菜鸟nginx源码剖析数据结构篇（四）红黑树ngx_rbtree_t

 

菜鸟nginx源码剖析数据结构篇（四）红黑树ngx_rbtree_t

 

Author：Echo Chen（陈斌）

Email：[e-mail]

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》已经详细介绍，这里就只探讨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，支持快速索引，插入，删除操作，也支持范围查询，遍历操作，应用非常广泛。

 

2.源代码位置

 

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

 

可以看到ngx_rbtree的结点ngx_rbtree_node_t结构跟一般的红黑树差不多，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，但根据官方文档记在，由于data只有一个字节，表示太少，很少使用到。

   1: typedef struct ngx_rbtree_node_s  ngx_rbtree_node_t;

   2:  

   3: struct ngx_rbtree_node_s {

   4:     ngx_rbtree_key_t       key;

   5:     ngx_rbtree_node_t     *left;

   6:     ngx_rbtree_node_t     *right;

   7:     ngx_rbtree_node_t     *parent;

   8:     u_char                 color;

   9:     u_char                 data;

  10: };

 

ngx_rbtree_t的结构也与一般红黑树相同，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，它决定了在添加结点是新加还是替换。

 

   1: typedef struct ngx_rbtree_s  ngx_rbtree_t;

   2:  

   3: typedef void (*ngx_rbtree_insert_pt) (ngx_rbtree_node_t *root,

   4:     ngx_rbtree_node_t *node, ngx_rbtree_node_t *sentinel);

   5:  

   6: struct ngx_rbtree_s {

   7:     ngx_rbtree_node_t     *root;

   8:     ngx_rbtree_node_t     *sentinel;

   9:     ngx_rbtree_insert_pt   insert;

  10: };

 

4.ngx_rbtree初始化 ngx_rbtree_init

 

其中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。

 

   1: #define ngx_rbtree_init(tree, s, i)                                           \

   2:     ngx_rbtree_sentinel_init(s);                                              \

   3:     (tree)->root = s;                                                         \

   4:     (tree)->sentinel = s;                                                     \

   5:     (tree)->insert = i

   6:  

   7: #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

 

可以看到，经典代码总是永恒的，ngx_rbtree的左旋右旋也是参考《算法导论》导论中的步骤和伪代码，对照我自己的实现的《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，我图解了详细的过程，有不清楚的可以参考《手把手实现红黑树》。

 

   1: static ngx_inline void

   2: ngx_rbtree_left_rotate(ngx_rbtree_node_t **root, ngx_rbtree_node_t *sentinel,

   3:     ngx_rbtree_node_t *node)

   4: {

   5:     ngx_rbtree_node_t  *temp;

   6:  

   7:     temp = node->right;

   8:     node->right = temp->left;

   9:  

  10:     if (temp->left != sentinel) {

  11:         temp->left->parent = node;

  12:     }

  13:  

  14:     temp->parent = node->parent;

  15:  

  16:     if (node == *root) {

  17:         *root = temp;

  18:  

  19:     } else if (node == node->parent->left) {

  20:         node->parent->left = temp;

  21:  

  22:     } else {

  23:         node->parent->right = temp;

  24:     }

  25:  

  26:     temp->left = node;

  27:     node->parent = temp;

  28: }

   1: static ngx_inline void

   2: ngx_rbtree_right_rotate(ngx_rbtree_node_t **root, ngx_rbtree_node_t *sentinel,

   3:     ngx_rbtree_node_t *node)

   4: {

   5:     ngx_rbtree_node_t  *temp;

   6:  

   7:     temp = node->left;

   8:     node->left = temp->right;

   9:  

  10:     if (temp->right != sentinel) {

  11:         temp->right->parent = node;

  12:     }

  13:  

  14:     temp->parent = node->parent;

  15:  

  16:     if (node == *root) {

  17:         *root = temp;

  18:  

  19:     } else if (node == node->parent->right) {

  20:         node->parent->right = temp;

  21:  

  22:     } else {

  23:         node->parent->left = temp;

  24:     }

  25:  

  26:     temp->right = node;

  27:     node->parent = temp;

  28: }

6.ngx_rbtree插入 ngx_rbtree_insert

ngx_rbtree_insert也是分为两步，插入和调整，由于这两项都在《手把手实现红黑树》中做了详细解释，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；并且它给出了 唯一值和时间类型的key 插入方法，可以满足一般需求，用户也可以实现自己的插入方法。

voidngx_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，如果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。

