1066 Root of AVL Tree (25分)(AVL树的实现)

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 (≤) 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

题目分析：写一个AVL树 背课文是好的 但也要理解清除AVL树的原理 之后还要学习各种平衡树 如红黑树什么的

 #define _CRT_SECURE_NO_WARNINGS
 #include <climits>
 #include<iostream>
 #include<vector>
 #include<queue>
 #include<map>
 #include<set>
 #include<stack>
 #include<algorithm>
 #include<string>
 #include<cmath>
 using namespace std;
 typedef struct TNode* Tree;
 struct TNode {
     int Data;
     Tree TL;
     Tree TR;
     int Height;  //要初始化为-1;
 };
 int GetHeight(Tree T) {
     if (T)
         return T->Height;
     else
         return -;
 }
 Tree singleLeftRotate(Tree T) {
     Tree TL = T->TL;
     T->TL = TL->TR;
     TL->TR = T;
     T->Height = max(GetHeight(T->TL), GetHeight(T->TR)) + ;
     TL->Height = max(GetHeight(TL->TL), GetHeight(TL->TR)) + ;
     return TL;
 }
 Tree singleRightRotate(Tree T) {
     Tree TR = T->TR;
     T->TR = TR->TL;
     TR->TL = T;
     T->Height = max(GetHeight(T->TL), GetHeight(T->TR)) + ;
     TR->Height = max(GetHeight(TR->TL), GetHeight(TR->TR)) + ;
     return TR;
 }
 Tree doubleLeftRightRotate(Tree T) {
     T->TL = singleRightRotate(T->TL);
     return singleLeftRotate(T);
 }
 Tree doubleRightLeftRotate(Tree T) {
     T->TR = singleLeftRotate(T->TR);
     return singleRightRotate(T);
 }
 Tree Insert(Tree T,int data) {
     if (!T)
     {
         T = new TNode();
         T->Data = data;
         T->Height = ;
         T->TL = T->TR = NULL;
     }
     else if (data > T->Data) {
         T->TR = Insert(T->TR, data);
         T->Height = max(GetHeight(T->TL), GetHeight(T->TR)) + ;
         if (GetHeight(T->TR) - GetHeight(T->TL) == ) {
             if (data > T->TR->Data)
                 T=singleRightRotate(T);
             else
                 T=doubleRightLeftRotate(T);
         }
     }
     else {
         T->TL = Insert(T->TL, data);
         T->Height = max(GetHeight(T->TL), GetHeight(T->TR)) + ;
         if (GetHeight(T->TL) - GetHeight(T->TR) == ) {
             if (data < T->TL->Data)
                 T=singleLeftRotate(T);
             else
                 T=doubleLeftRightRotate(T);
         }
     }
     return T;
 }

 int main()
 {
     int N;
     Tree T = NULL;
     int data;
     cin >> N;
     for (int i = ; i < N; i++)
     {
         cin >> data;
         T = Insert(T, data);
     }
     cout << T->Data;
 }