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 (≤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.

 

#include <iostream>
#include <algorithm>
using namespace std;

typedef struct AVLNode* AVLTree;
struct AVLNode{
    int data;           //结点的值
    AVLTree left;      //左儿子
    AVLTree right;     //右儿子
    int height;         //结点的高度
};


//获得树的高度
int getHeight(AVLTree a){
    return a == nullptr ? -1 : a->height;
}

//LL单旋 把b的右子树腾出来挂给A的左子树，再将a挂到b的右子树上去
AVLTree LLRotation(AVLTree a){
    //此时根结点是a
    AVLTree b = a->left;    //b为a的左子树
    a->left = b->right;     //b的右子树挂在a的左子树上
    b->right = a;           //a挂在b的右子树上
    a->height = max(getHeight(a->left), getHeight(a->right)) + 1;
    b->height = max(getHeight(b->left), a->height) + 1;
    return b;   //此时根结点为b
}

//RR单旋
AVLTree RRRotation(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;
}

//LR双旋
AVLTree LRRotation(AVLTree a){
    //先RR单旋
    a->left = RRRotation(a->left);
    //再LL单旋
    return LLRotation(a);
}

//RL双旋
AVLTree RLRotation(AVLTree a){
    //先LL单旋
    a->right = LLRotation(a->right);
    //再RR单旋
    return RRRotation(a);
}

AVLTree Insert(AVLTree t, int x){
    if(!t){   //结点为空
        t = (AVLTree)malloc(sizeof(struct AVLNode));
        t->data = x;
        t->left = t->right = nullptr;
        t->height = 0;
    }else{
        if(x < t->data){
            t->left = Insert(t->left, x);
            if(getHeight(t->left) - getHeight(t->right) == 2) {
                if(x < t->left->data)   //LL单旋
                    t = LLRotation(t);
                else if(t->left->data < x)  //LR双旋
                    t = LRRotation(t);
            }
        }else if(t->data < x){
            t->right = Insert(t->right, x);
            if(getHeight(t->right) - getHeight(t->left) == 2){
                if(x < t->right->data)   //RL双旋
                    t = RLRotation(t);
                else if(t->right->data < x)   //RR单旋
                    t = RRRotation(t);
            }
        }
    }
    //更新树高
    t->height = max(getHeight(t->left), getHeight(t->right)) + 1;
    return t;
}

int main()
{
    AVLTree t = nullptr;
    int n;
    cin >> n;
    for(int i = 0; i < n; i++){
        int tmp;
        cin >> tmp;
        t = Insert(t, tmp);
    }
    cout << t->data;
    return 0;
}