   1: void

   2: ngx_rbtree_insert_value(ngx_rbtree_node_t *temp, ngx_rbtree_node_t *node,

   3:     ngx_rbtree_node_t *sentinel)

   4: {

   5:     ngx_rbtree_node_t  **p;

   6:  

   7:     for ( ;; ) {

   8:  

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

  10:  

  11:         if (*p == sentinel) {

  12:             break;

  13:         }

  14:  

  15:         temp = *p;

  16:     }

  17:  

  18:     *p = node;

  19:     node->parent = temp;

  20:     node->left = sentinel;

  21:     node->right = sentinel;

  22:     ngx_rbt_red(node);

  23: }

如果有相等的结点，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

 

唯一区别就是判断大小时，采用了两个值相减，避免溢出。

   1: typedef ngx_int_t   ngx_rbtree_key_int_t;

   2: void

   3: ngx_rbtree_insert_timer_value(ngx_rbtree_node_t *temp, ngx_rbtree_node_t *node,

   4:     ngx_rbtree_node_t *sentinel)

   5: {

   6:     ngx_rbtree_node_t  **p;

   7:  

   8:     for ( ;; ) {

   9:  

  10:         /*

  11:          * Timer values

  12:          * 1) are spread in small range, usually several minutes,

  13:          * 2) and overflow each 49 days, if milliseconds are stored in 32 bits.

  14:          * The comparison takes into account that overflow.

  15:          */

  16:  

  17:         /*  node->key < temp->key */

  18:  

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

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

  21:  

  22:         if (*p == sentinel) {

  23:             break;

  24:         }

  25:  

  26:         temp = *p;

  27:     }

  28:  

  29:     *p = node;

  30:     node->parent = temp;

  31:     node->left = sentinel;

  32:     node->right = sentinel;

  33:     ngx_rbt_red(node);

  34: }

 

 

7.ngx_rbtree删除ngx_rbtree_delete

也是按照《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，请参考

   1: void

   2: ngx_rbtree_delete_delete(ngx_thread_volatile ngx_rbtree_t *tree,

   3:     ngx_rbtree_node_t *node)

   4: {

   5:     ngx_uint_t           red;

   6:     ngx_rbtree_node_t  **root, *sentinel, *subst, *temp, *w;

   7:  

   8:     /* a binary tree delete */

   9:  

  10:     root = (ngx_rbtree_node_t **) &tree->root;

  11:     sentinel = tree->sentinel;

  12:  

  13:     if (node->left == sentinel) {

  14:         temp = node->right;

  15:         subst = node;

  16:  

  17:     } else if (node->right == sentinel) {

  18:         temp = node->left;

  19:         subst = node;

  20:  

  21:     } else {

  22:         subst = ngx_rbtree_min(node->right, sentinel);

  23:  

  24:         if (subst->left != sentinel) {

  25:             temp = subst->left;

  26:         } else {

  27:             temp = subst->right;

  28:         }

  29:     }

  30:  

  31:     if (subst == *root) {

  32:         *root = temp;

  33:         ngx_rbt_black(temp);

  34:  

  35:         /* DEBUG stuff */

  36:         node->left = NULL;

  37:         node->right = NULL;

  38:         node->parent = NULL;

  39:         node->key = 0;

  40:  

  41:         return;

  42:     }

  43:  

  44:     red = ngx_rbt_is_red(subst);

  45:  

  46:     if (subst == subst->parent->left) {

  47:         subst->parent->left = temp;

  48:  

  49:     } else {

  50:         subst->parent->right = temp;

  51:     }

  52:  

  53:     if (subst == node) {

  54:  

  55:         temp->parent = subst->parent;

  56:  

  57:     } else {

  58:  

  59:         if (subst->parent == node) {

  60:             temp->parent = subst;

  61:  

  62:         } else {

  63:             temp->parent = subst->parent;

  64:         }

  65:  

  66:         subst->left = node->left;

  67:         subst->right = node->right;

  68:         subst->parent = node->parent;

  69:         ngx_rbt_copy_color(subst, node);

  70:  

  71:         if (node == *root) {

  72:             *root = subst;

  73:  

  74:         } else {

  75:             if (node == node->parent->left) {

  76:                 node->parent->left = subst;

  77:             } else {

  78:                 node->parent->right = subst;

  79:             }

  80:         }

  81:  

  82:         if (subst->left != sentinel) {

  83:             subst->left->parent = subst;

  84:         }

  85:  

  86:         if (subst->right != sentinel) {

  87:             subst->right->parent = subst;

  88:         }

  89:     }

  90:  

  91:     /* DEBUG stuff */

  92:     node->left = NULL;

