红黑树

红黑树1 2012-06-14 13:00:31

分类：

原文地址：红黑树1 作者：platinaluo

[EYUALUO] 红黑树在Linux Kernel中非常重要。1）Linux Kernel 2.6把内存描述符存放在红黑树中。红黑树的首部由内存描述符的mm_rb字段所指向。任何线性区对象都在类型为rb_node的vm_rb字段中存放节 点颜色以及指向双亲、左右孩子的指针。2）Linux Kernel2.6的进程调度CFS使用红黑树来组织可运行进程队列，并利用它迅速找到拥有最小vruntime值的进程。

所以在此转载这篇RB Tree算法文章，也是很有意义的。

========================================

红 黑树（Red-Black Tree）是一种二叉查找树（Binary Search Tree），但作了改进，即在每个结点上增加一个存储位表示结点的颜色，可以是RED或BLACK。通过对任何一条从根到叶子的路径上各个结点的着色方式 的限制，红黑树确保没有一条路径会比其他路径长出两倍，因而是接近平衡的。

　　红黑树的每个节点属性包含五个域：color、key、parent、lchild、rchild。红黑树除了具有二叉搜索树的所有性质之外，还具有以下性质：

　　1. 每个结点或是红的，或是黑的。

　　2. 根结点是黑的。

　　3. 每个叶结点是黑的。

　　4. 如果一个结点是红的，则它的两个孩子都是黑的。

　　5. 对每个结点，从该结点到其子孙结点的所有路径上包含相同数目的黑结点。

　　以上这些规则可以保证整棵树的平衡，红黑树的高度和查找时间都为O（log N）。

　 　二叉查找树在最坏的情况下可能会变成一个链表（当所有节点按从小到大的顺序依次插入后）。而红黑树在每一次插入或删除节点之后都会花O（log N）的时间来对树的结构作修改，以保证红黑树的性质，从而保持树的平衡。因此，红黑树的查找方法与二叉查找树相同，而Insert和Delete结点的的 方法前半部分与二叉查找树相同，而后半部分添加了一些修改树红黑树结构的操作。具体分析请参见“算法导论”一书第13章。下面给出一种红黑树的C实现，修 改自Linux内核源码中的红黑树实现(rbtree.h, rbtree.c)。

 

