04-树5 Root of AVL Tree (25分)

04-树5 Root of AVL Tree (25分)

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

提交代码：

#include <stdio.h>
#include <stdlib.h>

typedef int ElemType;
typedef struct AVLNode *Position;
typedef Position AVLTree;
struct AVLNode{
    ElemType Data;
    AVLTree Left;
    AVLTree Right;
    int Height;
};

int Max(int a, int b){
    return a > b ? a : b;
}

int GetHeight(AVLTree T){
    if(!T){
        return -1;
    }
    return T->Height;
}

AVLTree SingleLeftRotation( 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), GetHeight(B->Right)) + 1;
    return B;
}

AVLTree SingleRightRotation( 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->Left), GetHeight(B->Right)) + 1;
    return B;
}

AVLTree DoubleLeftRotation( AVLTree A ){
    A->Left = SingleRightRotation(A->Left);
    return SingleLeftRotation(A);
}

AVLTree DoubleRightRotation( AVLTree A ){
    A->Right = SingleLeftRotation(A->Right);
    return SingleRightRotation(A);
}

AVLTree Insert( AVLTree T, ElemType X ){
    if(!T){
        T = (AVLTree)malloc(sizeof(struct AVLNode));
        T->Data = X;
        T->Height = 0;
        T->Left = NULL;
        T->Right = NULL;
    }
    else if( X < T->Data ){
        T->Left = Insert( T->Left, X );
        if( GetHeight(T->Left) - GetHeight(T->Right) == 2){
            if( X < T->Left->Data){
                T = SingleLeftRotation(T);
            }else{
                T = DoubleLeftRotation(T);
            }
        }
    }
    else if( X > T->Data){
        T->Right = Insert(T->Right, X);
        if(GetHeight(T->Left) - GetHeight(T->Right) == -2){
            if( X > T->Right->Data){
                T = SingleRightRotation(T);
            }else{
                T = DoubleRightRotation(T);
            }
        }
    }
    T->Height = Max( GetHeight(T->Left), GetHeight(T->Right)) + 1;
    return T;
}

int main(){
    int N, X;
    AVLTree T = NULL;
    scanf("%d", &N);
    for(int i = 0; i < N; ++i){
        scanf("%d", &X);
        T = Insert(T, X);
    }
    printf("%d", T->Data);
    return 0;
}

提测结果：