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;

}