rbtree.h

#ifndef _RBTREE_H
#define _RBTREE_H
#include <stdio.h>
#define RB_RED      0
#define RB_BLACK    1
struct rb_key {
    int key;
};
struct rb_node {
    struct rb_node *rb_parent;
    struct rb_node *rb_right;
    struct rb_node *rb_left;
    struct rb_key rb_key;
    int rb_color;
};
struct rb_root {
        struct rb_node *rb_node;
};
#define rb_parent(r)   ((struct rb_node *)((r)->rb_parent))
#define rb_color(r)   ((r)->rb_color)
#define rb_is_red(r)   (!rb_color(r))
#define rb_is_black(r) rb_color(r)
#define rb_set_red(r)  do { (r)->rb_color = RB_RED; } while (0)
#define rb_set_black(r)  do { (r)->rb_color = RB_BLACK; } while (0)
static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
{
    rb->rb_parent = p;
}
static inline void rb_set_color(struct rb_node *rb, int color)
{
        rb->rb_color = color;
}
#define RB_ROOT (struct rb_root) { NULL, }
#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 *);
extern void rb_insert(struct rb_node *, struct rb_root *);
extern void rb_traverse(struct rb_node *);
extern struct rb_node *rb_newnode(struct rb_key *);
extern struct rb_node *rb_search(struct rb_root *, struct rb_key);
/* Find logical next and previous nodes in a tree */
extern struct rb_node *rb_next(struct rb_node *);
extern struct rb_node *rb_prev(struct rb_node *);
extern struct rb_node *rb_first(struct rb_root *);
extern struct rb_node *rb_last(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_node,
                            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 = parent;
        node->rb_left = node->rb_right = NULL;
        *rb_link = node;
}
#endif
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "rbtree.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);
        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)  { // node is left child of parent
            {
                struct rb_node *uncle = gparent->rb_right;
                if (uncle && rb_is_red(uncle)) { // case 1
                    rb_set_black(uncle);
                    rb_set_black(parent);
                    rb_set_red(gparent);
                    node = gparent;
                    continue;
                }
            }
            if (parent->rb_right == node) { // case 2
                struct rb_node *tmp;
                __rb_rotate_left(parent, root);
                tmp = parent;
                parent = node;
                node = tmp;
            }
            // case 3
            rb_set_black(parent);
            rb_set_red(gparent);
            __rb_rotate_right(gparent, root);
        } else { // node is right child of parent
            {
                struct rb_node *uncle = gparent->rb_left;
                if (uncle && rb_is_red(uncle)) { // case 1
                    rb_set_black(uncle);
                    rb_set_black(parent);
                    rb_set_red(gparent);
                    node = gparent;
                    continue;
                }
            }
            if (parent->rb_left == node) { // case 2
                struct rb_node *tmp;
                __rb_rotate_right(parent, root);
                tmp = parent;
                parent = node;
                node = tmp;
            }
            // case 3
            rb_set_black(parent);
            rb_set_red(gparent);
            __rb_rotate_left(gparent, root);
        }
    }
    rb_set_black(root->rb_node);
}
static int rb_compare(struct rb_key key1, struct rb_key key2)
{
    return (key1.key - key2.key);
}
struct rb_node* rb_newnode(struct rb_key *rb_key)
{
    struct rb_node *node = (struct rb_node *)malloc(sizeof(struct rb_node));
    if (node) {
        node->rb_parent = NULL;
        node->rb_left = NULL;
        node->rb_right = NULL;
        node->rb_color = RB_RED;
        memcpy(&node->rb_key, rb_key, sizeof(struct rb_key));
    }
    return node;
}
void rb_insert(struct rb_node *node, struct rb_root *root)
{
    struct rb_node *p = root->rb_node;
    struct rb_node *q = NULL;
    while (p != NULL) {
        q = p;
        if (rb_compare(node->rb_key, p->rb_key) < 0)
            p = p->rb_left;
        else
            p = p->rb_right;
    }
    node->rb_parent = q;
    if (q == NULL) {
        root->rb_node = node;
    } else {
        if (rb_compare(node->rb_key, q->rb_key) < 0)
            q->rb_left = node;
        else
            q->rb_right = node;
    }
    rb_insert_color(node, root);
}
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;
            // case 1
            if (rb_is_red(other))
            {
                rb_set_black(other);
                rb_set_red(parent);
                __rb_rotate_left(parent, root);
                other = parent->rb_right;
            }
            // case 2
            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
            {
                // case 3
                if (!other->rb_right || rb_is_black(other->rb_right))
                {
                    struct rb_node *o_left;
                    if ((o_left = other->rb_left))
                        rb_set_black(o_left);
                    rb_set_red(other);
                    __rb_rotate_right(other, root);
                    other = parent->rb_right;
                }
                // case 4
                rb_set_color(other, rb_color(parent));
                rb_set_black(parent);
                if (other->rb_right)
                    rb_set_black(other->rb_right);
                __rb_rotate_left(parent, root);
                node = root->rb_node;
                break;
            }
        }
        else
        {
            other = parent->rb_left;
            // case 1
            if (rb_is_red(other))
            {
                rb_set_black(other);
                rb_set_red(parent);
                __rb_rotate_right(parent, root);
                other = parent->rb_left;
            }
            // case 2
            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
            {
                // case 3
                if (!other->rb_left || rb_is_black(other->rb_left))
                {
                    register struct rb_node *o_right;
                    if ((o_right = other->rb_right))
                        rb_set_black(o_right);
                    rb_set_red(other);
                    __rb_rotate_left(other, root);
                    other = parent->rb_left;
                }
                // case 4
                rb_set_color(other, rb_color(parent));
                rb_set_black(parent);
                if (other->rb_left)
                    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;
        child = node->rb_right;
        parent = rb_parent(node);
        color = rb_color(node);
        if (child)
            rb_set_parent(child, parent);
        if (parent == old) {
            parent->rb_right = child;
            parent = node;
        } else
            parent->rb_left = child;
        node->rb_color = old->rb_color;
        node->rb_parent = old->rb_parent;
        node->rb_right = old->rb_right;
        node->rb_left = old->rb_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;
        rb_set_parent(old->rb_left, node);
        if (old->rb_right)
            rb_set_parent(old->rb_right, 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);
}
struct rb_node *rb_first(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(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(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 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(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 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_node, 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_node;
        else
            parent->rb_right = new_node;
    } else {
        root->rb_node = new_node;
    }
    if (victim->rb_left)
        rb_set_parent(victim->rb_left, new_node);
    if (victim->rb_right)
        rb_set_parent(victim->rb_right, new_node);
    /* Copy the pointers/colour from the victim to the replacement */
    *new_node = *victim;
}
struct rb_node *rb_search(struct rb_root *root, struct rb_key key)
{
    struct rb_node *p = root->rb_node;
    while(p != NULL && rb_compare(p->rb_key, key) != 0) {
        p = (rb_compare(p->rb_key, key) > 0) ? p->rb_left : p->rb_right;
    }
    return p;
}
void rb_traverse(struct rb_node *p)
{
    if (p) {
        if (p->rb_left)
            rb_traverse(p->rb_left);
        printf(" %d ", p->rb_key.key);
        if (p->rb_right)
            rb_traverse(p->rb_right);
    }
}