红黑树是一种自平衡二叉查找树，典型的用途是实现关联数组。它是复杂的，但它的操作有着良好的最坏情况运行时间，并且在实践中是高效的: 它可以在O(logn)时间内做查找，插入和删除，这里的n是树中元素的数目。红黑树是 2-3-4树的一种等同。换句话说，对于每个 2-3-4 树，都存在至少一个数据元素是同样次序的红黑树。详细的红黑树介绍参考我转载的一篇博文http://blog.csdn.net/pngynghay/article/details/8185351。本博文仅仅实现了rbtree以及如何使用rbtree。
本博文红黑树的实现取自Linux内核对红黑树的实现，只是，我去掉了内核实现中对内核的依赖，使得我们可以在用户态应用程序中依然可以使用。
rbtree.h
#ifndef RBTREE_H_
#define RBTREE_H_
#include <stdlib.h>
#include <stddef.h>
#include <stdio.h>
#include <string.h>
/*通过父结构体type中的成员member的已知地址ptr，来寻找当前ptr地址所属的父结构体type的地址*/
#define container_of(ptr, type, member) ({ const typeof( ((type *)0)->member ) *__mptr = (ptr); (type *)( (char *)__mptr - offsetof(type,member) );})
struct rb_node {
unsigned long rb_parent_color;
#define RB_RED 0
#define RB_BLACK 1
struct rb_node *rb_right;
struct rb_node *rb_left;
}__attribute__((aligned(sizeof(long))));
/* The alignment might seem pointless, but allegedly CRIS needs it */
struct rb_root {
struct rb_node *rb_node;
};
#define rb_parent(r) ((struct rb_node *)((r)->rb_parent_color & ~3))
#define rb_color(r) ((r)->rb_parent_color & 1)
#define rb_is_red(r) (!rb_color(r))
#define rb_is_black(r) rb_color(r)
#define rb_set_red(r) do { (r)->rb_parent_color &= ~1; } while (0)
#define rb_set_black(r) do { (r)->rb_parent_color |= 1; } while (0)
static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p) {
rb->rb_parent_color = (rb->rb_parent_color & 3) | (unsigned long) p;
}
static inline void rb_set_color(struct rb_node *rb, int color) {
rb->rb_parent_color = (rb->rb_parent_color & ~1) | color;
}
#define RB_ROOT (struct rb_root) { NULL, }
#define rb_entry(ptr, type, member) container_of(ptr, type, member)
#define RB_EMPTY_ROOT(root) ((root)->rb_node == NULL)
#define RB_EMPTY_NODE(node) (rb_parent(node) == node)
#define RB_CLEAR_NODE(node) (rb_set_parent(node, node))
extern void rb_insert_color(struct rb_node *, struct rb_root *);
extern void rb_erase(struct rb_node *, struct rb_root *);
/* Find logical next and previous nodes in a tree */
extern struct rb_node *rb_next(const struct rb_node *);
extern struct rb_node *rb_prev(const struct rb_node *);
extern struct rb_node *rb_first(const struct rb_root *);
extern struct rb_node *rb_last(const struct rb_root *);
/* Fast replacement of a single node without remove/rebalance/add/rebalance */
extern void rb_replace_node(struct rb_node *victim, struct rb_node *new,
struct rb_root *root);
static inline void rb_link_node(struct rb_node * node, struct rb_node * parent,
struct rb_node ** rb_link) {
node->rb_parent_color = (unsigned long) parent;
node->rb_left = node->rb_right = NULL;
*rb_link = node;
}
#endif /* RBTREE_H_ */
rbtree.c
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);
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 void __rb_rotate_right(struct rb_node *node, struct rb_root *root) {
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);
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);
}
void rb_insert_color(struct rb_node *node, struct rb_root *root) {
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;
}
}
if (parent->rb_right == node) {
register struct rb_node *tmp;
__rb_rotate_left(parent, root);
tmp = parent;
parent = node;
node = tmp;
}
rb_set_black(parent);
rb_set_red(gparent);
__rb_rotate_right(gparent, root);
} 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;
}
}
if (parent->rb_left == node) {
register struct rb_node *tmp;
__rb_rotate_right(parent, root);
tmp = parent;
parent = node;
node = tmp;
}
rb_set_black(parent);
rb_set_red(gparent);
__rb_rotate_left(gparent, root);
}
}
rb_set_black(root->rb_node);
}
static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
struct rb_root *root) {
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;
