Nginx之红黑树

/*
 * Copyright (C) Igor Sysoev
 * Copyright (C) Nginx, Inc.
 */




#ifndef _NGX_RBTREE_H_INCLUDED_
#define _NGX_RBTREE_H_INCLUDED_




#include <ngx_config.h>
#include <ngx_core.h>




typedef ngx_uint_t  ngx_rbtree_key_t;
typedef ngx_int_t   ngx_rbtree_key_int_t;




typedef struct ngx_rbtree_node_s  ngx_rbtree_node_t;


// 红黑树
struct ngx_rbtree_node_s {
    // 无符号整形的keyword
    ngx_rbtree_key_t       key;
    // 左子节点
    ngx_rbtree_node_t     *left;
    // 右子节点
    ngx_rbtree_node_t     *right;
    // 父节点
    ngx_rbtree_node_t     *parent;
    // 节点的颜色，0表示黑色。1表示红色
    u_char                 color;
    // 仅1个字节的节点数据。

因为表示的空间太小，所以一般非常少使用。
    u_char                 data;
};




typedef struct ngx_rbtree_s  ngx_rbtree_t;


typedef void (*ngx_rbtree_insert_pt) (ngx_rbtree_node_t *root,
    ngx_rbtree_node_t *node, ngx_rbtree_node_t *sentinel);


struct ngx_rbtree_s {
    // 指向树的根节点。
    ngx_rbtree_node_t     *root;
    // 指向NIL哨兵节点
    ngx_rbtree_node_t     *sentinel;
    // 表示红黑树加入元素的函数指针，它决定在加入新节点时的行为到底是替换还是新增
    ngx_rbtree_insert_pt   insert;
};




#define ngx_rbtree_init(tree, s, i)                                           \
    ngx_rbtree_sentinel_init(s);                                              \
    (tree)->root = s;                                                         \
    (tree)->sentinel = s;                                                     \
    (tree)->insert = i




void ngx_rbtree_insert(ngx_thread_volatile ngx_rbtree_t *tree,
    ngx_rbtree_node_t *node);
void ngx_rbtree_delete(ngx_thread_volatile ngx_rbtree_t *tree,
    ngx_rbtree_node_t *node);
void ngx_rbtree_insert_value(ngx_rbtree_node_t *root, ngx_rbtree_node_t *node,
    ngx_rbtree_node_t *sentinel);
void ngx_rbtree_insert_timer_value(ngx_rbtree_node_t *root,
    ngx_rbtree_node_t *node, ngx_rbtree_node_t *sentinel);




#define ngx_rbt_red(node)               ((node)->color = 1)
#define ngx_rbt_black(node)             ((node)->color = 0)
#define ngx_rbt_is_red(node)            ((node)->color)
#define ngx_rbt_is_black(node)          (!ngx_rbt_is_red(node))
#define ngx_rbt_copy_color(n1, n2)      (n1->color = n2->color)




/* a sentinel must be black */


#define ngx_rbtree_sentinel_init(node)  ngx_rbt_black(node)




static ngx_inline ngx_rbtree_node_t *
ngx_rbtree_min(ngx_rbtree_node_t *node, ngx_rbtree_node_t *sentinel)
{
    while (node->left != sentinel) {
        node = node->left;
    }


    return node;
}

#endif /* _NGX_RBTREE_H_INCLUDED_ */

/*
 * Copyright (C) Igor Sysoev
 * Copyright (C) Nginx, Inc.
 */


#include <ngx_config.h>
#include <ngx_core.h>


/*
 * The red-black tree code is based on the algorithm described in
 * the "Introduction to Algorithms" by Cormen, Leiserson and Rivest.
 */


static ngx_inline void ngx_rbtree_left_rotate(ngx_rbtree_node_t **root,
ngx_rbtree_node_t *sentinel, ngx_rbtree_node_t *node);
static ngx_inline void ngx_rbtree_right_rotate(ngx_rbtree_node_t **root,
ngx_rbtree_node_t *sentinel, ngx_rbtree_node_t *node);


void ngx_rbtree_insert(ngx_thread_volatile ngx_rbtree_t *tree,
ngx_rbtree_node_t *node) {
ngx_rbtree_node_t **root, *temp, *sentinel;


