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-/***
- This file is part of systemd. See COPYING for details.
-
- systemd is free software; you can redistribute it and/or modify it
- under the terms of the GNU Lesser General Public License as published by
- the Free Software Foundation; either version 2.1 of the License, or
- (at your option) any later version.
-
- systemd 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
- Lesser General Public License for more details.
-
- You should have received a copy of the GNU Lesser General Public License
- along with systemd; If not, see <http://www.gnu.org/licenses/>.
-***/
-
-/*
- * RB-Tree Implementation
- * This implements the insertion/removal of elements in RB-Trees. You're highly
- * recommended to have an RB-Tree documentation at hand when reading this. Both
- * insertion and removal can be split into a handful of situations that can
- * occur. Those situations are enumerated as "Case 1" to "Case n" here, and
- * follow closely the cases described in most RB-Tree documentations. This file
- * does not explain why it is enough to handle just those cases, nor does it
- * provide a proof of correctness. Dig out your algorithm 101 handbook if
- * you're interested.
- *
- * This implementation is *not* straightforward. Usually, a handful of
- * rotation, reparent, swap and link helpers can be used to implement the
- * rebalance operations. However, those often perform unnecessary writes.
- * Therefore, this implementation hard-codes all the operations. You're highly
- * recommended to look at the two basic helpers before reading the code:
- * c_rbtree_swap_child()
- * c_rbtree_set_parent_and_color()
- * Those are the only helpers used, hence, you should really know what they do
- * before digging into the code.
- *
- * For a highlevel documentation of the API, see the header file and docbook
- * comments.
- */
-
-#include <assert.h>
-#include <stddef.h>
-#include "c-rbtree.h"
-
-enum {
- C_RBNODE_RED = 0,
- C_RBNODE_BLACK = 1,
-};
-
-static inline unsigned long c_rbnode_color(CRBNode *n) {
- return (unsigned long)n->__parent_and_color & 1UL;
-}
-
-static inline _Bool c_rbnode_is_red(CRBNode *n) {
- return c_rbnode_color(n) == C_RBNODE_RED;
-}
-
-static inline _Bool c_rbnode_is_black(CRBNode *n) {
- return c_rbnode_color(n) == C_RBNODE_BLACK;
-}
-
-/**
- * c_rbnode_leftmost() - return leftmost child
- * @n: current node, or NULL
- *
- * This returns the leftmost child of @n. If @n is NULL, this will return NULL.
- * In all other cases, this function returns a valid pointer. That is, if @n
- * does not have any left children, this returns @n.
- *
- * Worst case runtime (n: number of elements in tree): O(log(n))
- *
- * Return: Pointer to leftmost child, or NULL.
- */
-CRBNode *c_rbnode_leftmost(CRBNode *n) {
- if (n)
- while (n->left)
- n = n->left;
- return n;
-}
-
-/**
- * c_rbnode_rightmost() - return rightmost child
- * @n: current node, or NULL
- *
- * This returns the rightmost child of @n. If @n is NULL, this will return
- * NULL. In all other cases, this function returns a valid pointer. That is, if
- * @n does not have any right children, this returns @n.
- *
- * Worst case runtime (n: number of elements in tree): O(log(n))
- *
- * Return: Pointer to rightmost child, or NULL.
- */
-CRBNode *c_rbnode_rightmost(CRBNode *n) {
- if (n)
- while (n->right)
- n = n->right;
- return n;
-}
-
-/**
- * c_rbnode_next() - return next node
- * @n: current node, or NULL
- *
- * An RB-Tree always defines a linear order of its elements. This function
- * returns the logically next node to @n. If @n is NULL, the last node or
- * unlinked, this returns NULL.
- *
- * Worst case runtime (n: number of elements in tree): O(log(n))
- *
- * Return: Pointer to next node, or NULL.
- */
-CRBNode *c_rbnode_next(CRBNode *n) {
- CRBNode *p;
-
- if (!c_rbnode_is_linked(n))
- return NULL;
- if (n->right)
- return c_rbnode_leftmost(n->right);
-
- while ((p = c_rbnode_parent(n)) && n == p->right)
- n = p;
-
- return p;
-}
-
-/**
- * c_rbnode_prev() - return previous node
- * @n: current node, or NULL
- *
- * An RB-Tree always defines a linear order of its elements. This function
- * returns the logically previous node to @n. If @n is NULL, the first node or
- * unlinked, this returns NULL.
