rb_node_data(struct rb_test_node, b, node);
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return tb->key - ta->key;
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}
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static void
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validate_tree_order(struct rb_tree *tree, unsigned expected_count)
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{
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struct rb_test_node *prev = NULL;
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int max_val = -1;
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unsigned count = 0;
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rb_tree_foreach(struct rb_test_node, n, tree, node) {
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/* Everything should be in increasing order */
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assert(n->key >= max_val);
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if (n->key > max_val) {
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max_val = n->key;
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} else {
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/* Things should be stable, i.e., given equal keys, they should
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* show up in the list in order of insertion. We insert them
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* in the order they are in in the array.
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*/
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assert(prev == NULL || prev < n);
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}
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prev = n;
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count++;
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}
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assert(count == expected_count);
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prev = NULL;
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max_val = -1;
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count = 0;
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rb_tree_foreach_safe(struct rb_test_node, n, tree, node) {
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/* Everything should be in increasing order */
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assert(n->key >= max_val);
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if (n->key > max_val) {
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max_val = n->key;
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} else {
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/* Things should be stable, i.e., given equal keys, they should
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* show up in the list in order of insertion. We insert them
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* in the order they are in in the array.
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*/
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assert(prev == NULL || prev < n);
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}
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prev = n;
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count++;
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}
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assert(count == expected_count);
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prev = NULL;
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int min_val = INT_MAX;
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count = 0;
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rb_tree_foreach_rev(struct rb_test_node, n, tree, node) {
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/* Everything should be in increasing order */
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assert(n->key <= min_val);
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if (n->key < min_val) {
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min_val = n->key;
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} else {
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/* Things should be stable, i.e., given equal keys, they should
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* show up in the list in order of insertion. We insert them
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* in the order they are in in the array.
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*/
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assert(prev == NULL || prev > n);
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}
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prev = n;
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count++;
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}
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assert(count == expected_count);
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prev = NULL;
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min_val = INT_MAX;
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count = 0;
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rb_tree_foreach_rev_safe(struct rb_test_node, n, tree, node) {
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/* Everything should be in increasing order */
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assert(n->key <= min_val);
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if (n->key < min_val) {
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min_val = n->key;
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} else {
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/* Things should be stable, i.e., given equal keys, they should
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* show up in the list in order of insertion. We insert them
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* in the order they are in in the array.
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*/
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assert(prev == NULL || prev > n);
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}
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prev = n;
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count++;
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}
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assert(count == expected_count);
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}
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static void
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validate_search(struct rb_tree *tree, int first_number,
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int last_number)
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{
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struct rb_node *n;
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struct rb_test_node *tn;
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/* Search for all of the values */
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for (int i = first_number; i <= last_number; i++) {
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n = rb_tree_search(tree, &test_numbers[i], rb_test_node_cmp_void);
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tn = rb_node_data(struct rb_test_node, n, node);
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assert(tn->key == test_numbers[i]);
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n = rb_tree_search_sloppy(tree, &test_numbers[i],
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rb_test_node_cmp_void);
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tn = rb_node_data(struct rb_test_node, n, node);
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assert(tn->key == test_numbers[i]);
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}
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int missing_key = NON_EXISTANT_NUMBER;
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n = rb_tree_search(tree, &missing_key, rb_test_node_cmp_void);
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assert(n == NULL);
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n = rb_tree_search_sloppy(tree, &missing_key, rb_test_node_cmp_void);
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if (rb_tree_is_empty(tree)) {
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assert(n == NULL);
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} else {
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assert(n != NULL);
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tn = rb_node_data(struct rb_test_node, n, node);
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assert(tn->key != missing_key);
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if (tn->key < missing_key) {
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struct rb_node *next = rb_node_next(n);
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if (next != NULL) {
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struct rb_test_node *tnext =
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rb_node_data(struct rb_test_node, next, node);
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assert(missing_key < tnext->key);
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}
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} else {
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struct rb_node *prev = rb_node_prev(n);
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if (prev != NULL) {
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struct rb_test_node *tprev =
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rb_node_data(struct rb_test_node, prev, node);
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assert(missing_key > tprev->key);
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}
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}
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}
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}
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TEST(RBTreeTest, InsertAndSearch)
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{
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struct rb_test_node nodes[ARRAY_SIZE(test_numbers)];
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struct rb_tree tree;
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rb_tree_init(&tree);
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for (unsigned i = 0; i < ARRAY_SIZE(test_numbers); i++) {
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nodes[i].key = test_numbers[i];
