PAT 甲级 1066  Root of AVL Tree

1066 Root of AVL Tree （25 point(s)）

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

经验总结：

这一题是经典的AVL树构造，根据题目所给序列，构造AVL树，构造完成后，输出根结点的值就行啦~(๑•̀ㅂ•́)و✧

AC代码

#include <cstdio>
#include <algorithm>
using namespace std;
struct node
{
  int data,height;
  node * lchild,* rchild;
  node(int v):data(v),height(1),lchild(NULL),rchild(NULL){}
};
int get_height(node *root)
{
  if(root==NULL)
    return 0;
  return root->height;
}
void update_height(node *root)
{
  root->height=max(get_height(root->lchild),get_height(root->rchild))+1;
}
int get_balance(node *root)
{
  return get_height(root->lchild)-get_height(root->rchild);
}
void L(node *&root)
{
  node * temp=root->rchild;
  root->rchild=temp->lchild;
  temp->lchild=root;
  update_height(root);
  update_height(temp);
  root=temp;
}
void R(node *&root)
{
  node * temp=root->lchild;
  root->lchild=temp->rchild;
  temp->rchild=root;
  update_height(root);
  update_height(temp);
  root=temp;
}
void insert(int data,node *&root)
{
  if(root==NULL)
  {
    root=new node(data);
    return ;
  }
  if(data<root->data)
  {
    insert(data,root->lchild);
    update_height(root);
    if(get_balance(root)==2)
      if(get_balance(root->lchild)==1)
        R(root);
      else
      {
        L(root->lchild);
        R(root);
      }
  }
  else
  {
    insert(data,root->rchild);
    update_height(root);
    if(get_balance(root)==-2)
      if(get_balance(root->rchild)==-1)
        L(root);
      else
      {
        R(root->rchild);
        L(root);
      }
  }
}
int main()
{
  int n,t;
  scanf("%d",&n);
  node *root=NULL;
  for(int i=0;i<n;++i)
  {
    scanf("%d",&t);
    insert(t,root);
  }
  printf("%d\n",root->data);
  return 0;
}