-/*
- * Red Black Trees
- * Copyright (C) 1999 Andrea Arcangeli <andrea@suse.de>
- * Copyright (C) 2002 David Woodhouse <dwmw2@infradead.org>
- * Copyright (C) 2012 Michel Lespinasse <walken@google.com>
- *
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation; either version 2 of the License, or
- * (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
-*/
-
-#ifdef HAVE_CONFIG_H
-# include "config.h"
-#endif
-
-#include "wimlib/rbtree.h"
-#include <stdbool.h>
-
-/*
- * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
- *
- * 1) A node is either red or black
- * 2) The root is black
- * 3) All leaves (NULL) are black
- * 4) Both children of every red node are black
- * 5) Every simple path from root to leaves contains the same number
- * of black nodes.
- *
- * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
- * consecutive red nodes in a path and every red node is therefore followed by
- * a black. So if B is the number of black nodes on every simple path (as per
- * 5), then the longest possible path due to 4 is 2B.
- *
- * We shall indicate color with case, where black nodes are uppercase and red
- * nodes will be lowercase. Unknown color nodes shall be drawn as red within
- * parentheses and have some accompanying text comment.
- */
-
-#define RB_RED 0
-#define RB_BLACK 1
-
-#define __rb_parent(pc) ((struct rb_node *)(pc & ~1))
-
-#define __rb_color(pc) ((pc) & 1)
-#define __rb_is_black(pc) __rb_color(pc)
-#define __rb_is_red(pc) (!__rb_color(pc))
-#define rb_color(rb) __rb_color((rb)->__rb_parent_color)
-#define rb_is_red(rb) __rb_is_red((rb)->__rb_parent_color)
-#define rb_is_black(rb) __rb_is_black((rb)->__rb_parent_color)
-
-static inline void
-rb_set_parent(struct rb_node *rb, struct rb_node *p)
-{
- rb->__rb_parent_color = rb_color(rb) | (uintptr_t)p;
-}
-
-static inline void
-rb_set_parent_color(struct rb_node *rb, struct rb_node *p, int color)
-{
- rb->__rb_parent_color = (uintptr_t)p | color;
-}
-
-static inline void
-rb_set_black(struct rb_node *rb)
-{
- rb->__rb_parent_color |= RB_BLACK;
-}
-
-static inline struct rb_node *
-rb_red_parent(struct rb_node *red)
-{
- return (struct rb_node *)red->__rb_parent_color;
-}
-
-static inline void
-rb_change_child(struct rb_node *old, struct rb_node *new,
- struct rb_node *parent, struct rb_root *root)
-{
- if (parent) {
- if (parent->rb_left == old)
- parent->rb_left = new;
- else
- parent->rb_right = new;
- } else
- root->rb_node = new;
-}
-
-/*
- * Helper function for rotations:
- * - old's parent and color get assigned to new
- * - old gets assigned new as a parent and 'color' as a color.
- */
-static inline void
-rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
- struct rb_root *root, int color)
-{
- struct rb_node *parent = rb_parent(old);
- new->__rb_parent_color = old->__rb_parent_color;
- rb_set_parent_color(old, new, color);
- rb_change_child(old, new, parent, root);
-}
-
-static void
-rb_erase_color(struct rb_node *parent, struct rb_root *root)
-{
- struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
-
- for (;;) {
- /*
- * Loop invariants:
- * - node is black (or NULL on first iteration)
- * - node is not the root (parent is not NULL)
- * - All leaf paths going through parent and node have a
- * black node count that is 1 lower than other leaf paths.