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rb_tree_insert(&tree, &nodes[i].node, rb_test_node_cmp);
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rb_tree_validate(&tree);
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validate_tree_order(&tree, i + 1);
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validate_search(&tree, 0, i);
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}
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for (unsigned i = 0; i < ARRAY_SIZE(test_numbers); i++) {
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rb_tree_remove(&tree, &nodes[i].node);
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rb_tree_validate(&tree);
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validate_tree_order(&tree, ARRAY_SIZE(test_numbers) - i - 1);
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validate_search(&tree, i + 1, ARRAY_SIZE(test_numbers) - 1);
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}
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}
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TEST(RBTreeTest, FindFirst)
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{
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struct rb_test_node nodes[100];
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struct rb_tree tree;
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rb_tree_init(&tree);
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const int x = 13;
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for (unsigned i = 0; i < ARRAY_SIZE(nodes); i++) {
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nodes[i].key = x;
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rb_tree_insert(&tree, &nodes[i].node, rb_test_node_cmp);
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}
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struct rb_node *n = rb_tree_search(&tree, &x, rb_test_node_cmp_void);
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ASSERT_NE(nullptr, n);
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EXPECT_EQ(nullptr, rb_node_prev(n));
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EXPECT_EQ(n, rb_tree_first(&tree));
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}
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TEST(RBTreeTest, FindFirstOfMiddle)
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{
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struct rb_test_node nodes[3 * 33];
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struct rb_tree tree;
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rb_tree_init(&tree);
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unsigned i;
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for (i = 0; i < ARRAY_SIZE(nodes) / 3; i++) {
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nodes[i].key = i * 13;
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rb_tree_insert(&tree, &nodes[i].node, rb_test_node_cmp);
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}
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const int x = i * 13;
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for (/* empty */; i < 2 * ARRAY_SIZE(nodes) / 3; i++) {
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nodes[i].key = x;
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rb_tree_insert(&tree, &nodes[i].node, rb_test_node_cmp);
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}
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for (/* empty */; i < ARRAY_SIZE(nodes); i++) {
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nodes[i].key = i * 13;
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rb_tree_insert(&tree, &nodes[i].node, rb_test_node_cmp);
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}
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struct rb_node *n = rb_tree_search(&tree, &x, rb_test_node_cmp_void);
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ASSERT_NE(nullptr, n);
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struct rb_node *prev = rb_node_prev(n);
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ASSERT_NE(nullptr, prev);
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EXPECT_NE(rb_test_node_cmp(prev, n), 0);
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}
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struct uinterval_test_node {
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struct uinterval_node node;
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};
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static void
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validate_interval_search(struct rb_tree *tree,
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struct uinterval_test_node *nodes,
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int first_node, int last_node,
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unsigned start,
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unsigned end)
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{
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/* Count the number of intervals intersecting */
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unsigned actual_count = 0;
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for (int i = first_node; i <= last_node; i++) {
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if (nodes[i].node.interval.start <= end &&
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nodes[i].node.interval.end >= start)
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actual_count++;
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}
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/* iterate over matching intervals */
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struct uinterval interval = { start, end };
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unsigned max_val = 0;
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struct uinterval_test_node *prev = NULL;
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unsigned count = 0;
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uinterval_tree_foreach (struct uinterval_test_node, n, interval, tree, node) {
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assert(n->node.interval.start <= end &&
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n->node.interval.end >= start);
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/* Everything should be in increasing order */
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assert(n->node.interval.start >= max_val);
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if (n->node.interval.start > max_val) {
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max_val = n->node.interval.start;
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} else {
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/* Things should be stable, i.e., given equal keys, they should
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* show up in the list in order of insertion. We insert them
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* in the order they are in in the array.
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*/
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assert(prev == NULL || prev < n);
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}
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prev = n;
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count++;
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}
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assert(count == actual_count);
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}
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TEST(IntervalTreeTest, InsertAndSearch)
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{
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struct uinterval_test_node nodes[ARRAY_SIZE(test_numbers) / 2];
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struct rb_tree tree;
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rb_tree_init(&tree);
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for (unsigned i = 0; 2 * i < ARRAY_SIZE(test_numbers); i++) {
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nodes[i].node.interval.start = MIN2(test_numbers[2 * i], test_numbers[2 * i + 1]);
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nodes[i].node.interval.end = MAX2(test_numbers[2 * i], test_numbers[2 * i + 1]);
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uinterval_tree_insert(&tree, &nodes[i].node);
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rb_tree_validate(&tree);
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validate_interval_search(&tree, nodes, 0, i, 0, 100);
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validate_interval_search(&tree, nodes, 0, i, 0, 50);
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validate_interval_search(&tree, nodes, 0, i, 50, 100);
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validate_interval_search(&tree, nodes, 0, i, 0, 2);
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}
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for (unsigned i = 0; 2 * i < ARRAY_SIZE(test_numbers); i++) {
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uinterval_tree_remove(&tree, &nodes[i].node);
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rb_tree_validate(&tree);
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validate_interval_search(&tree, nodes, i + 1,
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ARRAY_SIZE(test_numbers) / 2 - 1,
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0, 100);
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validate_interval_search(&tree, nodes, i + 1,
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ARRAY_SIZE(test_numbers) / 2 - 1,
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0, 50);
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validate_interval_search(&tree, nodes, i + 1,
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ARRAY_SIZE(test_numbers) / 2 - 1,
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50, 100);
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validate_interval_search(&tree, nodes, i + 1,
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ARRAY_SIZE(test_numbers) / 2 - 1,
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0, 2);
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}
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}
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