04-树5 Root of AVL Tree

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

思路：

基础题，建一个AVL树

#include <iostream>

using namespace std;

typedef struct TNode* AVLTree;
struct TNode
{
int height;
AVLTree left;
AVLTree right;
int data;
};
int Max(int x,int y)
{
int q;
x>y?q=x:q=y;
return q;
}
int Height(AVLTree t)
{
if(t == NULL)
return -1;
else
return t->height;
}
AVLTree SingleRotateWithLeft(AVLTree T) //LL
{
AVLTree k;
k = T->left;
T->left = k->right;
k->right = T;
k->height = Max(Height(k->left), Height(k->right)) + 1;
T->height = Max(Height(T->left), Height(T->right)) + 1;
return k;
}
AVLTree SingleRotateWithRight(AVLTree T) //RR
{
AVLTree k;
k = T->right;
T->right = k->left;
k->left = T;
k->height = Max(Height(k->left), Height(k->right)) + 1;
T->height = Max(Height(T->left), Height(T->right)) + 1;
return k;
}
AVLTree DoubleRotateWithLeft(AVLTree T) //LR
{
T->left = SingleRotateWithRight(T->left);
T = SingleRotateWithLeft(T);
return T;
}
AVLTree DoubleRotateWithRight(AVLTree T) //RL
{
T->right = SingleRotateWithLeft(T->right);
T = SingleRotateWithRight(T);
return T;
}
AVLTree Insert(AVLTree T, int x)
{
if(T == NULL)
{
T = new TNode;
T->left = T->right = NULL;
T->data = x;
}
else if(x < T->data)  //left child
{
T->left = Insert(T->left, x);
if(Height(T->left) - Height(T->right) == 2)
{
if(x < T->left->data)
T = SingleRotateWithLeft(T);//LL
else if(x > T->left->data)
T = DoubleRotateWithLeft(T);//LR
}
}
else if(x > T->data)  //right child
{
T->right = Insert(T->right, x);
if(Height(T->right) - Height(T->left) == 2)
{
if(x > T->right->data)
T = SingleRotateWithRight(T);//RR
else if(x < T->right->data)
T = DoubleRotateWithRight(T);//RL
}
}

//update T's height
T->height = Max(Height(T->left), Height(T->right)) + 1;
return T;
}
int main()
{
int n,x;
AVLTree T = NULL;
cin>>n;
for(int i=0; i<n; i++)
{
cin>>x;
T = Insert(T,x);
}
cout << T->data << endl;
return 0;
}