PAT_A1066#Root of AVL Tree

Source:

PAT A1066 Root of AVL Tree (25 分)

Description:

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 (≤) 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

Keys:

• 平衡二叉树（Self-balancing Binary Search Tree）

Code:

 /*
 Data: 2019-06-24 15:44:17
 Problem: PAT_A1066#Root of AVL Tree
 AC: 12:20

 题目大意：
 构造AVL树，打印根结点
 */
 #include<cstdio>
 #include<algorithm>
 using namespace std;
 struct node
 {
     int data,height;
     node *lchild,*rchild;
 };

 int GetHeight(node *root)
 {
     if(root == NULL)
         return ;
     else
         return root->height;
 }

 void UpdataHeight(node *&root)
 {
     root->height = max(GetHeight(root->lchild),GetHeight(root->rchild))+;
 }

 int GetBalanceFactor(node *root)
 {
     return GetHeight(root->lchild) - GetHeight(root->rchild);
 }

 void LeftRotation(node *&root)
 {
     node *temp = root->rchild;
     root->rchild = temp->lchild;
     temp->lchild = root;
     UpdataHeight(root);
     UpdataHeight(temp);
     root = temp;
 }

 void RightRotation(node *&root)
 {
     node *temp = root->lchild;
     root->lchild = temp->rchild;
     temp->rchild = root;
     UpdataHeight(root);
     UpdataHeight(temp);
     root = temp;
 }

 void Insert(node *&root, int x)
 {
     if(root == NULL)
     {
         root = new node;
         root->data = x;
         root->height=;
         root->lchild = root->rchild = NULL;
     }
     else if(x < root->data)
     {
         Insert(root->lchild, x);
         UpdataHeight(root);
         if(GetBalanceFactor(root) == )
         {
             if(GetBalanceFactor(root->lchild) == )
                 RightRotation(root);
             else
             {
                 LeftRotation(root->lchild);
                 RightRotation(root);
             }
         }
     }
     else
     {
         Insert(root->rchild, x);
         UpdataHeight(root);
         if(GetBalanceFactor(root) == -)
         {
             if(GetBalanceFactor(root->rchild) == -)
                 LeftRotation(root);
             else
             {
                 RightRotation(root->rchild);
                 LeftRotation(root);
             }
         }
     }
 }

 int main()
 {
 #ifdef ONLINE_JUDGE
 #else
     freopen("Test.txt", "r", stdin);
 #endif // ONLINE_JUDGE

     int n,x;
     scanf("%d", &n);
     node *root = NULL;
     for(int i=; i<n; i++)
     {
         scanf("%d", &x);
         Insert(root, x);
     }
     printf("%d", root->data);

     return ;
 }