Date: 2019-04-11 18:49:18
AVL树的基本操作
1 //存储结构
2 struct node
3 {
4 int data;
5 int height; //记录当前子树的高度(叶子->根)
6 //存储平衡因子的话，无法通过其子树算得该树的平衡因子
7 node *lchild, *rchild;
8 };
9
10
11 //新建结点
12 node *newNode(int v)
13 {
14 node *root = new node;
15 root->data = v;
16 root->height = 1;
17 root->lchild = root->rchild = NULL;
18 return root;
19 }
20
21 //获取当前结点所在高度
22 int GetHeight(node *root)
23 {
24 if(root == NULL)
25 return 0;
26 return root->height;
27 }
28
29 //计算结点的平衡因子
30 int GetBalanceFactors(node *root)
31 {
32 return GetHeight(root->lchild)-GetHeight(root->rchild);
33 }
34
35 //更新结点高度
36 void UpdataHeight(node *root)
37 {
38 root->height = max(GetHeight(root->lchild), GetHeight(root->rchild))+1;
39 }
40
41 //查找
42 void Search(node *root, int x)
43 {
44 if(root == NULL)
45 return;
46 if(x == root->data)
47 //visit
48 else if(x < root->data)
49 Search(root->lchild, x);
50 else
51 Search(root->rchild, x);
52 }
53
54 //左右旋互为逆操作
55 //左旋
56 void LeftRotation(node *&root)
57 {
58 node *temp = root->lchild; //temp指向新的根结点B
59 root->rchild = temp->lchild; //B的左子树给A的右子树
60 temp->lchild = root; //B的左子树变为A
61 UpdataHeight(root); //更新结点高度
62 UpdataHeight(temp);
63 root = temp; //令B成为新的根结点
64 }
65
66 //右旋
67 void RightRotation(node *&root)
68 {
69 node *temp = root->lchild;
70 root->lchild = temp->rchild;
71 temp->rchild = root;
72 UpdataHeight(root);
73 UpdataHeight(temp);
74 root = temp;
75 }
76
77 /*
78 1.LL: A==+2, A->lchild=+1
79 A作为root进行右旋
80 2.LR: A==+2, A->lchild=-1
81 A->lchild作为root进行左旋 --> 转化为LL
82 A作为root进行右旋
83 3.RR: A==-2, A->rchild=-1
84 A作为root进行左旋
85 4.RL: A==-2, A->rchild=+1
86 A->rchild作为root进行右旋 --> 转化为RR
87 A作为root进行左旋
88 */
89
90 //插入
91 void Insert(node *&root, int v)
92 {
93 if(root == NULL)
94 {
95 root = newNode(v);
96 return;
97 }
98 if(v < root->data)
99 {
100 Insert(root->lchild, v);
101 UpdataHeight(root); //更新树高
102 if(GetBalanceFactor(root) == 2)
103 {
104 if(GetBalanceFactor(root->lchild) == 1)
105 RightRotation(root);
106 else
107 {
108 LeftRotation(root->lchild);
109 RightRotation(root);
110 }
111 }
112 }
113 else
114 {
115 Insert(root->rchild, v);
116 UpdataHeight(root);
117 if(GetBalanceFactor(root) == -2)
118 {
119 if(GetBalanceFactor(root->rchild) == -1)
120 LeftRotation(root);
121 else
122 {
123 RightRotation(root->rchild);
124 LeftRotation(root);
125 }
126 }
127 }
128 }
129
130 //建立
131 node *Create(int data[], int n)
132 {
133 node *root = NULL;
134 for(int i=0; i<n; i++)
135 Insert(root, data[i]);
136 return root;
137 }
判断一棵树是否为AVL树
1 #include <cstdio>
2 const int M = 10;
3 int pre[M]={50,38,30,45,40,48,70,60,75,80};
4 int in[M]={30,38,40,45,48,50,60,70,75,80};
5 struct node
6 {
7 int data;
8 node *lchild, *rchild;
9 };
10
11 node *Create(int preL, int preR, int inL, int inR)
12 {
13 if(preL > preR)
14 return NULL;
15 node *root = new node;
16 root->data = pre[preL];
17 int k;
18 for(k=inL; k<=inR; k++)
19 if(in[k] == root->data)
20 break;
21 int numLeft = k-inL;
22 root->lchild = Create(preL+1, preL+numLeft, inL, k-1);
23 root->rchild = Create(preL+numLeft+1, preR, k+1, inR);
24 }
25
26 int IsAvl = true;
27 int IsAVL(node *root)
28 {
29 if(root == NULL)
30 return -1;
31 int bl = IsAVL(root->lchild)+1;
32 int br = IsAVL(root->rchild)+1;
33 if(bl-br>1 || bl-br<-1)
34 IsAvl = false;
35 return bl>br?bl:br;
36 }
37
38 int main()
39 {
40 #ifdef ONLINE_JUDGE
41 #else
42 freopen("Test.txt", "r", stdin);
43 #endif
44
45 node *root = Create(0,M-1,0,M-1);
46 IsAVL(root);
47 if(IsAvl)
48 printf("Yes.");
49 else
50 printf("No.");
51
52 return 0;
53 }
