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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
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。
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。
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
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。
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
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》。
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。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。
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: }
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。
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
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
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
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: }
执行结果：
–
Echo Chen：Blog.csdn.net/chen19870707
–
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