/* a binary tree insert */


root = (ngx_rbtree_node_t **) &tree->root;
sentinel = tree->sentinel;


if (*root == sentinel) { //空树
node->parent = NULL;
node->left = sentinel;
node->right = sentinel;
ngx_rbt_black(node);
*root = node;


return;
}


tree->insert(*root, node, sentinel);


/* re-balance tree */


while (node != *root && ngx_rbt_is_red(node->parent)) {


if (node->parent == node->parent->parent->left) {
temp = node->parent->parent->right;


if (ngx_rbt_is_red(temp)) {
ngx_rbt_black(node->parent);
ngx_rbt_black(temp);
ngx_rbt_red(node->parent->parent);
node = node->parent->parent;


} else {
if (node == node->parent->right) {
node = node->parent;
ngx_rbtree_left_rotate(root, sentinel, node);
}


ngx_rbt_black(node->parent);
ngx_rbt_red(node->parent->parent);
ngx_rbtree_right_rotate(root, sentinel, node->parent->parent);
}


} else {
temp = node->parent->parent->left;


if (ngx_rbt_is_red(temp)) {
ngx_rbt_black(node->parent);
ngx_rbt_black(temp);
ngx_rbt_red(node->parent->parent);
node = node->parent->parent;


} else {
if (node == node->parent->left) {
node = node->parent;
ngx_rbtree_right_rotate(root, sentinel, node);
}


ngx_rbt_black(node->parent);
ngx_rbt_red(node->parent->parent);
ngx_rbtree_left_rotate(root, sentinel, node->parent->parent);
}
}
}


ngx_rbt_black(*root);
}


void ngx_rbtree_insert_value(ngx_rbtree_node_t *temp, ngx_rbtree_node_t *node,
ngx_rbtree_node_t *sentinel) {
ngx_rbtree_node_t **p;


for (;;) {


p = (node->key < temp->key) ? &temp->left : &temp->right;


if (*p == sentinel) {
break;
}


temp = *p;
}


*p = node;
node->parent = temp;
node->left = sentinel;
node->right = sentinel;
ngx_rbt_red(node);
}


void ngx_rbtree_insert_timer_value(ngx_rbtree_node_t *temp,
ngx_rbtree_node_t *node, ngx_rbtree_node_t *sentinel) {
ngx_rbtree_node_t **p;


for (;;) {


/*
* Timer values
* 1) are spread in small range, usually several minutes,
* 2) and overflow each 49 days, if milliseconds are stored in 32 bits.
* The comparison takes into account that overflow.
*/


/*  node->key < temp->key */


p = ((ngx_rbtree_key_int_t) node->key - (ngx_rbtree_key_int_t) temp->key
< 0) ?

&temp->left : &temp->right;


if (*p == sentinel) {
break;
}


temp = *p;
}


*p = node;
node->parent = temp;
node->left = sentinel;
node->right = sentinel;
ngx_rbt_red(node);
}


void ngx_rbtree_delete(ngx_thread_volatile ngx_rbtree_t *tree,
ngx_rbtree_node_t *node) {


ngx_uint_t red;
ngx_rbtree_node_t **root, *sentinel, *subst, *temp, *w;


/* a binary tree delete */


root = (ngx_rbtree_node_t **) &tree->root;
sentinel = tree->sentinel;
//找到y和x节点
if (node->left == sentinel) {
temp = node->right;
subst = node;


} else if (node->right == sentinel) {
temp = node->left;
subst = node;


} else {
subst = ngx_rbtree_min(node->right, sentinel);


if (subst->left != sentinel) {
temp = subst->left;
} else {
temp = subst->right;
}
}
//y节点为root节点
if (subst == *root) {
*root = temp;
ngx_rbt_black(temp);


/* DEBUG stuff */
node->left = NULL;
node->right = NULL;
node->parent = NULL;
node->key = 0;


return;
}


//
red = ngx_rbt_is_red(subst);//记录y节点颜色
//y父的孩子节点
if (subst == subst->parent->left) {
subst->parent->left = temp;


