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：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。

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，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: }

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