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 ythe 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 <stdio.h> 2 #include <stdlib.h> 3 #include <iostream> 4 #include <string.h> 5 #include <math.h> 6 #include <algorithm> 7 #include <string> 8 #include <stack> 9 #include <queue> 10 using namespace std; 11 const int maxn=110; 12 int n,m,s; 13 struct node{ 14 node *left; 15 node *right; 16 int v,height;//高度可理解为以该节点为根的树的层数 17 }*root,*null; 18 void init(){ 19 null=new node; 20 null->height=0; 21 root=null;//null为 高度为0 22 } 23 node* newNode(int v)//设置新的节点 24 { 25 node* t=new node(); 26 t->v=v; 27 t->height=1; 28 t->left=t->right=null; 29 return t; 30 } 31 32 void getNewheight(node *root) 33 { 34 root->height=max(root->left->height,root->right->height)+1; 35 } 36 void L(node *&root) 37 { 38 node *tmp=root->right; 39 root->right=tmp->left; 40 tmp->left=root; 41 getNewheight(root); 42 getNewheight(tmp); 43 root=tmp; 44 45 } 46 47 void R(node *&root) 48 { 49 node* tmp=root->left; 50 root->left=tmp->right; 51 tmp->right=root; 52 getNewheight(root); 53 getNewheight(tmp); 54 root=tmp; 55 } 56 void insert(node *&root,int v) 57 { 58 if(root==null) 59 { 60 root=newNode(v); 61 return; 62 } 63 if(v<root->v) 64 { 65 insert(root->left,v); 66 getNewheight(root); 67 if((root->left->height)-(root->right->height)==2) 68 { 69 //ll型 70 if((root->left->left->height)-(root->left->right->height)==1) 71 { 72 R(root); 73 }else if((root->left->left->height)-(root->left->right->height)==-1) 74 { 75 //lr 76 L(root->left); 77 R(root); 78 } 79 } 80 }else 81 { 82 insert(root->right,v); 83 getNewheight(root); 84 if((root->left->height)-(root->right->height)==-2) 85 { 86 if((root->right->left->height)-(root->right->right->height)==1) 87 { 88 R(root->right); 89 L(root); 90 }else if((root->right->left->height)-(root->right->right->height)==-1) 91 { 92 L(root); 93 } 94 } 95 } 96 } 97 int main(){ 98 int n,v; 99 init(); 100 scanf("%d",&n); 101 for(int i=0;i<n;i++) 102 { 103 scanf("%d",&v); 104 insert(root,v); 105 } 106 printf("%d ",root->v); 107 return 0; 108 }