diff options
Diffstat (limited to 'lib/rbtree.c')
| -rw-r--r-- | lib/rbtree.c | 656 |
1 files changed, 350 insertions, 306 deletions
diff --git a/lib/rbtree.c b/lib/rbtree.c index d4175565dc2c..4f56a11d67fa 100644 --- a/lib/rbtree.c +++ b/lib/rbtree.c @@ -2,7 +2,8 @@ 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 @@ -20,339 +21,382 @@ linux/lib/rbtree.c */ -#include <linux/rbtree.h> +#include <linux/rbtree_augmented.h> #include <linux/export.h> -static void __rb_rotate_left(struct rb_node *node, struct rb_root *root) -{ - struct rb_node *right = node->rb_right; - struct rb_node *parent = rb_parent(node); - - if ((node->rb_right = right->rb_left)) - rb_set_parent(right->rb_left, node); - right->rb_left = node; - - rb_set_parent(right, parent); +/* + * 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. + */ - if (parent) - { - if (node == parent->rb_left) - parent->rb_left = right; - else - parent->rb_right = right; - } - else - root->rb_node = right; - rb_set_parent(node, right); +static inline void rb_set_black(struct rb_node *rb) +{ + rb->__rb_parent_color |= RB_BLACK; } -static void __rb_rotate_right(struct rb_node *node, struct rb_root *root) +static inline struct rb_node *rb_red_parent(struct rb_node *red) { - struct rb_node *left = node->rb_left; - struct rb_node *parent = rb_parent(node); - - if ((node->rb_left = left->rb_right)) - rb_set_parent(left->rb_right, node); - left->rb_right = node; - - rb_set_parent(left, parent); + return (struct rb_node *)red->__rb_parent_color; +} - if (parent) - { - if (node == parent->rb_right) - parent->rb_right = left; - else - parent->rb_left = left; - } - else - root->rb_node = left; - rb_set_parent(node, left); +/* + * 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); } -void rb_insert_color(struct rb_node *node, struct rb_root *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, *gparent; - - while ((parent = rb_parent(node)) && rb_is_red(parent)) - { - gparent = rb_parent(parent); - - if (parent == gparent->rb_left) - { - { - register struct rb_node *uncle = gparent->rb_right; - if (uncle && rb_is_red(uncle)) - { - rb_set_black(uncle); - rb_set_black(parent); - rb_set_red(gparent); - node = gparent; - continue; - } + 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; } - if (parent->rb_right == node) - { - register struct rb_node *tmp; - __rb_rotate_left(parent, root); - tmp = parent; + 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; - node = tmp; + tmp = node->rb_right; } - rb_set_black(parent); - rb_set_red(gparent); - __rb_rotate_right(gparent, root); + /* + * 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 { - { - register struct rb_node *uncle = gparent->rb_left; - if (uncle && rb_is_red(uncle)) - { - rb_set_black(uncle); - rb_set_black(parent); - rb_set_red(gparent); - node = gparent; - continue; - } + 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; } - if (parent->rb_left == node) - { - register struct rb_node *tmp; - __rb_rotate_right(parent, root); - tmp = parent; + 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; - node = tmp; + tmp = node->rb_left; } - rb_set_black(parent); - rb_set_red(gparent); - __rb_rotate_left(gparent, root); + /* 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; } } - - rb_set_black(root->rb_node); } -EXPORT_SYMBOL(rb_insert_color); -static void __rb_erase_color(struct rb_node *node, struct rb_node *parent, - struct rb_root *root) +__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 *other; - - while ((!node || rb_is_black(node)) && node != root->rb_node) - { - if (parent->rb_left == node) - { - other = parent->rb_right; - if (rb_is_red(other)) - { - rb_set_black(other); - rb_set_red(parent); - __rb_rotate_left(parent, root); - other = parent->rb_right; + 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; } - if ((!other->rb_left || rb_is_black(other->rb_left)) && - (!other->rb_right || rb_is_black(other->rb_right))) - { - rb_set_red(other); - node = parent; - parent = rb_parent(node); - } - else - { - if (!other->rb_right || rb_is_black(other->rb_right)) - { - rb_set_black(other->rb_left); - rb_set_red(other); - __rb_rotate_right(other, root); - other = parent->rb_right; + 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; } - rb_set_color(other, rb_color(parent)); - rb_set_black(parent); - rb_set_black(other->rb_right); - __rb_rotate_left(parent, root); - node = root->rb_node; - break; - } - } - else - { - other = parent->rb_left; - if (rb_is_red(other)) - { - rb_set_black(other); - rb_set_red(parent); - __rb_rotate_right(parent, root); - other = parent->rb_left; + /* + * 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; } - if ((!other->rb_left || rb_is_black(other->rb_left)) && - (!other->rb_right || rb_is_black(other->rb_right))) - { - rb_set_red(other); - node = parent; - parent = rb_parent(node); + /* + * 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; } - else - { - if (!other->rb_left || rb_is_black(other->rb_left)) - { - rb_set_black(other->rb_right); - rb_set_red(other); - __rb_rotate_left(other, root); - other = parent->rb_left; + 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; } - rb_set_color(other, rb_color(parent)); - rb_set_black(parent); - rb_set_black(other->rb_left); - __rb_rotate_right(parent, root); - node = root->rb_node; - 