04-树4 是否同一棵二叉搜索树

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 NN (\le 20≤20) which is the total number of keys to be inserted. Then NN 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

题目大意：输入一段序列，构成AVL树，输出顶点

思路：用构成二叉搜索树的方法，当层次树大于或等于二的时候，旋转调整。

#include <iostream>

using namespace std;
#define Elemment int

typedef struct Avltree{
Elemment data;
struct Avltree* left;
struct Avltree* right;
int height;
}Avltree;

int getheight(Avltree* t)
{
if (t == NULL)
return -1;
else
return t->height;

}

int max(int leftHeight, int rightHeight)
{
if (leftHeight >= rightHeight)
return leftHeight;
else
return rightHeight;
}

Avltree* rrrotation(Avltree* t)
{
Avltree* top = t->right;
//t->right = top->left;
//top->left = t;
t->right = top->left;
top->left = t;

t->height = max(getheight(t->left), getheight(t->right)) + 1;
top->height = max(getheight(top->right), getheight(top->left)) + 1;

return top;
}

Avltree* llrotation(Avltree* t)
{
Avltree* top = t->left;
//t->left = top->right;
//top->right = t;
t->left = top->right;
top->right = t;

t->height = max(getheight(t->left), getheight(t->right)) + 1;
top->height = max(getheight(top->left), getheight(top->right)) + 1;

return top;
}

Avltree* rlrotation(Avltree* t)
{
t->right = llrotation(t->right);

return rrrotation(t);
}

Avltree* lrrotation(Avltree* t)
{
t->left = rrrotation(t->left);
return llrotation(t);
}

Avltree* insert(Elemment x, Avltree* t)
{
if (t == NULL)
{
t = new Avltree;
t->data = x;
t->height = 0;
t->left = NULL;
t->right = NULL;
}

else if (x < t->data)
{
t->left = insert(x, t->left);
if (getheight(t->left) - getheight(t->right) == 2)
{
if (x < t->left->data)
{
t = llrotation(t);
}

else
{
t = lrrotation(t);
}
}

}
else if (x>t->data)
{
t->right = insert(x, t->right);
if (getheight(t->right) - getheight(t->left) == 2)
{
if (x > t->right->data)
{
t = rrrotation(t);
}
else
{
t = rlrotation(t);
}
}
}

t->height = max(getheight(t->left), getheight(t->right)) + 1;
return t;
}

void input()
{
int num,data;
Avltree* top = NULL;
cin >> num;
for (int i = 0; i < num; i++)
{
cin >> data;
top = insert(data, top);
}

cout << top->data;
}

int main()
{
input();

return 0;
}