04-树5 AVL树的根

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 (≤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:

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

谷歌翻译

04-树5 AVL树的根（25分）

AVL树是一种自平衡二进制搜索树。 在AVL树中，任何节点的两个子树的高度最多相差1个。 如果它们之间的任何时间差超过一个，则将进行重新平衡以恢复此属性。 图1-4说明了旋转规则。

现在给出了一系列插入，您应该告诉得到的AVL树的根。

输入规格：

每个输入文件包含一个测试用例。 对于每种情况，第一行都包含一个正整数N（≤20），它是要插入的键的总数。 然后在下一行中给出N个不同的整数键。 一行中的所有数字都用空格分隔。

输出规格：

对于每个测试用例，将结果AVL树的根打印在一行中。

样本输入1：

5
88 70 61 96 120

样本输出1：

70

样本输入2：

7
88 70 61 96 120 90 65

样本输出2：

88

代码

#include <bits/stdc++.h>
using namespace std;

typedef struct Node* Tree; 
struct Node{
    int data;
    Tree left,right;
    int height;
};
int height(Tree t){
    if(t){
        return max(height(t->left),height(t->right))+1;
    }else{
        return 0;
    }
}
//左旋 
Tree singleLeft(Tree t){
    Tree q=t->left;
    t->left=q->right;
    q->right=t;
    t->height=max(height(t->right),height(t->left));
    q->height=max(height(q->right),height(q->left));
    return q;
}
//右旋 
Tree singleRight(Tree t){
    Tree q=t->right;
    t->right=q->left;
    q->left=t;
    q->height=max(height(q->right),height(q->left));
    t->height=max(height(t->right),height(t->left));
    return q; 
}
//左右旋 
Tree doubleSingleLeft(Tree t){
    t->left=singleRight(t->left);
    return singleLeft(t);
}
//右左旋 
Tree doubleSingleRight(Tree t){
    t->right=singleLeft(t->right);
    return singleRight(t);
}
Tree create(Tree t ,int x){
    if(t==NULL){
        t=(Tree)malloc(sizeof(struct Node));
        t->data=x;
        t->left=t->right=NULL;
        t->height=0;
    }else if(x<t->data){
        t->left = create(t->left,x);
        if(height(t->left)-height(t->right)==2){
            if(x<t->left->data){
                t=singleLeft(t);
            }else{
                t=doubleSingleLeft(t);
            }
        }
    }else if(x>t->data){
        t->right=create(t->right,x);
        if(height(t->right)-height(t->left)==2){
            if(x>t->right->data){
                t=singleRight(t);
            }else{
                t=doubleSingleRight(t);
            }
        }
    } 
    t->height=max(height(t->left),height(t->right));
    return t;
    
}
int main(){
    int n;
    cin>>n;
    Tree t=NULL;
    for(int i=1;i<=n;i++){
        int x;
        cin>>x;
        t=create(t,x);
    }
    cout<<t->data;
    return 0;
}