| /* |
| Red Black Trees |
| (C) 1999 Andrea Arcangeli <andrea@suse.de> |
| (C) 2002 David Woodhouse <dwmw2@infradead.org> |
| (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 |
| |
| linux/lib/rbtree.c |
| */ |
| |
| #include <linux/rbtree_augmented.h> |
| #include <linux/export.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. |
| */ |
| |
| 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; |
| } |
| |
| /* |
| * 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 __always_inline void |
| __rb_insert(struct rb_node *node, struct rb_root *root, |
| void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
| { |
| 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); |
| augment_rotate(parent, node); |
| 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); |
| augment_rotate(gparent, parent); |
| 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); |
| augment_rotate(parent, node); |
| 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); |
| augment_rotate(gparent, parent); |
| break; |
| } |
| } |
| } |
| |
| __always_inline void |
| __rb_erase_color(struct rb_node *parent, struct rb_root *root, |
| void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
| { |
| struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; |
| |
| while (true) { |
| /* |
| * 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); |
| augment_rotate(parent, sibling); |
| 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); |
| augment_rotate(sibling, tmp2); |
| 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); |
| augment_rotate(parent, sibling); |
| 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); |
| augment_rotate(parent, sibling); |
| 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); |
| augment_rotate(sibling, tmp2); |
| 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); |
| augment_rotate(parent, sibling); |
| break; |
| } |
| } |
| } |
| EXPORT_SYMBOL(__rb_erase_color); |
| |
| /* |
| * Non-augmented rbtree manipulation functions. |
| * |
| * We use dummy augmented callbacks here, and have the compiler optimize them |
| * out of the rb_insert_color() and rb_erase() function definitions. |
| */ |
| |
| static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} |
| static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {} |
| static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {} |
| |
| static const struct rb_augment_callbacks dummy_callbacks = { |
| dummy_propagate, dummy_copy, dummy_rotate |
| }; |
| |
| void rb_insert_color(struct rb_node *node, struct rb_root *root) |
| { |
| __rb_insert(node, root, dummy_rotate); |
| } |
| EXPORT_SYMBOL(rb_insert_color); |
| |
| void rb_erase(struct rb_node *node, struct rb_root *root) |
| { |
| rb_erase_augmented(node, root, &dummy_callbacks); |
| } |
| EXPORT_SYMBOL(rb_erase); |
| |
| /* |
| * Augmented rbtree manipulation functions. |
| * |
| * This instantiates the same __always_inline functions as in the non-augmented |
| * case, but this time with user-defined callbacks. |
| */ |
| |
| void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, |
| void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
| { |
| __rb_insert(node, root, augment_rotate); |
| } |
| EXPORT_SYMBOL(__rb_insert_augmented); |
| |
| /* |
| * 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; |
| } |
| EXPORT_SYMBOL(rb_first); |
| |
| struct rb_node *rb_last(const struct rb_root *root) |
| { |
| struct rb_node *n; |
| |
| n = root->rb_node; |
| if (!n) |
| return NULL; |
| while (n->rb_right) |
| n = n->rb_right; |
| return n; |
| } |
| EXPORT_SYMBOL(rb_last); |
| |
| struct rb_node *rb_next(const struct rb_node *node) |
| { |
| struct rb_node *parent; |
| |
| if (RB_EMPTY_NODE(node)) |
| return NULL; |
| |
| /* |
| * 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; |
| } |
| EXPORT_SYMBOL(rb_next); |
| |
| struct rb_node *rb_prev(const struct rb_node *node) |
| { |
| struct rb_node *parent; |
| |
| if (RB_EMPTY_NODE(node)) |
| return NULL; |
| |
| /* |
| * If we have a left-hand child, go down and then right as far |
| * as we can. |
| */ |
| if (node->rb_left) { |
| node = node->rb_left; |
| while (node->rb_right) |
| node=node->rb_right; |
| return (struct rb_node *)node; |
| } |
| |
| /* |
| * No left-hand children. Go up till we find an ancestor which |
| * is a right-hand child of its parent. |
| */ |
| while ((parent = rb_parent(node)) && node == parent->rb_left) |
| node = parent; |
| |
| return parent; |
| } |
| EXPORT_SYMBOL(rb_prev); |
| |
| void rb_replace_node(struct rb_node *victim, struct rb_node *new, |
| struct rb_root *root) |
| { |
| struct rb_node *parent = rb_parent(victim); |
| |
| /* Set the surrounding nodes to point to the replacement */ |
| __rb_change_child(victim, new, parent, root); |
| if (victim->rb_left) |
| rb_set_parent(victim->rb_left, new); |
| if (victim->rb_right) |
| rb_set_parent(victim->rb_right, new); |
| |
| /* Copy the pointers/colour from the victim to the replacement */ |
| *new = *victim; |
| } |
| EXPORT_SYMBOL(rb_replace_node); |
