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@@ -0,0 +1,507 @@
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+
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+#include "rbtree.h"
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+#include <stdbool.h>
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+
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+static inline void rb_set_black(struct rb_node *rb)
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+{
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+ rb->__rb_parent_color |= RB_BLACK;
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+}
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+
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+static inline struct rb_node *rb_red_parent(struct rb_node *red)
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+{
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+ return (struct rb_node *)red->__rb_parent_color;
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+}
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+
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+/*
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+ * Helper function for rotations:
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+ * - old's parent and color get assigned to new
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+ * - old gets assigned new as a parent and 'color' as a color.
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+ */
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+static inline void
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+__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
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+ struct rb_root *root, int color)
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+{
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+ struct rb_node *parent = rb_parent(old);
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+ new->__rb_parent_color = old->__rb_parent_color;
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+ rb_set_parent_color(old, new, color);
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+ __rb_change_child(old, new, parent, root);
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+}
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+
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+static inline void
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+__rb_insert(struct rb_node *node, struct rb_root *root,
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+ void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
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+{
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+ struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
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+
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+ while (true) {
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+ /*
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+ * Loop invariant: node is red
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+ *
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+ * If there is a black parent, we are done.
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+ * Otherwise, take some corrective action as we don't
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+ * want a red root or two consecutive red nodes.
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+ */
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+ if (!parent) {
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+ rb_set_parent_color(node, NULL, RB_BLACK);
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+ break;
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+ } else if (rb_is_black(parent))
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+ break;
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+
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+ gparent = rb_red_parent(parent);
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+
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+ tmp = gparent->rb_right;
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+ if (parent != tmp) { /* parent == gparent->rb_left */
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+ if (tmp && rb_is_red(tmp)) {
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+ /*
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+ * Case 1 - color flips
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+ *
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+ * G g
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+ * / \ / \
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+ * p u --> P U
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+ * / /
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+ * n n
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+ *
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+ * However, since g's parent might be red, and
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+ * 4) does not allow this, we need to recurse
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+ * at g.
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+ */
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+ rb_set_parent_color(tmp, gparent, RB_BLACK);
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+ rb_set_parent_color(parent, gparent, RB_BLACK);
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+ node = gparent;
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+ parent = rb_parent(node);
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+ rb_set_parent_color(node, parent, RB_RED);
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+ continue;
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+ }
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+
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+ tmp = parent->rb_right;
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+ if (node == tmp) {
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+ /*
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+ * Case 2 - left rotate at parent
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+ *
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+ * G G
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+ * / \ / \
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+ * p U --> n U
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+ * \ /
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+ * n p
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+ *
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+ * This still leaves us in violation of 4), the
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+ * continuation into Case 3 will fix that.
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+ */
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+ parent->rb_right = tmp = node->rb_left;
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+ node->rb_left = parent;
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+ if (tmp)
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+ rb_set_parent_color(tmp, parent,
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+ RB_BLACK);
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+ rb_set_parent_color(parent, node, RB_RED);
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+ augment_rotate(parent, node);
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+ parent = node;
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+ tmp = node->rb_right;
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+ }
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+
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+ /*
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+ * Case 3 - right rotate at gparent
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+ *
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+ * G P
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+ * / \ / \
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+ * p U --> n g
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+ * / \
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+ * n U
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+ */
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+ gparent->rb_left = tmp; /* == parent->rb_right */
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+ parent->rb_right = gparent;
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+ if (tmp)
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+ rb_set_parent_color(tmp, gparent, RB_BLACK);
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+ __rb_rotate_set_parents(gparent, parent, root, RB_RED);
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+ augment_rotate(gparent, parent);
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+ break;
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+ } else {
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+ tmp = gparent->rb_left;
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+ if (tmp && rb_is_red(tmp)) {
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+ /* Case 1 - color flips */
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+ rb_set_parent_color(tmp, gparent, RB_BLACK);
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+ rb_set_parent_color(parent, gparent, RB_BLACK);
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+ node = gparent;
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+ parent = rb_parent(node);
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+ rb_set_parent_color(node, parent, RB_RED);
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+ continue;
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+ }
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+
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+ tmp = parent->rb_left;
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+ if (node == tmp) {
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+ /* Case 2 - right rotate at parent */
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+ parent->rb_left = tmp = node->rb_right;
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+ node->rb_right = parent;
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+ if (tmp)
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+ rb_set_parent_color(tmp, parent,
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+ RB_BLACK);
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+ rb_set_parent_color(parent, node, RB_RED);
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+ augment_rotate(parent, node);
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+ parent = node;
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+ tmp = node->rb_left;
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+ }
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+
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+ /* Case 3 - left rotate at gparent */
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+ gparent->rb_right = tmp; /* == parent->rb_left */
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+ parent->rb_left = gparent;
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+ if (tmp)
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+ rb_set_parent_color(tmp, gparent, RB_BLACK);
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+ __rb_rotate_set_parents(gparent, parent, root, RB_RED);
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+ augment_rotate(gparent, parent);
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+ break;
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+ }
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+ }
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+}
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+
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+/*
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+ * Inline version for rb_erase() use - we want to be able to inline
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+ * and eliminate the dummy_rotate callback there
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+ */
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+static inline void
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+____rb_erase_color(struct rb_node *parent, struct rb_root *root,
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+ void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
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+{
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+ struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
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+
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+ while (true) {
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+ /*
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+ * Loop invariants:
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+ * - node is black (or NULL on first iteration)
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+ * - node is not the root (parent is not NULL)
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+ * - All leaf paths going through parent and node have a
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+ * black node count that is 1 lower than other leaf paths.