- */
- sibling = parent->rb_right;
- if (node != sibling) { /* node == parent->rb_left */
- if (rb_is_red(sibling)) {
- /*
- * Case 1 - left rotate at parent
- *
- * P S
- * / \ / \
- * N s --> p Sr
- * / \ / \
- * Sl Sr N Sl
- */
- parent->rb_right = tmp1 = sibling->rb_left;
- sibling->rb_left = parent;
- rb_set_parent_color(tmp1, parent, RB_BLACK);
- rb_rotate_set_parents(parent, sibling, root, RB_RED);
- sibling = tmp1;
- }
- tmp1 = sibling->rb_right;
- if (!tmp1 || rb_is_black(tmp1)) {
- tmp2 = sibling->rb_left;
- if (!tmp2 || rb_is_black(tmp2)) {
- /*
- * Case 2 - sibling color flip
- * (p could be either color here)
- *
- * (p) (p)
- * / \ / \
- * N S --> N s
- * / \ / \
- * Sl Sr Sl Sr
- *
- * This leaves us violating 5) which
- * can be fixed by flipping p to black
- * if it was red, or by recursing at p.
- * p is red when coming from Case 1.
- */
- rb_set_parent_color(sibling, parent,
- RB_RED);
- if (rb_is_red(parent))
- rb_set_black(parent);
- else {
- node = parent;
- parent = rb_parent(node);
- if (parent)
- continue;
- }
- break;
- }
- /*
- * Case 3 - right rotate at sibling
- * (p could be either color here)
- *
- * (p) (p)
- * / \ / \
- * N S --> N Sl
- * / \ \
- * sl Sr s
- * \
- * Sr
- */
- sibling->rb_left = tmp1 = tmp2->rb_right;
- tmp2->rb_right = sibling;
- parent->rb_right = tmp2;
- if (tmp1)
- rb_set_parent_color(tmp1, sibling,
- RB_BLACK);
- tmp1 = sibling;
- sibling = tmp2;
- }
- /*
- * Case 4 - left rotate at parent + color flips
- * (p and sl could be either color here.
- * After rotation, p becomes black, s acquires
- * p's color, and sl keeps its color)
- *
- * (p) (s)
- * / \ / \
- * N S --> P Sr
- * / \ / \
- * (sl) sr N (sl)
- */
- parent->rb_right = tmp2 = sibling->rb_left;
- sibling->rb_left = parent;
- rb_set_parent_color(tmp1, sibling, RB_BLACK);
- if (tmp2)
- rb_set_parent(tmp2, parent);
- rb_rotate_set_parents(parent, sibling, root, RB_BLACK);
- break;
- } else {
- sibling = parent->rb_left;
- if (rb_is_red(sibling)) {
- /* Case 1 - right rotate at parent */
- parent->rb_left = tmp1 = sibling->rb_right;
- sibling->rb_right = parent;
- rb_set_parent_color(tmp1, parent, RB_BLACK);
- rb_rotate_set_parents(parent, sibling, root,
- RB_RED);
- sibling = tmp1;
- }
- tmp1 = sibling->rb_left;
- if (!tmp1 || rb_is_black(tmp1)) {
- tmp2 = sibling->rb_right;
- if (!tmp2 || rb_is_black(tmp2)) {
- /* Case 2 - sibling color flip */
- rb_set_parent_color(sibling, parent,
- RB_RED);
- if (rb_is_red(parent))
- rb_set_black(parent);
- else {
- node = parent;
- parent = rb_parent(node);
- if (parent)
- continue;
- }
- break;
- }
- /* Case 3 - right rotate at sibling */
- sibling->rb_right = tmp1 = tmp2->rb_left;
- tmp2->rb_left = sibling;
- parent->rb_left = tmp2;
- if (tmp1)
- rb_set_parent_color(tmp1, sibling,
- RB_BLACK);
- tmp1 = sibling;
- sibling = tmp2;
- }
- /* Case 4 - left rotate at parent + color flips */
- parent->rb_left = tmp2 = sibling->rb_right;
- sibling->rb_right = parent;
- rb_set_parent_color(tmp1, sibling, RB_BLACK);
- if (tmp2)
- rb_set_parent(tmp2, parent);
- rb_rotate_set_parents(parent, sibling, root, RB_BLACK);
- break;
- }
- }
-}
-
-void
-rb_erase(struct rb_node *node, struct rb_root *root)
-{
- struct rb_node *child = node->rb_right, *tmp = node->rb_left;
- struct rb_node *parent, *rebalance;
- uintptr_t pc;
-
- if (!tmp) {
- /*
- * Case 1: node to erase has no more than 1 child (easy!)