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; } } - if (node) - rb_set_black(node); } +EXPORT_SYMBOL(__rb_erase_color); -void rb_erase(struct rb_node *node, struct rb_root *root) -{ - struct rb_node *child, *parent; - int color; - - if (!node->rb_left) - child = node->rb_right; - else if (!node->rb_right) - child = node->rb_left; - else - { - struct rb_node *old = node, *left; - - node = node->rb_right; - while ((left = node->rb_left) != NULL) - node = left; - - if (rb_parent(old)) { - if (rb_parent(old)->rb_left == old) - rb_parent(old)->rb_left = node; - else - rb_parent(old)->rb_right = node; - } else - root->rb_node = node; - - child = node->rb_right; - parent = rb_parent(node); - color = rb_color(node); - - if (parent == old) { - parent = node; - } else { - if (child) - rb_set_parent(child, parent); - parent->rb_left = child; - - node->rb_right = old->rb_right; - rb_set_parent(old->rb_right, node); - } - - node->rb_parent_color = old->rb_parent_color; - node->rb_left = old->rb_left; - rb_set_parent(old->rb_left, node); +/* + * 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. + */ - goto color; - } +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) {} - parent = rb_parent(node); - color = rb_color(node); - - if (child) - rb_set_parent(child, parent); - if (parent) - { - if (parent->rb_left == node) - parent->rb_left = child; - else - parent->rb_right = child; - } - else - root->rb_node = child; +static const struct rb_augment_callbacks dummy_callbacks = { + dummy_propagate, dummy_copy, dummy_rotate +}; - color: - if (color == RB_BLACK) - __rb_erase_color(child, parent, root); -} -EXPORT_SYMBOL(rb_erase); - -static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data) +void rb_insert_color(struct rb_node *node, struct rb_root *root) { - struct rb_node *parent; - -up: - func(node, data); - parent = rb_parent(node); - if (!parent) - return; - - if (node == parent->rb_left && parent->rb_right) - func(parent->rb_right, data); - else if (parent->rb_left) - func(parent->rb_left, data); - - node = parent; - goto up; + __rb_insert(node, root, dummy_rotate); } +EXPORT_SYMBOL(rb_insert_color); -/* - * after inserting @node into the tree, update the tree to account for - * both the new entry and any damage done by rebalance - */ -void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data) +void rb_erase(struct rb_node *node, struct rb_root *root) { - if (node->rb_left) - node = node->rb_left; - else if (node->rb_right) - node = node->rb_right; - - rb_augment_path(node, func, data); + rb_erase_augmented(node, root, &dummy_callbacks); } -EXPORT_SYMBOL(rb_augment_insert); +EXPORT_SYMBOL(rb_erase); /* - * before removing the node, find the deepest node on the rebalance path - * that will still be there after @node gets removed + * Augmented rbtree manipulation functions. + * + * This instantiates the same __always_inline functions as in the non-augmented + * case, but this time with user-defined callbacks. */ -struct rb_node *rb_augment_erase_begin(struct rb_node *node) -{ - struct rb_node *deepest; - - if (!node->rb_right && !node->rb_left) - deepest = rb_parent(node); - else if (!node->rb_right) - deepest = node->rb_left; - else if (!node->rb_left) - deepest = node->rb_right; - else { - deepest = rb_next(node); - if (deepest->rb_right) - deepest = deepest->rb_right; - else if (rb_parent(deepest) != node) - deepest = rb_parent(deepest); - } - - return deepest; -} -EXPORT_SYMBOL(rb_augment_erase_begin); -/* - * after removal, update the tree to account for the removed entry - * and any rebalance damage. - */ -void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data) +void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, + void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) { - if (node) - rb_augment_path(node, func, data); + __rb_insert(node, root, augment_rotate); } -EXPORT_SYMBOL(rb_augment_erase_end); +EXPORT_SYMBOL(__rb_insert_augmented); /* * This function returns the first node (in sort order) of the tree. @@ -387,11 +431,13 @@ struct rb_node *rb_next(const struct rb_node *node) { struct rb_node *parent; - if (rb_parent(node) == node) + 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 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) @@ -399,12 +445,13 @@ struct rb_node *rb_next(const struct rb_node *node) 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. */ + /* + * 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; @@ -416,11 +463,13 @@ struct rb_node *rb_prev(const struct rb_node *node) { struct rb_node *parent; - if (rb_parent(node) == node) + 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 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) @@ -428,8 +477,10 @@ struct rb_node *rb_prev(const struct rb_node *node) 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 */ + /* + * 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; @@ -443,14 +494,7 @@ void rb_replace_node(struct rb_node *victim, struct rb_node *new, struct rb_node *parent = rb_parent(victim); /* Set the surrounding nodes to point to the replacement */ - if (parent) { - if (victim == parent->rb_left) - parent->rb_left = new; - else - parent->rb_right = new; - } else { - root->rb_node = new; - } + __rb_change_child(victim, new, parent, root); if (victim->rb_left) rb_set_parent(victim->rb_left, new); if (victim->rb_right) |