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

#include <cstdio>
#include <stdlib.h>


typedef struct AVLNode * AVLTree;
typedef AVLTree Position;

struct AVLNode {
    int data;
    AVLTree left;
    AVLTree right;
    int height;
};


int max(int a, int b) {
    return a>b ? a: b;
}
int getHeight(AVLTree T);
void calcHeight(AVLTree T);

//core function
AVLTree rightRotation (AVLTree );
AVLTree RLRotation(AVLTree );
AVLTree leftRotation(AVLTree );
AVLTree LRRotation(AVLTree );
AVLTree Insert(AVLTree T, int x);

int main() {
    int n, v;
    scanf("%d", &n);
    AVLTree avt = NULL;
    for(int i=0; i<n; i++) {
        scanf("%d", &v);
        avt = Insert(avt, v);
    }
    printf("%d\n", avt->data);
}

AVLTree Insert(AVLTree T, int x) {
    if(!T) {
        T = (AVLTree) malloc(sizeof(struct AVLNode));
        T->data = x;
        T->left = NULL;
        T->right = NULL;
    }
    
    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 = rightRotation(T);
            }
            else T = RLRotation(T);
        }
    } /* else if right_insertion*/
    
    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 = leftRotation(T);
            }
            else T = LRRotation(T);
        }
    } /* else if left_insertion*/
    
    
    
    //update height
    calcHeight(T);
    
    return T;
}


int getHeight(AVLTree T) {
    if (!T) {
        return 0;
    }
    else return T->height;
}
void calcHeight(AVLTree T) {
    T->height = max(getHeight(T->left), getHeight(T->right)) + 1;
}

AVLTree rightRotation (AVLTree A) {
    AVLTree B = A->right;
    A->right = B->left;
    B->left = A;
    
    calcHeight(A);
    calcHeight(B);
    return B;
}
AVLTree leftRotation(AVLTree A) {
    AVLTree B = A->left;
    A->left = B->right;
    B->right = A;
    
    calcHeight(A);
    calcHeight(B);
    return B;
}


AVLTree RLRotation(AVLTree T) {
    T->right = leftRotation(T->right);
    return rightRotation(T);
}
AVLTree LRRotation(AVLTree T) {
    T->left = rightRotation(T->left);
    return leftRotation(T);
}