}
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;
}
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;
}
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_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;
}
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;
}
}
}
if (node)
rb_set_black(node);
}
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);
goto color;
}
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;
color: if (color == RB_BLACK
)
__rb_erase_color(child, parent, root);
}
/*
* 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;
}
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;
}
struct rb_node *rb_next(const struct rb_node *node) {
struct rb_node *parent;
if (rb_parent(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;
}
struct rb_node *rb_prev(const struct rb_node *node) {
struct rb_node *parent;
if (rb_parent(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 */
if (parent) {
if (victim == parent->rb_left)
parent->rb_left = new;
else
parent->rb_right = new;
} else {
root->rb_node = new;
}
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;
}
若要使用上面的rbtree，需要根据需要实现自己的rbtree插入和查询函数。本博文实现如下：
//关联到红黑树的数据结构
struct int_rbtree {
struct rb_node rbnode;
int i;
};
//红黑树最大节点数目
#define MAX_NUM 20
struct int_rbtree * int_search(struct rb_root *root, int key) {
struct rb_node *node = root->rb_node;
while (node) {
struct int_rbtree *data = container_of(node, struct int_rbtree, rbnode);
if (key < data->i)
node = node->rb_left;
else if (key > data->i)
node = node->rb_right;
else
return data;
}
return NULL;
}
int int_insert(struct rb_root *root, struct int_rbtree *data) {
struct rb_node **newnode = &(root->rb_node), *parent = NULL;
/* Figure out where to put new node */
while (*newnode) {
struct int_rbtree *thisnode =
container_of(*newnode, struct int_rbtree, rbnode);
parent = *newnode;
if (data->i < thisnode->i)
newnode = &((*newnode)->rb_left);
else if (data->i > thisnode->i)
newnode = &((*newnode)->rb_right);
else
return 0;
}
/* Add new node and rebalance tree. */
rb_link_node(&data->rbnode, parent, newnode);
rb_insert_color(&data->rbnode, root);
return 1;
}
测试主程序
void testrbtree() {
struct rb_node *node; // rb node
struct rb_root root = RB_ROOT; //root node
int i = 0;
//insert
for (i = 0; i < MAX_NUM; i = i + 2) {
//分配节点，删除时需释放节点
struct int_rbtree *inttree = malloc(sizeof(struct int_rbtree));
memset(inttree, 0, sizeof(struct int_rbtree));
inttree->i = i;
int res = int_insert(&root, inttree);
if (res) {
printf("insert %d succeed\n", i);
} else {
printf("insert %d failed\n", i);
}
}
for (i = 1; i < MAX_NUM; i = i + 2) {
struct int_rbtree *inttree = malloc(sizeof(struct int_rbtree));
memset(inttree, 0, sizeof(struct int_rbtree));
inttree->i = i;
int res = int_insert(&root, inttree);
if (res) {
printf("insert %d succeed\n", i);
} else {
printf("insert %d failed\n", i);
}
}
//travel
printf("begin to travel tree\n");
for (node = rb_first(&root); node; node = rb_next(node)) {
printf("key %d \n", rb_entry(node, struct int_rbtree, rbnode)->i);
}
printf("end to travel tree\n");
//delete
srand(time(NULL));
int key = rand() % MAX_NUM;
struct int_rbtree *data = int_search(&root, key);
if (NULL != data) {
rb_erase(&data->rbnode, &root);
//删除时需释放节点
free(data);
data = NULL;
printf("is going to delete key %d \n", key);
} else {
printf("key %d is not in the tree\n", key);
return;
}
data = int_search(&root, key);
if (NULL != data) {
printf("delete key %d failed\n", key);
} else {
printf("delete key %d succeed\n", key);
}
return;
}
只要在main函数中调用这个测试函数即可。
同时，有需要的朋友可以从http://download.csdn.net/detail/it_pcode/6632917下载本博文代码。
原文：http://blog.csdn.net/pngynghay/article/details/21881369