} else {
subst->parent->right = temp;
}
//y孩子的父节点
if (subst == node) {//仅仅有一个孩子节点


temp->parent = subst->parent;


} else {


if (subst->parent == node) {
temp->parent = subst;


} else {
temp->parent = subst->parent;
}
//y节点copy z节点属性
subst->left = node->left;
subst->right = node->right;
subst->parent = node->parent;
ngx_rbt_copy_color(subst, node);




if (node == *root) {
*root = subst;


} else {//删除节点的父节点的孩子节点
if (node == node->parent->left) {
node->parent->left = subst;
} else {
node->parent->right = subst;
}
}
//y节点的父节点
if (subst->left != sentinel) {
subst->left->parent = subst;
}


if (subst->right != sentinel) {
subst->right->parent = subst;
}
}


/* DEBUG stuff */
node->left = NULL;
node->right = NULL;
node->parent = NULL;
node->key = 0;


if (red) {
return;
}


/* a delete fixup */


while (temp != *root && ngx_rbt_is_black(temp)) {


if (temp == temp->parent->left) {
w = temp->parent->right;


if (ngx_rbt_is_red(w)) {
ngx_rbt_black(w);
ngx_rbt_red(temp->parent);
ngx_rbtree_left_rotate(root, sentinel, temp->parent);
w = temp->parent->right;
}


if (ngx_rbt_is_black(w->left) && ngx_rbt_is_black(w->right)) {
ngx_rbt_red(w);
temp = temp->parent;


} else {
if (ngx_rbt_is_black(w->right)) {
ngx_rbt_black(w->left);
ngx_rbt_red(w);
ngx_rbtree_right_rotate(root, sentinel, w);
w = temp->parent->right;
}


ngx_rbt_copy_color(w, temp->parent);
ngx_rbt_black(temp->parent);
ngx_rbt_black(w->right);
ngx_rbtree_left_rotate(root, sentinel, temp->parent);
temp = *root;
}


} else {
w = temp->parent->left;


if (ngx_rbt_is_red(w)) {
ngx_rbt_black(w);
ngx_rbt_red(temp->parent);
ngx_rbtree_right_rotate(root, sentinel, temp->parent);
w = temp->parent->left;
}


if (ngx_rbt_is_black(w->left) && ngx_rbt_is_black(w->right)) {
ngx_rbt_red(w);
temp = temp->parent;


} else {
if (ngx_rbt_is_black(w->left)) {
ngx_rbt_black(w->right);
ngx_rbt_red(w);
ngx_rbtree_left_rotate(root, sentinel, w);
w = temp->parent->left;
}


ngx_rbt_copy_color(w, temp->parent);
ngx_rbt_black(temp->parent);
ngx_rbt_black(w->left);
ngx_rbtree_right_rotate(root, sentinel, temp->parent);
temp = *root;
}
}
}


ngx_rbt_black(temp);
}


static ngx_inline void ngx_rbtree_left_rotate(ngx_rbtree_node_t **root,
ngx_rbtree_node_t *sentinel, ngx_rbtree_node_t *node) {


ngx_rbtree_node_t *temp;


//1、设置节点y
temp = node->right;
//2、将y的左子树作为x的右子树
node->right = temp->left;
if (temp->left != sentinel) {
temp->left->parent = node;
}
//3、链接y与x的父节点
temp->parent = node->parent;


if (node == *root) {
*root = temp;
} else if (node == node->parent->left) {
node->parent->left = temp;
} else {
node->parent->right = temp;
}
//4、x作为y的左子树
temp->left = node;
node->parent = temp;
}


static ngx_inline void ngx_rbtree_right_rotate(ngx_rbtree_node_t **root,
ngx_rbtree_node_t *sentinel, ngx_rbtree_node_t *node) {
ngx_rbtree_node_t *temp;


temp = node->left;


node->left = temp->right;
if (temp->right != sentinel) {
temp->right->parent = node;
}


temp->parent = node->parent;
if (node == *root) {
*root = temp;
} else if (node == node->parent->right) {
node->parent->right = temp;
} else {
node->parent->left = temp;
}


temp->right = node;
node->parent = temp;
}