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+ */
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+ sibling = parent->rb_right;
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+ if (node != sibling) { /* node == parent->rb_left */
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+ if (rb_is_red(sibling)) {
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+ /*
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+ * Case 1 - left rotate at parent
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+ *
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+ * P S
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+ * / \ / \
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+ * N s --> p Sr
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+ * / \ / \
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+ * Sl Sr N Sl
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+ */
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+ parent->rb_right = tmp1 = sibling->rb_left;
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+ sibling->rb_left = parent;
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+ rb_set_parent_color(tmp1, parent, RB_BLACK);
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+ __rb_rotate_set_parents(parent, sibling, root,
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+ RB_RED);
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+ augment_rotate(parent, sibling);
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+ sibling = tmp1;
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+ }
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+ tmp1 = sibling->rb_right;
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+ if (!tmp1 || rb_is_black(tmp1)) {
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+ tmp2 = sibling->rb_left;
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+ if (!tmp2 || rb_is_black(tmp2)) {
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+ /*
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+ * Case 2 - sibling color flip
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+ * (p could be either color here)
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+ *
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+ * (p) (p)
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+ * / \ / \
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+ * N S --> N s
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+ * / \ / \
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+ * Sl Sr Sl Sr
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+ *
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+ * This leaves us violating 5) which
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+ * can be fixed by flipping p to black
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+ * if it was red, or by recursing at p.
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+ * p is red when coming from Case 1.
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+ */
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+ rb_set_parent_color(sibling, parent,
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+ RB_RED);
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+ if (rb_is_red(parent))
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+ rb_set_black(parent);
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+ else {
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+ node = parent;
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+ parent = rb_parent(node);
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+ if (parent)
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+ continue;
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+ }
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+ break;
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+ }
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+ /*
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+ * Case 3 - right rotate at sibling
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+ * (p could be either color here)
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+ *
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+ * (p) (p)
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+ * / \ / \
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+ * N S --> N Sl
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+ * / \ \
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+ * sl Sr s
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+ * \
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+ * Sr
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+ */
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+ sibling->rb_left = tmp1 = tmp2->rb_right;
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+ tmp2->rb_right = sibling;
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+ parent->rb_right = tmp2;
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+ if (tmp1)
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+ rb_set_parent_color(tmp1, sibling,
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+ RB_BLACK);
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+ augment_rotate(sibling, tmp2);
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+ tmp1 = sibling;
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+ sibling = tmp2;
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+ }
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+ /*
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+ * Case 4 - left rotate at parent + color flips
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+ * (p and sl could be either color here.
