新秀nginx源代码分析数据结构篇（四）红黑树ngx_rbtree_t

 

新秀nginx源代码分析数据结构篇（四）红黑树ngx_rbtree_t

 

Author：Echo Chen（陈斌）

Email：chenb19870707@gmail.com

Blog：Blog.csdn.net/chen19870707

Date：October 27h, 2014

 

 

1.ngx_rbtree优势和特点

 

    ngx_rbtree是一种使用红黑树实现的关联容器。关于红黑树的特性，在《手把手实现红黑树》已经具体介绍，这里就仅仅探讨ngx_rbtree与众不同的地方；ngx_rbtree红黑树容器中的元素都是有序的，支持高速索引，插入，删除操作，也支持范围查询，遍历操作。应用很广泛。

 

2.源码位置

 

头文件：http://trac.nginx.org/nginx/browser/nginx/src/core/ngx_rbtree.h

源文件：http://trac.nginx.org/nginx/browser/nginx/src/core/ngx_rbtree.c

 

3.数据结构定义

 

能够看到ngx_rbtree的结点ngx_rbtree_node_t结构跟一般的红黑树差点儿相同，都是由键值key、左孩子left、右孩子right、父亲结点parent、颜色值color，不同的是ngx_rbtree_node_t这里多了一个data。但依据官方文档记在，因为data仅仅有一个字节，表示太少，非常少使用到。

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;
};

 

ngx_rbtree_t的结构也与一般红黑树同样，右root结点和哨兵叶子结点（sentinel）组成，不同的是这里多了一个 函数指针inserter。它决定了在加入结点是新加还是替换。

 

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;
};

 

4.ngx_rbtree初始化 ngx_rbtree_init

 

当中tree为ngx_rbtree_t类型，即为红黑树。s为ngx_rbtree_node_t，是rbtree的根节点，i即为上节提到的决定插入是新结点还是替换的函数指针。首先将根节点涂成 黑色（红黑树基本性质）。然后把 红黑树的 根节点和 哨兵结点 都指向这个结点。

 

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

#define ngx_rbtree_sentinel_init(node)  ngx_rbt_black(node)

 

5.ngx_rbtree 左旋 ngx_rbtree_left_rotate 和 右旋 ngx_rbtree_right_rotate

 

能够看到，经典代码总是永恒的，ngx_rbtree的左旋右旋也是參考《算法导论》导论中的步骤和伪代码。对比我自己的实现的《手把手实现红黑树》，与我自己实现的左旋右旋代码基本一致。我图解了具体的过程，有不清楚的能够參考《手把手实现红黑树》。

 

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;
}

6.ngx_rbtree插入 ngx_rbtree_insert

ngx_rbtree_insert也是分为两步，插入和调整。因为这两项都在《手把手实现红黑树》中做了详解，这里就不在啰嗦。这里值得一提的是，还记得node_rbtree_t 结构中的insert指针吗？这里就是通过这个函数指针来实现的插入。

一个小小的技巧就实现了多态。而且它给出了 唯一值和时间类型的key 插入方法。能够满足一般需求，用户也能够实现自己的插入方法。

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) {
        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);
}

6.1 唯一值类型插入

 

这个即为一般红黑树的插入方法，循环，假设插入的值比当前节点小，就进入左子树，否则进入右子树。直至遇到叶子结点。叶子节点就是要链入红黑树的位置。

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);
}

假设有相等的结点。会直接被覆盖，如上图插入key为2的结点，则当tmp 为2的结点时。p为叶子遍历结束。这样p就会被覆盖为新的值。

 

6.2 唯一时间类型插入

 

唯一差别就是推断大小时，採用了两个值相减，避免溢出。

typedef ngx_int_t   ngx_rbtree_key_int_t;
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);
}

 

 

7.ngx_rbtree删除ngx_rbtree_delete

也是依照《算法导论》上的步骤，先删除后调整，在《手把手实现红黑树》已介绍，请參考

void
ngx_rbtree_delete_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;

    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);
}

 

8.实战

 

因为ngx_rbtree_t未牵涉到内存池，所以很easy抽出来使用，例如以下为实现了插入、打印最小值、删除的样例

#include <iostream>
#include <algorithm>
#include <pthread.h>
#include <time.h>
#include <stdio.h>
#include <errno.h>
#include <string.h>
#include "ngx_queue.h"
#include "ngx_rbtree.h"


int main()
{

    ngx_rbtree_t tree;
    ngx_rbtree_node_t sentinel;

    ngx_rbtree_init(&tree,&sentinel,ngx_rbtree_insert_value);

    ngx_rbtree_node_t *rbnode = new ngx_rbtree_node_t[100];
    for(int i = 99; i >= 0 ;i--)
    {
        rbnode[i].key = i;
        rbnode[i].parent = NULL;
        rbnode[i].left = NULL;
        rbnode[i].right = NULL;
        ngx_rbtree_insert(&tree,&rbnode[i]);
    }

    for(int i = 0; i < 100;i++)
    {
         ngx_rbtree_node_t *p = ngx_rbtree_min(tree.root,&sentinel);
         std::cout << p->key << "  ";
         ngx_rbtree_delete(&tree,p);
     }


    delete[] rbnode;

    return 0;
}

 

执行结果：

-

Echo Chen：Blog.csdn.net/chen19870707

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