1066 Root of AVL Tree (25)

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

 

 

Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=20) which is the total number of keys to be inserted. Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print the root of the resulting AVL tree in one line.

Sample Input 1:

5
88 70 61 96 120

Sample Output 1:

70

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88

 1 #include<iostream>
 2 using namespace std;
 3 class node{
 4 public:
 5   int val;
 6   node *left, *right;
 7   node(){left=NULL; right=NULL;}
 8 };
 9 
10 node* rightRoate(node* root){
11   node* temp=root->left;
12   root->left=temp->right;
13   temp->right=root;
14   return temp;
15 }
16 
17 node* leftRoate(node* root){
18   node* temp=root->right;
19   root->right=temp->left;
20   temp->left=root;
21   return temp;
22 }
23 
24 node* leftRightRoate(node* root){
25    root->left=leftRoate(root->left);
26    return rightRoate(root);
27 }
28 
29 
30 
31 node* rightLeftRoate(node* root){
32    root->right=rightRoate(root->right);
33    return leftRoate(root);
34 }
35 
36 int getHeight(node* root){
37   if(root==NULL) return 0;
38   int l=getHeight(root->left), r=getHeight(root->right);
39   return l>r? (l+1):(r+1);
40 }
41 
42 node* insert(node* root, int val){
43   if(root==NULL){
44     node *newnode=new node();
45     newnode->val=val;
46     return newnode;
47   }
48   if(root->val>val){ 
49     root->left=insert(root->left, val);
50     if(getHeight(root->left)-getHeight(root->right)>1){
51       if(getHeight(root->left->left)>getHeight(root->left->right)) root=rightRoate(root);
52       else root=leftRightRoate(root);
53     }
54   }
55   else {
56     root->right=insert(root->right, val);
57     if(getHeight(root->right)-getHeight(root->left)>1){
58       if(getHeight(root->right->right)>getHeight(root->right->left)) root=leftRoate(root);
59       else root=rightLeftRoate(root);
60     }
61   }
62   return root;
63 }
64 
65 
66  
67 int main(){
68   node *root=NULL;
69   int i, n, t;
70   cin>>n;
71   for(i=0; i<n; i++){
72     cin>>t;
73     root=insert(root, t);
74   }
75   cout<<root->val<<endl;
76   return 0;
77 }