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:

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 ;
}

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