An interesting observation for rb_erase() is that when a node has
exactly one child, the node must be black and the child must be red.
An interesting consequence is that removing such a node can be done by
simply replacing it with its child and making the child black,
which we can do efficiently in rb_erase(). __rb_erase_color() then
only needs to handle the no-childs case and can be modified accordingly.
Signed-off-by: Michel Lespinasse <walken@xxxxxxxxxx>
Acked-by: Rik van Riel <riel@xxxxxxxxxx>
---
lib/rbtree.c | 105 ++++++++++++++++++++++++++++++++++------------------------
1 files changed, 62 insertions(+), 43 deletions(-)
diff --git a/lib/rbtree.c b/lib/rbtree.c
index bde1b5c5fb33..80b092538fa9 100644
--- a/lib/rbtree.c
+++ b/lib/rbtree.c
@@ -2,7 +2,8 @@
Red Black Trees
(C) 1999 Andrea Arcangeli <andrea@xxxxxxx>
(C) 2002 David Woodhouse <dwmw2@xxxxxxxxxxxxx>
-
+ (C) 2012 Michel Lespinasse <walken@xxxxxxxxxx>
+
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
@@ -50,6 +51,11 @@
#define rb_is_red(r) (!rb_color(r))
#define rb_is_black(r) rb_color(r)
+static inline void rb_set_black(struct rb_node *rb)
+{
+ rb->__rb_parent_color |= RB_BLACK;
+}
+
static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
{
rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
@@ -214,27 +220,18 @@ void rb_insert_color(struct rb_node *node, struct rb_root *root)
}
EXPORT_SYMBOL(rb_insert_color);
-static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
- struct rb_root *root)
+static void __rb_erase_color(struct rb_node *parent, struct rb_root *root)
{
- struct rb_node *sibling, *tmp1, *tmp2;
+ struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
while (true) {
/*
- * Loop invariant: all leaf paths going through node have a
- * black node count that is 1 lower than other leaf paths.
- *
- * If node is red, we can flip it to black to adjust.
- * If node is the root, all leaf paths go through it.
- * Otherwise, we need to adjust the tree through color flips
- * and tree rotations as per one of the 4 cases below.
+ * 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.
*/
- if (node && rb_is_red(node)) {
- rb_set_parent_color(node, parent, RB_BLACK);
- break;
- } else if (!parent) {
- break;
- }
sibling = parent->rb_right;
if (node != sibling) { /* node == parent->rb_left */
if (rb_is_red(sibling)) {
@@ -268,17 +265,22 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
* / \ / \
* Sl Sr Sl Sr
*
- * This leaves us violating 5), so
- * recurse at p. If p is red, the
- * recursion will just flip it to black
- * and exit. If coming from Case 1,
- * p is known to be red.
+ * 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);
- node = parent;
- parent = rb_parent(node);
- continue;
+ 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
@@ -339,9 +341,15 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
/* Case 2 - sibling color flip */
rb_set_parent_color(sibling, parent,
RB_RED);
- node = parent;
- parent = rb_parent(node);
- continue;
+ 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;
@@ -369,23 +377,31 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
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;
- int color;
+ struct rb_node *parent, *rebalance;
if (!tmp) {
- case1:
- /* Case 1: node to erase has no more than 1 child (easy!) */
+ /*
+ * 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.
+ */
parent = rb_parent(node);
- color = rb_color(node);
-
- if (child)
- rb_set_parent(child, parent);
__rb_change_child(node, child, parent, root);
+ if (child) {
+ rb_set_parent_color(child, parent, RB_BLACK);
+ rebalance = NULL;
+ } else {
+ rebalance = rb_is_black(node) ? parent : NULL;
+ }
} else if (!child) {
/* Still case 1, but this time the child is node->rb_left */
- child = tmp;
- goto case1;
+ parent = rb_parent(node);
+ __rb_change_child(node, tmp, parent, root);
+ rb_set_parent_color(tmp, parent, RB_BLACK);
+ rebalance = NULL;
} else {
struct rb_node *old = node, *left;
@@ -397,26 +413,29 @@ void rb_erase(struct rb_node *node, struct rb_root *root)
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);
}
+ if (child) {
+ rb_set_parent_color(child, parent, RB_BLACK);
+ rebalance = NULL;
+ } else {
+ rebalance = rb_is_black(node) ? parent : NULL;
+ }
node->__rb_parent_color = old->__rb_parent_color;
node->rb_left = old->rb_left;
rb_set_parent(old->rb_left, node);
}
- if (color == RB_BLACK)
- __rb_erase_color(child, parent, root);
+ if (rebalance)
+ __rb_erase_color(rebalance, root);
}
EXPORT_SYMBOL(rb_erase);
--
1.7.7.3
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