- *
- * Note that if there is one child it must be red due to 5)
- * and node must be black due to 4). We adjust colors locally
- * so as to bypass __rb_erase_color() later on.
- */
- pc = node->__rb_parent_color;
- parent = __rb_parent(pc);
- rb_change_child(node, child, parent, root);
- if (child) {
- child->__rb_parent_color = pc;
- rebalance = NULL;
- } else
- rebalance = __rb_is_black(pc) ? parent : NULL;
- tmp = parent;
- } else if (!child) {
- /* Still case 1, but this time the child is node->rb_left */
- tmp->__rb_parent_color = pc = node->__rb_parent_color;
- parent = __rb_parent(pc);
- rb_change_child(node, tmp, parent, root);
- rebalance = NULL;
- tmp = parent;
- } else {
- struct rb_node *successor = child, *child2;
- tmp = child->rb_left;
- if (!tmp) {
- /*
- * Case 2: node's successor is its right child
- *
- * (n) (s)
- * / \ / \
- * (x) (s) -> (x) (c)
- * \
- * (c)
- */
- parent = successor;
- child2 = successor->rb_right;
- } else {
- /*
- * Case 3: node's successor is leftmost under
- * node's right child subtree
- *
- * (n) (s)
- * / \ / \
- * (x) (y) -> (x) (y)
- * / /
- * (p) (p)
- * / /
- * (s) (c)
- * \
- * (c)
- */
- do {
- parent = successor;
- successor = tmp;
- tmp = tmp->rb_left;
- } while (tmp);
- parent->rb_left = child2 = successor->rb_right;
- successor->rb_right = child;
- rb_set_parent(child, successor);
- }
-
- successor->rb_left = tmp = node->rb_left;
- rb_set_parent(tmp, successor);
-
- pc = node->__rb_parent_color;
- tmp = __rb_parent(pc);
- rb_change_child(node, successor, tmp, root);
- if (child2) {
- successor->__rb_parent_color = pc;
- rb_set_parent_color(child2, parent, RB_BLACK);
- rebalance = NULL;
- } else {
- uintptr_t pc2 = successor->__rb_parent_color;
- successor->__rb_parent_color = pc;
- rebalance = __rb_is_black(pc2) ? parent : NULL;
- }
- tmp = successor;
- }
-
- if (rebalance)
- rb_erase_color(rebalance, root);
-}
-
-void
-rb_insert_color(struct rb_node *node, struct rb_root *root)
-{
- struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
-
- while (true) {
- /*
- * Loop invariant: node is red
- *
- * If there is a black parent, we are done.
- * Otherwise, take some corrective action as we don't
- * want a red root or two consecutive red nodes.
- */
- if (!parent) {
- rb_set_parent_color(node, NULL, RB_BLACK);
- break;
- } else if (rb_is_black(parent))
- break;
-
- gparent = rb_red_parent(parent);
-
- tmp = gparent->rb_right;
- if (parent != tmp) { /* parent == gparent->rb_left */
- if (tmp && rb_is_red(tmp)) {
- /*
- * Case 1 - color flips
- *
- * G g
- * / \ / \
- * p u --> P U
- * / /
- * n N
- *
- * However, since g's parent might be red, and
- * 4) does not allow this, we need to recurse
- * at g.
- */
- rb_set_parent_color(tmp, gparent, RB_BLACK);
- rb_set_parent_color(parent, gparent, RB_BLACK);
- node = gparent;
- parent = rb_parent(node);
- rb_set_parent_color(node, parent, RB_RED);
- continue;
- }
-
- tmp = parent->rb_right;
- if (node == tmp) {
- /*
- * Case 2 - left rotate at parent
- *
- * G G
- * / \ / \
- * p U --> n U
- * \ /
- * n p
- *
- * This still leaves us in violation of 4), the
- * continuation into Case 3 will fix that.
