1066 Root of AVL Tree （25 分)

2019-04-01

1066 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 (≤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:

1 2	5 88 70 61 96 120

Sample Output 1:

Sample Input 2:

1 2	7 88 70 61 96 120 90 65

Sample Output 2:

作者: CHEN, Yue

单位: 浙江大学

时间限制: 400 ms

内存限制: 64 MB

代码长度限制: 16 KB

题目大意

要求根据给出的结点，构造一颗avl树，返回根结点上的值。构造相应的树即可。

代码

#include <iostream>
#include <vector>
#include <algorithm>
#include <deque>
#include <map>
#include <set>
#include <cstring>
#include <cmath>
#include<sstream>

using namespace std;
struct node{
    int v;
    node* left;
    node* right;
    int height;
};
int height(node *root){
    return root==NULL?-1:root->height;
}
node* rr(node* root){
    node*t=root->right;
    root->right=t->left;
    t->left=root;
    root->height=max(height(root->left),height(root->right))+1;
    t->height=max(height(t->left),height(t->right))+1;
    return t;
}
node* ll(node* root){
    node*t=root->left;
    root->left=t->right;
    t->right=root;
    root->height=max(height(root->left),height(root->right))+1;
    t->height=max(height(t->left),height(t->right))+1;
    return t;
}
node* rl(node* root){
    root->right=ll(root->right);
    root=rr(root);
    return root;
}

node* lr(node* root){
    root->left=rr(root->left);
    root=ll(root);
    return root;
}
node* insert(node* root,int v){
    if(root==NULL){
        root=new node;
        root->height=0;
        root->v=v;
        root->left=NULL;
        root->right=NULL;
    }else if(v>root->v){
        root->right=insert(root->right,v);
        if(height(root->right)-height(root->left)==2)
            if(v>root->right->v)
                root=rr(root);
            else
                root=rl(root);

    }else if(v<root->v){
        root->left=insert(root->left,v);
        if(height(root->left)-height(root->right)==2)
            if(v<root->left->v)
                root=ll(root);
            else
                root=lr(root);
    }
    root->height=max(height(root->left),height(root->right))+1;
    return  root;

}
int main() {
    int n;
    cin>>n;
    int v;
    node *root;
    for(int i=0;i<n;i++){
        cin>>v;
        root=insert(root,v);
    }
    cout<<root->v<<endl;
    return 0;

}