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+ * After rotation, p becomes black, s acquires
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+ * p's color, and sl keeps its color)
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+ *
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+ * (p) (s)
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+ * / \ / \
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+ * N S --> P Sr
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+ * / \ / \
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+ * (sl) sr N (sl)
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+ */
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+ parent->rb_right = tmp2 = sibling->rb_left;
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+ sibling->rb_left = parent;
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+ rb_set_parent_color(tmp1, sibling, RB_BLACK);
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+ if (tmp2)
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+ rb_set_parent(tmp2, parent);
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+ __rb_rotate_set_parents(parent, sibling, root,
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+ RB_BLACK);
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+ augment_rotate(parent, sibling);
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+ break;
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+ } else {
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+ sibling = parent->rb_left;
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+ if (rb_is_red(sibling)) {
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+ /* Case 1 - right rotate at parent */
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+ parent->rb_left = tmp1 = sibling->rb_right;
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+ sibling->rb_right = parent;
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+ rb_set_parent_color(tmp1, parent, RB_BLACK);
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+ __rb_rotate_set_parents(parent, sibling, root,
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+ RB_RED);
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+ augment_rotate(parent, sibling);
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+ sibling = tmp1;
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+ }
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+ tmp1 = sibling->rb_left;
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+ if (!tmp1 || rb_is_black(tmp1)) {
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+ tmp2 = sibling->rb_right;
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+ if (!tmp2 || rb_is_black(tmp2)) {
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+ /* Case 2 - sibling color flip */
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+ rb_set_parent_color(sibling, parent,
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+ RB_RED);
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+ if (rb_is_red(parent))
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+ rb_set_black(parent);
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+ else {
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+ node = parent;
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+ parent = rb_parent(node);
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+ if (parent)
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+ continue;
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+ }
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+ break;
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+ }
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+ /* Case 3 - right rotate at sibling */
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+ sibling->rb_right = tmp1 = tmp2->rb_left;
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+ tmp2->rb_left = sibling;
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+ parent->rb_left = tmp2;
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+ if (tmp1)
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+ rb_set_parent_color(tmp1, sibling,
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+ RB_BLACK);
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+ augment_rotate(sibling, tmp2);
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+ tmp1 = sibling;
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+ sibling = tmp2;
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+ }
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+ /* Case 4 - left rotate at parent + color flips */
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+ parent->rb_left = tmp2 = sibling->rb_right;
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+ sibling->rb_right = parent;
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+ rb_set_parent_color(tmp1, sibling, RB_BLACK);
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+ if (tmp2)
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+ rb_set_parent(tmp2, parent);
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+ __rb_rotate_set_parents(parent, sibling, root,
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+ RB_BLACK);
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+ augment_rotate(parent, sibling);
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+ break;
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+ }
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+ }
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+}
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+
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+/* Non-inline version for rb_erase_augmented() use */
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+void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
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+ void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
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+{
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+ ____rb_erase_color(parent, root, augment_rotate);
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+}
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+
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+/*
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+ * Non-augmented rbtree manipulation functions.
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+ *
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+ * We use dummy augmented callbacks here, and have the compiler optimize them
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+ * out of the rb_insert_color() and rb_erase() function definitions.
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+ */
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+
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+static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
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+static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
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+static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
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+
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+static const struct rb_augment_callbacks dummy_callbacks = {
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+ dummy_propagate, dummy_copy, dummy_rotate
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+};
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+
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+void rb_insert_color(struct rb_node *node, struct rb_root *root)
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+{
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+ __rb_insert(node, root, dummy_rotate);
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+}
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+
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+void rb_erase(struct rb_node *node, struct rb_root *root)
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+{
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+ struct rb_node *rebalance;
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+ rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
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+ if (rebalance)
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+ ____rb_erase_color(rebalance, root, dummy_rotate);
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+}
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+
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+/*
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+ * Augmented rbtree manipulation functions.
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+ *
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+ * This instantiates the same inline functions as in the non-augmented
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+ * case, but this time with user-defined callbacks.
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+ */
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+
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+void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
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+ void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
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+{
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+ __rb_insert(node, root, augment_rotate);
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+}
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+
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+/*
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+ * This function returns the first node (in sort order) of the tree.
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+ */
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+struct rb_node *rb_first(const struct rb_root *root)
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+{
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+ struct rb_node *n;
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+
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+ n = root->rb_node;
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+ if (!n)
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+ return NULL;
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+ while (n->rb_left)
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+ n = n->rb_left;
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+ return n;
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+}
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+
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+struct rb_node *rb_last(const struct rb_root *root)
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+{
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+ struct rb_node *n;
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+
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+ n = root->rb_node;
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+ if (!n)
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+ return NULL;
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+ while (n->rb_right)
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+ n = n->rb_right;
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+ return n;
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+}
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+
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+struct rb_node *rb_next(const struct rb_node *node)
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+{
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+ struct rb_node *parent;
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+
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+ if (RB_EMPTY_NODE(node))
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+ return NULL;
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+
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+ /*
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+ * If we have a right-hand child, go down and then left as far
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+ * as we can.
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+ */
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+ if (node->rb_right) {
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+ node = node->rb_right;
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+ while (node->rb_left)
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+ node=node->rb_left;
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+ return (struct rb_node *)node;
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+ }
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+
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+ /*
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+ * No right-hand children. Everything down and left is smaller than us,
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+ * so any 'next' node must be in the general direction of our parent.
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+ * Go up the tree; any time the ancestor is a right-hand child of its
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+ * parent, keep going up. First time it's a left-hand child of its
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+ * parent, said parent is our 'next' node.
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+ */
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+ while ((parent = rb_parent(node)) && node == parent->rb_right)
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+ node = parent;
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+
|
|
|
+ return parent;
|
|
|
+}
|
|
|
+
|
|
|
+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;
|
|
|
+}
|
|
|
+
|
|
|
+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;
|
|
|
+}
|
|
|
+
|
|
|
+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 (!node)
|
|
|
+ return NULL;
|
|
|
+ parent = rb_parent(node);
|
|
|
+
|
|
|
+ /* 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);
|
|
|
+}
|
Nick Peng