- */
- parent->rb_right = tmp = node->rb_left;
- node->rb_left = parent;
- if (tmp)
- rb_set_parent_color(tmp, parent,
- RB_BLACK);
- rb_set_parent_color(parent, node, RB_RED);
- parent = node;
- tmp = node->rb_right;
- }
-
- /*
- * Case 3 - right rotate at gparent
- *
- * G P
- * / \ / \
- * p U --> n g
- * / \
- * n U
- */
- gparent->rb_left = tmp; /* == parent->rb_right */
- parent->rb_right = gparent;
- if (tmp)
- rb_set_parent_color(tmp, gparent, RB_BLACK);
- rb_rotate_set_parents(gparent, parent, root, RB_RED);
- break;
- } else {
- tmp = gparent->rb_left;
- if (tmp && rb_is_red(tmp)) {
- /* Case 1 - color flips */
- rb_set_parent_color(tmp, gparent, RB_BLACK);
- rb_set_parent_color(parent, gparent, RB_BLACK);
- node = gparent;
- parent = rb_parent(node);
- rb_set_parent_color(node, parent, RB_RED);
- continue;
- }
-
- tmp = parent->rb_left;
- if (node == tmp) {
- /* Case 2 - right rotate at parent */
- parent->rb_left = tmp = node->rb_right;
- node->rb_right = parent;
- if (tmp)
- rb_set_parent_color(tmp, parent,
- RB_BLACK);
- rb_set_parent_color(parent, node, RB_RED);
- parent = node;
- tmp = node->rb_left;
- }
-
- /* Case 3 - left rotate at gparent */
- gparent->rb_right = tmp; /* == parent->rb_left */
- parent->rb_left = gparent;
- if (tmp)
- rb_set_parent_color(tmp, gparent, RB_BLACK);
- rb_rotate_set_parents(gparent, parent, root, RB_RED);
- break;
- }
- }
-}
-
-static struct rb_node *
-rb_left_deepest_node(const struct rb_node *node)
-{
- for (;;) {
- if (node->rb_left)
- node = node->rb_left;
- else if (node->rb_right)
- node = node->rb_right;
- else
- return (struct rb_node *)node;
- }
-}
-
-struct rb_node *
-rb_next_postorder(const struct rb_node *node, const struct rb_node *parent)
-{
- /* If we're sitting on node, we've already seen our children */
- if (parent && node == parent->rb_left && parent->rb_right) {
- /* If we are the parent's left node, go to the parent's right
- * node then all the way down to the left */
- return rb_left_deepest_node(parent->rb_right);
- } else
- /* Otherwise we are the parent's right node, and the parent
- * should be next */
- return (struct rb_node *)parent;
-}
-
-struct rb_node *
-rb_first_postorder(const struct rb_root *root)
-{
- if (!root->rb_node)
- return NULL;
-
- return rb_left_deepest_node(root->rb_node);
-}
-
-struct rb_node *
-rb_next(const struct rb_node *node)
-{
- struct rb_node *parent;
-
- /*
- * If we have a right-hand child, go down and then left as far
- * as we can.
- */
- if (node->rb_right) {
- node = node->rb_right;
- while (node->rb_left)
- node = node->rb_left;
- return (struct rb_node *)node;
- }
-
- /*
- * No right-hand children. Everything down and left is smaller than us,
- * so any 'next' node must be in the general direction of our parent.
- * Go up the tree; any time the ancestor is a right-hand child of its
- * parent, keep going up. First time it's a left-hand child of its
- * parent, said parent is our 'next' node.
- */
- while ((parent = rb_parent(node)) && node == parent->rb_right)
- node = parent;
-
- return parent;
-}
-
-/*
- * This function returns the first node (in sort order) of the tree.
- */
-struct rb_node *
-rb_first(const struct rb_root *root)
-{
- struct rb_node *n;
-
- n = root->rb_node;
- if (!n)
- return NULL;
- while (n->rb_left)
- n = n->rb_left;
- return n;
-}