Nginx的红黑树结构

ngx_rbtree_t是使用红黑树实现的一种关联容器，Nginx的核心模块(如定时器模块、文件缓存模块等)在需要快速检索、查找的情况下都使用了ngx_rbtree_t结构。关于红黑树的代码实现点击：数据结构-红黑树。更多关于红黑树的介绍请点击：红黑树理解。

Nginx中ngx_rbtree_t相关源码

ngx_rbtree.h文件

#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;

struct ngx_rbtree_node_s {
    ngx_rbtree_key_t       key;
    ngx_rbtree_node_t     *left;
    ngx_rbtree_node_t     *right;
    ngx_rbtree_node_t     *parent;
    u_char                 color;
    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 {
    ngx_rbtree_node_t     *root;
    ngx_rbtree_node_t     *sentinel;
    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_rbtree_t *tree, ngx_rbtree_node_t *node);
void ngx_rbtree_delete(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_ */

ngx_rbtree.c文件

#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);

// 插入函数，调用自定义的插入操作，然后在负责红黑树平衡操作
void
ngx_rbtree_insert(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) {
        node->parent = NULL;
        node->left = sentinel;
        node->right = sentinel;
        ngx_rbt_black(node);
        *root = node;

        return;
    }
	// 调用自定义的插入函数，该插入函数只负责插入操作，不负责平衡操作
    tree->insert(*root, node, sentinel);

    /* re-balance tree */
	// node为新插入的节点，如果node的父节点为红色，则需要旋转操作
    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)) {
				// case 1: node的uncle节点是红色的
                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) {
					// case 2: node为右孩子，且uncle节点是黑色的，进行左旋操作
                    node = node->parent;
                    ngx_rbtree_left_rotate(root, sentinel, node);
                }
				// case 3: node为左孩子，且uncle节点是黑色的，进行右旋操作
                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 - 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_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;

    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;
        }
    }

    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);

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

    } else {
        subst->parent->right = temp;
    }

    if (subst == node) {

        temp->parent = subst->parent;

    } else {

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

        } else {
            temp->parent = subst->parent;
        }

        subst->left = node->left;
        subst->right = node->right;
        subst->parent = node->parent;
        ngx_rbt_copy_color(subst, node);

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

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

        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;

    temp = node->right;
    node->right = temp->left;

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

    temp->parent = node->parent;

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

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

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

    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;
}

参考资料

https://github.com/luoxn28/algorithm_data_structure

Nginx的红黑树结构

Nginx中ngx_rbtree_t相关源码

参考资料

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