- *
- * Worst case runtime (n: number of elements in tree): O(log(n))
- *
- * Return: Pointer to previous node, or NULL.
- */
-CRBNode *c_rbnode_prev(CRBNode *n) {
- CRBNode *p;
-
- if (!c_rbnode_is_linked(n))
- return NULL;
- if (n->left)
- return c_rbnode_rightmost(n->left);
-
- while ((p = c_rbnode_parent(n)) && n == p->left)
- n = p;
-
- return p;
-}
-
-/**
- * c_rbtree_first() - return first node
- * @t: tree to operate on
- *
- * An RB-Tree always defines a linear order of its elements. This function
- * returns the logically first node in @t. If @t is empty, NULL is returned.
- *
- * Fixed runtime (n: number of elements in tree): O(log(n))
- *
- * Return: Pointer to first node, or NULL.
- */
-CRBNode *c_rbtree_first(CRBTree *t) {
- assert(t);
- return c_rbnode_leftmost(t->root);
-}
-
-/**
- * c_rbtree_last() - return last node
- * @t: tree to operate on
- *
- * An RB-Tree always defines a linear order of its elements. This function
- * returns the logically last node in @t. If @t is empty, NULL is returned.
- *
- * Fixed runtime (n: number of elements in tree): O(log(n))
- *
- * Return: Pointer to last node, or NULL.
- */
-CRBNode *c_rbtree_last(CRBTree *t) {
- assert(t);
- return c_rbnode_rightmost(t->root);
-}
-
-/*
- * Set the color and parent of a node. This should be treated as a simple
- * assignment of the 'color' and 'parent' fields of the node. No other magic is
- * applied. But since both fields share its backing memory, this helper
- * function is provided.
- */
-static inline void c_rbnode_set_parent_and_color(CRBNode *n, CRBNode *p, unsigned long c) {
- assert(!((unsigned long)p & 1));
- assert(c < 2);
- n->__parent_and_color = (CRBNode*)((unsigned long)p | c);
-}
-
-/* same as c_rbnode_set_parent_and_color(), but keeps the current color */
-static inline void c_rbnode_set_parent(CRBNode *n, CRBNode *p) {
- c_rbnode_set_parent_and_color(n, p, c_rbnode_color(n));
-}
-
-/*
- * This function partially replaces an existing child pointer to a new one. The
- * existing child must be given as @old, the new child as @new. @p must be the
- * parent of @old (or NULL if it has no parent).
- * This function ensures that the parent of @old now points to @new. However,
- * it does *NOT* change the parent pointer of @new. The caller must ensure
- * this.
- * If @p is NULL, this function ensures that the root-pointer is adjusted
- * instead (given as @t).
- */
-static inline void c_rbtree_swap_child(CRBTree *t, CRBNode *p, CRBNode *old, CRBNode *new) {
- if (p) {
- if (p->left == old)
- p->left = new;
- else
- p->right = new;
- } else {
- t->root = new;
- }
-}
-
-static inline CRBNode *c_rbtree_paint_one(CRBTree *t, CRBNode *n) {
- CRBNode *p, *g, *gg, *u, *x;
-
- /*
- * Paint a single node according to RB-Tree rules. The node must
- * already be linked into the tree and painted red.
- * We repaint the node or rotate the tree, if required. In case a
- * recursive repaint is required, the next node to be re-painted
- * is returned.
