数组a[9] = {4,2,6,1,3,5,7,16,15};
说明：1、层序遍历AVL树，括号内为每个节点的高度值
2、第二行为删除节点“5”之后的AVL树
Reference: https://blog.csdn.net/silence2015/article/details/50966748
https://blog.csdn.net/u010552731/article/details/47393549
1 /*
2 * FILE: AVL.c
3 * DATE: 20180324
4 * ==============
5 */
6 #include <stdio.h>
7 #include <stdlib.h>
8
9 struct node{
10 int data;
11 struct node *left;
12 struct node *right;
13 int height;
14 };
15
16 #define NODENUMBER 9
17
18 struct node *createNode(int value);
19 struct node *insertNode(struct node *head, struct node *new);
20 void printNode(struct node *p);
21 void levelTraverse(struct node *head, void (*fun)(struct node *));
22 struct node *deleteNode(struct node *head, int value);
23
24 int main(int argc, char *argv[])
25 {
26 int a[9] = {4,2,6,1,3,5,7,16,15};
27 struct node *head = NULL;
28 int i;
29 for(i=0; i<NODENUMBER; i++)
30 head = insertNode(head, createNode(a[i]));
31 levelTraverse(head, printNode);
32 printf("\n");
33 head = deleteNode(head, 5);
34 levelTraverse(head, printNode);
35 printf("\n");
36 return 0;
37 }
38 // 新建节点
39 struct node *createNode(int value)
40 {
41 struct node *p = (struct node *)malloc(sizeof(struct node));
42 p->data = value;
43 p->left = p->right = NULL;
44 p->height = 1;
45 }
46 // 左旋：头节点的右子树向左旋转
47 struct node *rotationLeft(struct node *head)
48 {
49 struct node *new = head->right;
50 head->right = new->left;
51 new->left = head;
52 head->height = getHeight(head); // 旋转后更新两节点的高度值
53 new->height = getHeight(head);
54 return new;
55 }
56 // 右旋
57 struct node *rotationRight(struct node *head)
58 {
59 struct node *new = head->left;
60 head->left = new->right;
61 new->right = head;
62 head->height = getHeight(head); // 更新节点高度值
63 new->height = getHeight(new);
64 return new;
65 }
66 // 左右旋：头节点左孩子的右孩子向左旋，头节点的左孩子向右旋
67 struct node *rotationLeftRight(struct node *head)
68 {
69 head->left = rotationLeft(head->left);
70 head = rotationRight(head);
71 return head;
72 }
73 // 右左旋
74 struct node *rotationRightLeft(struct node *head)
75 {
76 head->right = rotationRight(head->right);
77 head = rotationLeft(head);
78 return head;
79 }
80 // 节点高度：从下往上
81 int getHeight(struct node *head)
82 {
83 if(head == NULL)
84 return 0;
85 int height_left = getHeight(head->left);
86 int height_right = getHeight(head->right);
87 return (height_left>height_right)?(height_left+1):(height_right+1);
88 }
89 // 插入节点：AVL平衡二叉树
90 struct node *insertNode(struct node *head, struct node *new)
91 {
92 if(head == NULL)
93 return new;
94 if(new->data < head->data) // 将插入于头节点的左子树中
95 {
96 head->left = insertNode(head->left, new); // 递归
97 if(getHeight(head->left)-getHeight(head->right) == 2) // 新插节点后，左右子树高度差
98 if(new->data < head->left->data) // 新节点插入于外部：LL
99 head = rotationRight(head); // 右旋
100 else // 新节点插入于内部：LR
101 head = rotationLeftRight(head); // 左右旋
102 }
103 else if(new->data > head->data) // 将插入于头节点的右子树中
104 {
105 head->right = insertNode(head->right, new);
106 if(getHeight(head->left)-getHeight(head->right) == -2)
107 if(new->data > head->right->data) // 新节点插入于外部：RR
108 head = rotationLeft(head); // 左旋
109 else // 新节点插入于内部：RL
110 head = rotationRightLeft(head); // 右左旋
111 }
112 head->height = getHeight(head);
113 return head;
114 }
115 // 最小值：递归
116 struct node *findMin(struct node *head)
117 {
118 if(head==NULL || head->left==NULL)
119 return head;
120 findMin(head->left);
121 }
122 // 删除节点
123 struct node *deleteNode(struct node *head, int value)
124 {
125 if(head == NULL)
126 return NULL;
127 if(value < head->data) // 需删除的节点位于左子树
128 {
129 head->left = deleteNode(head->left, value); // 递归
130 if(getHeight(head->right)-getHeight(head->left) == 2) // 删除节点后，左右子树高度差
131 if((head->right->left!=NULL) && (getHeight(head->right->left)>getHeight(head->right->left)))
132 head = rotationRightLeft(head); // 右左旋
133 else
134 head = rotationLeft(head); // 左旋
135 }
136 else if(value > head->data) // 需删除的节点位于右子树
137 {
138 head->right = deleteNode(head->right, value);
139 if(getHeight(head->right)-getHeight(head->left) == -2)
140 if((head->left->right!=NULL) && (getHeight(head->left->right)>getHeight(head->left->left)))
141 head = rotationLeftRight(head); // 左右旋
142 else
143 head = rotationRight(head); // 右旋
144 }
145 else // 找到要删除的节点
146 if(head->left && head->right) // 该节点左右子树都有
147 {
148 struct node *temp = findMin(head->right); // 寻找该节点右子树的最小值
149 head->data = temp->data;
150 head->right = deleteNode(head->right, temp->data);
151 }
152 else // 该节点只有一个孩子 或为 叶子节点
153 {
154 struct node *del = head;
155 /* if(head->left != NULL)
156 head = head->left;
157 else if(head->right != NULL)
158 head = head->right;
159 else
160 head = NULL;
161 */
162 head = (head->left!=NULL)?head->left:head->right;
163 free(del);
164 }
165 if(head != NULL)
166 head->height = getHeight(head); // 更新节点高度值
167 return head;
168 }
169 // 打印节点内容
170 void printNode(struct node *p)
171 {
172 printf("%d(%d) ", p->data, p->height); // 节点值、节点高度
173 }
174 // 层序遍历：队列
175 void levelTraverse(struct node *head, void (*fun)(struct node *))
176 {
177 struct node *queue[NODENUMBER];
178 int front = 0, last = 1;
179 int index = 0, level = 0;
180 queue[index++] = head;
181 while(front < index)
182 {
183 struct node *p = queue[front++];
184 (*fun)(p);
185 if(p->left != NULL) queue[index++]=p->left; // 入队
186 if(p->right != NULL) queue[index++]=p->right;
187 if(front == last)
188 {
189 last = index; level++;
190 }
191 }
192 }