04-树5 Root of AVL Tree

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$N$ ($\le 20$) 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:

588 70 61 96 120

Sample Output 1:

70

Sample Input 2:

788 70 61 96 120 90 65

Sample Output 2:

88

主要是调整平衡二叉树，LL，RR，LR，RL.....

#include <stdio.h>#include <stdlib.h>#define ElementType int#define Max(a,b) ((a)>(b)?(a):(b))typedef struct AVLTreeNode{    ElementType Data;    struct AVLTreeNode *Left;    struct AVLTreeNode *Right;    int Height;} *AVLTree;int GetHeight(AVLTree T){    if(!T)         return 0;    else        return T->Height;}AVLTreeSingleLeftRotation(AVLTree A){    AVLTree B=A->Left;    A->Left=B->Right;    B->Right=A;    A->Height=Max(GetHeight(A->Left),GetHeight(A->Right))+1;    B->Height=Max(GetHeight(B->Left),A->Height)+1;        return B;}AVLTreeSingleRightRotation(AVLTree A){    AVLTree B=A->Right;    A->Right=B->Left;    B->Left=A;    A->Height=Max(GetHeight(A->Left),GetHeight(A->Right))+1;    B->Height=Max(GetHeight(B->Right),A->Height)+1;        return B;}AVLTreeDoubleLeftRightRotation(AVLTree A){    A->Left=SingleRightRotation(A->Left);    return SingleLeftRotation(A);}AVLTreeDoubleRightLeftRotation(AVLTree A){    A->Right=SingleLeftRotation(A->Right);    return SingleRightRotation(A);}AVLTree AVL_Insertion(ElementType X, AVLTree T){    if(!T){        T=(AVLTree)malloc(sizeof(struct AVLTreeNode));        T->Data=X;        T->Height=0;        T->Left=T->Right=NULL;    }else if(X<T->Data){        T->Left=AVL_Insertion(X,T->Left);        if(GetHeight(T->Left)-GetHeight(T->Right)==2)//判断左右两边的树平衡不            if(X<T->Left->Data)                T=SingleLeftRotation(T);//LL旋转            else                T=DoubleLeftRightRotation(T);//LR旋转    }else if(X>T->Data){        T->Right=AVL_Insertion(X,T->Right);        if(GetHeight(T->Left)-GetHeight(T->Right)==-2)            if(X>T->Right->Data)                T=SingleRightRotation(T);//RR旋转            else                T=DoubleRightLeftRotation(T);//RL旋转    }        T->Height=Max(GetHeight(T->Left),GetHeight(T->Right))+1;//height为此子树的高度    return T;}int main(){    int i,NodeNum,tmpkey;    AVLTree tree=NULL;    scanf("%d",&NodeNum);    for(i=0;i<NodeNum;i++){        scanf("%d",&tmpkey);        tree=AVL_Insertion(tmpkey,tree);            }        printf("%d",tree->Data);        return 0;      }