- * p: parent
- * g: grandparent
- * gg: grandgrandparent
- * u: uncle
- * x: temporary
- */
-
- /* node is red, so we can access the parent directly */
- p = n->__parent_and_color;
-
- if (!p) {
- /* Case 1:
- * We reached the root. Mark it black and be done. As all
- * leaf-paths share the root, the ratio of black nodes on each
- * path stays the same. */
- c_rbnode_set_parent_and_color(n, p, C_RBNODE_BLACK);
- n = NULL;
- } else if (c_rbnode_is_black(p)) {
- /* Case 2:
- * The parent is already black. As our node is red, we did not
- * change the number of black nodes on any path, nor do we have
- * multiple consecutive red nodes. */
- n = NULL;
- } else if (p == p->__parent_and_color->left) { /* parent is red, so grandparent exists */
- g = p->__parent_and_color;
- gg = c_rbnode_parent(g);
- u = g->right;
-
- if (u && c_rbnode_is_red(u)) {
- /* Case 3:
- * Parent and uncle are both red. We know the
- * grandparent must be black then. Repaint parent and
- * uncle black, the grandparent red and recurse into
- * the grandparent. */
- c_rbnode_set_parent_and_color(p, g, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(u, g, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(g, gg, C_RBNODE_RED);
- n = g;
- } else {
- /* parent is red, uncle is black */
-
- if (n == p->right) {
- /* Case 4:
- * We're the right child. Rotate on parent to
- * become left child, so we can handle it the
- * same as case 5. */
- x = n->left;
- p->right = n->left;
- n->left = p;
- if (x)
- c_rbnode_set_parent_and_color(x, p, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(p, n, C_RBNODE_RED);
- p = n;
- }
-
- /* 'n' is invalid from here on! */
- n = NULL;
-
- /* Case 5:
- * We're the red left child or a red parent, black
- * grandparent and uncle. Rotate on grandparent and
- * switch color with parent. Number of black nodes on
- * each path stays the same, but we got rid of the
- * double red path. As the grandparent is still black,
- * we're done. */
- x = p->right;
- g->left = x;
- p->right = g;
- if (x)
- c_rbnode_set_parent_and_color(x, g, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(p, gg, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(g, p, C_RBNODE_RED);
- c_rbtree_swap_child(t, gg, g, p);
- }
- } else /* if (p == p->__parent_and_color->left) */ { /* same as above, but mirrored */
- g = p->__parent_and_color;
- gg = c_rbnode_parent(g);
- u = g->left;
-
- if (u && c_rbnode_is_red(u)) {
- c_rbnode_set_parent_and_color(p, g, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(u, g, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(g, gg, C_RBNODE_RED);
- n = g;
- } else {
- if (n == p->left) {
- x = n->right;
- p->left = n->right;
- n->right = p;
- if (x)
- c_rbnode_set_parent_and_color(x, p, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(p, n, C_RBNODE_RED);
- p = n;
- }
-
- n = NULL;
-
- x = p->left;
- g->right = x;
- p->left = g;
- if (x)
- c_rbnode_set_parent_and_color(x, g, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(p, gg, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(g, p, C_RBNODE_RED);
- c_rbtree_swap_child(t, gg, g, p);
- }
- }
-
- return n;
-}
-
-static inline void c_rbtree_paint(CRBTree *t, CRBNode *n) {
- assert(t);
- assert(n);
-
- while (n)
- n = c_rbtree_paint_one(t, n);
-}
-
-/**
- * c_rbtree_add() - add node to tree
- * @t: tree to operate one
- * @p: parent node to link under, or NULL
- * @l: left/right slot of @p (or root) to link at
- * @n: node to add
- *
- * This links @n into the tree given as @t. The caller must provide the exact
- * spot where to link the node. That is, the caller must traverse the tree
- * based on their search order. Once they hit a leaf where to insert the node,
- * call this function to link it and rebalance the tree.
- *
- * A typical insertion would look like this (@t is your tree, @n is your node):
- *
- * CRBNode **i, *p;
- *
- * i = &t->root;
- * p = NULL;
- * while (*i) {
- * p = *i;
- * if (compare(n, *i) < 0)
- * i = &(*i)->left;
- * else
- * i = &(*i)->right;
- * }
- *
- * c_rbtree_add(t, p, i, n);
- *
- * Once the node is linked into the tree, a simple lookup on the same tree can
- * be coded like this:
- *
- * CRBNode *i;
- *
- * i = t->root;
- * while (i) {
- * int v = compare(n, i);
- * if (v < 0)
- * i = (*i)->left;
- * else if (v > 0)
- * i = (*i)->right;
- * else
- * break;
- * }
- *
- * When you add nodes to a tree, the memory contents of the node do not matter.
- * That is, there is no need to initialize the node via c_rbnode_init().
- * However, if you relink nodes multiple times during their lifetime, it is
- * usually very convenient to use c_rbnode_init() and c_rbtree_remove_init().
- * In those cases, you should validate that a node is unlinked before you call
- * c_rbtree_add().
- */
-void c_rbtree_add(CRBTree *t, CRBNode *p, CRBNode **l, CRBNode *n) {
- assert(t);
- assert(l);
- assert(n);
- assert(!p || l == &p->left || l == &p->right);
- assert(p || l == &t->root);
-
- c_rbnode_set_parent_and_color(n, p, C_RBNODE_RED);
- n->left = n->right = NULL;
- *l = n;
-
- c_rbtree_paint(t, n);
-}
-
-static inline CRBNode *c_rbtree_rebalance_one(CRBTree *t, CRBNode *p, CRBNode *n) {
- CRBNode *s, *x, *y, *g;
-
- /*
- * Rebalance tree after a node was removed. This happens only if you
- * remove a black node and one path is now left with an unbalanced
- * number or black nodes.
