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/* Copyright (c) 2013, Ben Noordhuis <info@bnoordhuis.nl>
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* Permission to use, copy, modify, and/or distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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#ifndef UV_SRC_HEAP_H_
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#define UV_SRC_HEAP_H_
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#include <stddef.h> /* NULL */
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# define HEAP_EXPORT(declaration) __attribute__((unused)) static declaration
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# define HEAP_EXPORT(declaration) static declaration
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struct heap_node* left;
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struct heap_node* right;
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struct heap_node* parent;
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/* A binary min heap. The usual properties hold: the root is the lowest
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* element in the set, the height of the tree is at most log2(nodes) and
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* it's always a complete binary tree.
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* The heap function try hard to detect corrupted tree nodes at the cost
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* of a minor reduction in performance. Compile with -DNDEBUG to disable.
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struct heap_node* min;
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/* Return non-zero if a < b. */
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typedef int (*heap_compare_fn)(const struct heap_node* a,
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const struct heap_node* b);
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/* Public functions. */
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HEAP_EXPORT(void heap_init(struct heap* heap));
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HEAP_EXPORT(struct heap_node* heap_min(const struct heap* heap));
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HEAP_EXPORT(void heap_insert(struct heap* heap,
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struct heap_node* newnode,
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heap_compare_fn less_than));
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HEAP_EXPORT(void heap_remove(struct heap* heap,
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struct heap_node* node,
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heap_compare_fn less_than));
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HEAP_EXPORT(void heap_dequeue(struct heap* heap, heap_compare_fn less_than));
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/* Implementation follows. */
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HEAP_EXPORT(void heap_init(struct heap* heap)) {
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HEAP_EXPORT(struct heap_node* heap_min(const struct heap* heap)) {
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/* Swap parent with child. Child moves closer to the root, parent moves away. */
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static void heap_node_swap(struct heap* heap,
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struct heap_node* parent,
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struct heap_node* child) {
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struct heap_node* sibling;
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parent->parent = child;
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if (child->left == child) {
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sibling = child->right;
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child->right = parent;
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sibling = child->left;
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sibling->parent = child;
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if (parent->left != NULL)
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parent->left->parent = parent;
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if (parent->right != NULL)
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parent->right->parent = parent;
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if (child->parent == NULL)
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else if (child->parent->left == parent)
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child->parent->left = child;
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child->parent->right = child;
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HEAP_EXPORT(void heap_insert(struct heap* heap,
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struct heap_node* newnode,
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heap_compare_fn less_than)) {
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struct heap_node** parent;
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struct heap_node** child;
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newnode->left = NULL;
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newnode->right = NULL;
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newnode->parent = NULL;
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/* Calculate the path from the root to the insertion point. This is a min
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* heap so we always insert at the left-most free node of the bottom row.
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for (k = 0, n = 1 + heap->nelts; n >= 2; k += 1, n /= 2)
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path = (path << 1) | (n & 1);
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/* Now traverse the heap using the path we calculated in the previous step. */
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parent = child = &heap->min;
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child = &(*child)->right;
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child = &(*child)->left;
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/* Insert the new node. */
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newnode->parent = *parent;
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/* Walk up the tree and check at each node if the heap property holds.
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* It's a min heap so parent < child must be true.
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while (newnode->parent != NULL && less_than(newnode, newnode->parent))
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heap_node_swap(heap, newnode->parent, newnode);
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HEAP_EXPORT(void heap_remove(struct heap* heap,
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struct heap_node* node,
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heap_compare_fn less_than)) {
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struct heap_node* smallest;
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struct heap_node** max;
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struct heap_node* child;
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if (heap->nelts == 0)
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/* Calculate the path from the min (the root) to the max, the left-most node
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for (k = 0, n = heap->nelts; n >= 2; k += 1, n /= 2)
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path = (path << 1) | (n & 1);
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/* Now traverse the heap using the path we calculated in the previous step. */
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max = &(*max)->right;
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/* Unlink the max node. */
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/* We're removing either the max or the last node in the tree. */
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if (child == heap->min) {
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/* Replace the to be deleted node with the max node. */
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child->left = node->left;
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child->right = node->right;
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child->parent = node->parent;
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if (child->left != NULL) {
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child->left->parent = child;
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if (child->right != NULL) {
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child->right->parent = child;
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if (node->parent == NULL) {
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} else if (node->parent->left == node) {
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node->parent->left = child;
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node->parent->right = child;
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/* Walk down the subtree and check at each node if the heap property holds.
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* It's a min heap so parent < child must be true. If the parent is bigger,
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* swap it with the smallest child.
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if (child->left != NULL && less_than(child->left, smallest))
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smallest = child->left;
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if (child->right != NULL && less_than(child->right, smallest))
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smallest = child->right;
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if (smallest == child)
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heap_node_swap(heap, child, smallest);
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/* Walk up the subtree and check that each parent is less than the node
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* this is required, because `max` node is not guaranteed to be the
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* actual maximum in tree
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while (child->parent != NULL && less_than(child, child->parent))
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heap_node_swap(heap, child->parent, child);
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HEAP_EXPORT(void heap_dequeue(struct heap* heap, heap_compare_fn less_than)) {
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heap_remove(heap, heap->min, less_than);
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#endif /* UV_SRC_HEAP_H_ */