  93:     node->right = NULL;

  94:     node->parent = NULL;

  95:     node->key = 0;

  96:  

  97:     if (red) {

  98:         return;

  99:     }

 100:  

 101:     /* a delete fixup */

 102:  

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

 104:  

 105:         if (temp == temp->parent->left) {

 106:             w = temp->parent->right;

 107:  

 108:             if (ngx_rbt_is_red(w)) {

 109:                 ngx_rbt_black(w);

 110:                 ngx_rbt_red(temp->parent);

 111:                 ngx_rbtree_left_rotate(root, sentinel, temp->parent);

 112:                 w = temp->parent->right;

 113:             }

 114:  

 115:             if (ngx_rbt_is_black(w->left) && ngx_rbt_is_black(w->right)) {

 116:                 ngx_rbt_red(w);

 117:                 temp = temp->parent;

 118:  

 119:             } else {

 120:                 if (ngx_rbt_is_black(w->right)) {

 121:                     ngx_rbt_black(w->left);

 122:                     ngx_rbt_red(w);

 123:                     ngx_rbtree_right_rotate(root, sentinel, w);

 124:                     w = temp->parent->right;

 125:                 }

 126:  

 127:                 ngx_rbt_copy_color(w, temp->parent);

 128:                 ngx_rbt_black(temp->parent);

 129:                 ngx_rbt_black(w->right);

 130:                 ngx_rbtree_left_rotate(root, sentinel, temp->parent);

 131:                 temp = *root;

 132:             }

 133:  

 134:         } else {

 135:             w = temp->parent->left;

 136:  

 137:             if (ngx_rbt_is_red(w)) {

 138:                 ngx_rbt_black(w);

 139:                 ngx_rbt_red(temp->parent);

 140:                 ngx_rbtree_right_rotate(root, sentinel, temp->parent);

 141:                 w = temp->parent->left;

 142:             }

 143:  

 144:             if (ngx_rbt_is_black(w->left) && ngx_rbt_is_black(w->right)) {

 145:                 ngx_rbt_red(w);

 146:                 temp = temp->parent;

 147:  

 148:             } else {

 149:                 if (ngx_rbt_is_black(w->left)) {

 150:                     ngx_rbt_black(w->right);

 151:                     ngx_rbt_red(w);

 152:                     ngx_rbtree_left_rotate(root, sentinel, w);

 153:                     w = temp->parent->left;

 154:                 }

 155:  

 156:                 ngx_rbt_copy_color(w, temp->parent);

 157:                 ngx_rbt_black(temp->parent);

 158:                 ngx_rbt_black(w->left);

 159:                 ngx_rbtree_right_rotate(root, sentinel, temp->parent);

 160:                 temp = *root;

 161:             }

 162:         }

 163:     }

 164:  

 165:     ngx_rbt_black(temp);

 166: }

 

8.实战

 

由于ngx_rbtree_t未牵涉到内存池，所以非常容易抽出来使用，如下为实现了插入、打印最小值、删除的例子

   1: #include <iostream>

   2: #include <algorithm>

   3: #include <pthread.h>

   4: #include <time.h>

   5: #include <stdio.h>

   6: #include <errno.h>

   7: #include <string.h>

   8: #include "ngx_queue.h"

   9: #include "ngx_rbtree.h"

  10:  

  11:  

  12: int main()

  13: {

  14:  

  15:     ngx_rbtree_t tree;

  16:     ngx_rbtree_node_t sentinel;

  17:  

  18:     ngx_rbtree_init(&tree,&sentinel,ngx_rbtree_insert_value);

  19:  

  20:     ngx_rbtree_node_t *rbnode = new ngx_rbtree_node_t[100];

  21:     for(int i = 99; i >= 0 ;i--)

  22:     {

  23:         rbnode[i].key = i;

  24:         rbnode[i].parent = NULL;

  25:         rbnode[i].left = NULL;

  26:         rbnode[i].right = NULL;

  27:         ngx_rbtree_insert(&tree,&rbnode[i]);

  28:     }

  29:  

  30:     for(int i = 0; i < 100;i++)

  31:     {

  32:          ngx_rbtree_node_t *p = ngx_rbtree_min(tree.root,&sentinel);

  33:          std::cout << p->key << "  ";

  34:          ngx_rbtree_delete(&tree,p);

  35:      }

  36:  

  37:  

  38:     delete[] rbnode;

  39:  

  40:     return 0;

  41: }

 

运行结果：

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Echo Chen：Blog.csdn.net/chen19870707

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