- * This function assumes all paths through p and n have one black node
- * less than all other paths. If recursive fixup is required, the
- * current node is returned.
- */
-
- if (n == p->left) {
- s = p->right;
- if (c_rbnode_is_red(s)) {
- /* Case 3:
- * We have a red node as sibling. Rotate it onto our
- * side so we can later on turn it black. This way, we
- * gain the additional black node in our path. */
- g = c_rbnode_parent(p);
- x = s->left;
- p->right = x;
- s->left = p;
- c_rbnode_set_parent_and_color(x, p, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(s, g, c_rbnode_color(p));
- c_rbnode_set_parent_and_color(p, s, C_RBNODE_RED);
- c_rbtree_swap_child(t, g, p, s);
- s = x;
- }
-
- x = s->right;
- if (!x || c_rbnode_is_black(x)) {
- y = s->left;
- if (!y || c_rbnode_is_black(y)) {
- /* Case 4:
- * Our sibling is black and has only black
- * children. Flip it red and turn parent black.
- * This way we gained a black node in our path,
- * or we fix it recursively one layer up, which
- * will rotate the red sibling as parent. */
- c_rbnode_set_parent_and_color(s, p, C_RBNODE_RED);
- if (c_rbnode_is_black(p))
- return p;
-
- c_rbnode_set_parent_and_color(p, c_rbnode_parent(p), C_RBNODE_BLACK);
- return NULL;
- }
-
- /* Case 5:
- * Left child of our sibling is red, right one is black.
- * Rotate on parent so the right child of our sibling is
- * now red, and we can fall through to case 6. */
- x = y->right;
- s->left = y->right;
- y->right = s;
- p->right = y;
- if (x)
- c_rbnode_set_parent_and_color(x, s, C_RBNODE_BLACK);
- x = s;
- s = y;
- }
-
- /* Case 6:
- * The right child of our sibling is red. Rotate left and flip
- * colors, which gains us an additional black node in our path,
- * that was previously on our sibling. */
- g = c_rbnode_parent(p);
- y = s->left;
- p->right = y;
- s->left = p;
- c_rbnode_set_parent_and_color(x, s, C_RBNODE_BLACK);
- if (y)
- c_rbnode_set_parent_and_color(y, p, c_rbnode_color(y));
- c_rbnode_set_parent_and_color(s, g, c_rbnode_color(p));
- c_rbnode_set_parent_and_color(p, s, C_RBNODE_BLACK);
- c_rbtree_swap_child(t, g, p, s);
- } else /* if (!n || n == p->right) */ { /* same as above, but mirrored */
- s = p->left;
- if (c_rbnode_is_red(s)) {
- g = c_rbnode_parent(p);
- x = s->right;
- p->left = x;
- s->right = p;
- c_rbnode_set_parent_and_color(x, p, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(s, g, C_RBNODE_BLACK);
- c_rbnode_set_parent_and_color(p, s, C_RBNODE_RED);
- c_rbtree_swap_child(t, g, p, s);
- s = x;
- }
-
- x = s->left;
- if (!x || c_rbnode_is_black(x)) {
- y = s->right;
- if (!y || c_rbnode_is_black(y)) {
- c_rbnode_set_parent_and_color(s, p, C_RBNODE_RED);
- if (c_rbnode_is_black(p))
- return p;
-
- c_rbnode_set_parent_and_color(p, c_rbnode_parent(p), C_RBNODE_BLACK);
- return NULL;
- }
-
- x = y->left;
- s->right = y->left;
- y->left = s;
- p->left = y;
- if (x)
- c_rbnode_set_parent_and_color(x, s, C_RBNODE_BLACK);
- x = s;
- s = y;
- }
-
- g = c_rbnode_parent(p);
- y = s->right;
- p->left = y;
- s->right = p;
- c_rbnode_set_parent_and_color(x, s, C_RBNODE_BLACK);
- if (y)
- c_rbnode_set_parent_and_color(y, p, c_rbnode_color(y));
- c_rbnode_set_parent_and_color(s, g, c_rbnode_color(p));
- c_rbnode_set_parent_and_color(p, s, C_RBNODE_BLACK);
- c_rbtree_swap_child(t, g, p, s);
- }
-
- return NULL;
-}
-
-static inline void c_rbtree_rebalance(CRBTree *t, CRBNode *p) {
- CRBNode *n = NULL;
-
- assert(t);
- assert(p);
-
- do {
- n = c_rbtree_rebalance_one(t, p, n);
- p = n ? c_rbnode_parent(n) : NULL;
- } while (p);
-}
-
-/**
- * c_rbtree_remove() - remove node from tree
- * @t: tree to operate one
- * @n: node to remove
- *
- * This removes the given node from its tree. Once unlinked, the tree is
- * rebalanced.
