PAT甲级1066

1066. Root of AVL Tree (25)

时间限制

100 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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 ythe 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<algorithm>
using namespace std;
struct node
{
  int v;
  int height;
  node*lchild, *rchild;
  node(){}
  node(int x):v(x),height(1),lchild(NULL),rchild(NULL){}
};
int getHeight(node*root)
{
  if (!root)return 0;
  return root->height;
}//获得高度
int getBalanceFactor(node*root)
{
  return getHeight(root->lchild)-getHeight(root->rchild);
}//获得平衡因子
void updateHeight(node*&root)
{
  root->height = max(getHeight(root->lchild), getHeight(root->rchild)) + 1;
}
void L(node*&root)
{
  node*temp = root->rchild;
  root->rchild = temp->lchild;
  temp->lchild = root;
  updateHeight(root);
  updateHeight(temp);
  root = temp;
}
void R(node*&root)
{
  node*temp = root->lchild;
  root->lchild = temp->rchild;
  temp->rchild = root;
  updateHeight(root);
  updateHeight(temp);
  root = temp;
}
void insert(node*&root, int x)
{
  if (!root)
  {
    root = new node(x);
    return;
  }
  if (x < root->v)
  {
    insert(root->lchild, x);
    updateHeight(root);
    if (getBalanceFactor(root) == 2)//确定树形
    {
      if (getBalanceFactor(root->lchild) == 1)
      {
        R(root);
      }
      else if (getBalanceFactor(root->lchild) == -1)
      {
        L(root->lchild);
        R(root);
      }
    }
  }
  else
  {
    insert(root->rchild, x);
    updateHeight(root);
    if (getBalanceFactor(root) == -2)//确定树形
    {
      if (getBalanceFactor(root->rchild) == -1)
      {
        L(root);
      }
      else if (getBalanceFactor(root->rchild) == 1)
      {
        R(root->rchild);
        L(root);
      }
    }
  }
}
int main()
{
  int N;
  scanf("%d", &N);
  int x;
  node*root = NULL;
  for (int i = 0; i < N; i++)
  {
    scanf("%d", &x);
    insert(root, x);
  }
  printf("%d\n", root->v);
  return 0;
}