- * The caller *must* ensure that the given tree is actually the tree it is
- * linked on. Otherwise, behavior is undefined.
- *
- * This does *NOT* reset @n to being unlinked (for performance reason, this
- * function *never* modifies @n at all). If you need this, use
- * c_rbtree_remove_init().
- */
-void c_rbtree_remove(CRBTree *t, CRBNode *n) {
- CRBNode *p, *s, *gc, *x, *next = NULL;
- unsigned long c;
-
- assert(t);
- assert(n);
- assert(c_rbnode_is_linked(n));
-
- /*
- * There are three distinct cases during node removal of a tree:
- * * The node has no children, in which case it can simply be removed.
- * * The node has exactly one child, in which case the child displaces
- * its parent.
- * * The node has two children, in which case there is guaranteed to
- * be a successor to the node (successor being the node ordered
- * directly after it). This successor cannot have two children by
- * itself (two interior nodes can never be successive). Therefore,
- * we can simply swap the node with its successor (including color)
- * and have reduced this case to either of the first two.
- *
- * Whenever the node we removed was black, we have to rebalance the
- * tree. Note that this affects the actual node we _remove_, not @n (in
- * case we swap it).
- *
- * p: parent
- * s: successor
- * gc: grand-...-child
- * x: temporary
- * next: next node to rebalance on
- */
-
- if (!n->left) {
- /*
- * Case 1:
- * The node has no left child. If it neither has a right child,
- * it is a leaf-node and we can simply unlink it. If it also
- * was black, we have to rebalance, as always if we remove a
- * black node.
- * But if the node has a right child, the child *must* be red
- * (otherwise, the right path has more black nodes as the
- * non-existing left path), and the node to be removed must
- * hence be black. We simply replace the node with its child,
- * turning the red child black, and thus no rebalancing is
- * required.
- */
- p = c_rbnode_parent(n);
- c = c_rbnode_color(n);
- c_rbtree_swap_child(t, p, n, n->right);
- if (n->right)
- c_rbnode_set_parent_and_color(n->right, p, c);
- else
- next = (c == C_RBNODE_BLACK) ? p : NULL;
- } else if (!n->right) {
- /*
- * Case 1.1:
- * The node has exactly one child, and it is on the left. Treat
- * it as mirrored case of Case 1 (i.e., replace the node by its
- * child).
- */
- p = c_rbnode_parent(n);
- c = c_rbnode_color(n);
- c_rbtree_swap_child(t, p, n, n->left);
- c_rbnode_set_parent_and_color(n->left, p, c);
- } else {
- /*
- * Case 2:
- * We are dealing with a full interior node with a child not on
- * both sides. Find its successor and swap it. Then remove the
- * node similar to Case 1. For performance reasons we don't
- * perform the full swap, but skip links that are about to be
- * removed, anyway.
- */
- s = n->right;
- if (!s->left) {
- /* right child is next, no need to touch grandchild */
- p = s;
- gc = s->right;
- } else {
- /* find successor and swap partially */
- s = c_rbnode_leftmost(s);
- p = c_rbnode_parent(s);
-
- gc = s->right;
- p->left = s->right;
- s->right = n->right;
- c_rbnode_set_parent(n->right, s);
- }
-
- /* node is partially swapped, now remove as in Case 1 */
- s->left = n->left;
- c_rbnode_set_parent(n->left, s);
-
- x = c_rbnode_parent(n);
- c = c_rbnode_color(n);
- c_rbtree_swap_child(t, x, n, s);
- if (gc)
- c_rbnode_set_parent_and_color(gc, p, C_RBNODE_BLACK);
- else
- next = c_rbnode_is_black(s) ? p : NULL;
- c_rbnode_set_parent_and_color(s, x, c);
- }
-
- if (next)
- c_rbtree_rebalance(t, next);
-}