04-樹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

 題目要求給出一個輸入順序，要你建立一個平衡二叉搜尋樹，然後輸出根

#include <iostream>

typedef struct _Tree_node
{
	int data;
	int Hight;
	_Tree_node *Left;
	_Tree_node *Right;
}Tree_node;

Tree_node* AVL_insert_node(Tree_node * node, int X);//插入節點,調節樹高
int GetHight(Tree_node *);
Tree_node *SingleLeftRotation(Tree_node *);			//左單旋
Tree_node *SingleLeftRightRotation(Tree_node *);	//左右雙旋
Tree_node *SingleRightRotation(Tree_node *);		//右單旋
Tree_node *SingleRightLeftRotation(Tree_node *);	//右左雙旋

int max(int a, int b)
{
	return a > b ? a : b;
}

using namespace std;

int main()
{
	Tree_node *root = NULL;
	int N, X;
	cin >> N;
	for (int i = 0; i < N; i++)
	{
		cin >> X;
		root = AVL_insert_node(root, X);
		//cout << root->data << endl;
	}
	cout << root->data;

	return 0;
}

//插入節點
Tree_node* AVL_insert_node(Tree_node * node, int X)
{
	if (node == NULL)
	{
		node = new Tree_node;
		node->Left = node->Right = NULL;
		node->Hight = 0;
		node->data = X;
	}
	else if (node->data < X)
	{
		node->Right = AVL_insert_node(node->Right, X);
		if (GetHight(node->Left) - GetHight(node->Right) == -2)
		{
			if (node->Right->data < X)
				node = SingleRightRotation(node);
			else 
				node = SingleRightLeftRotation(node);
		}
	}
	else if (node->data > X)
	{
		node->Left = AVL_insert_node(node->Left, X);
		if (GetHight(node->Left) - GetHight(node->Right) == 2) 
		{
			if (node->Left->data > X)
				node = SingleLeftRotation(node);
			else
				node = SingleLeftRightRotation(node);
		}
	}
	//每次插入要更新樹高
	node->Hight = max(GetHight(node->Left), GetHight(node->Right)) + 1;

	return node;
}

//獲得樹高
int GetHight(Tree_node *node)
{
	if (node == NULL)
		return 0;
	return max(GetHight(node->Left), GetHight(node->Right)) + 1;
}

//二叉樹的旋轉
Tree_node *SingleLeftRotation(Tree_node *A)
{
	Tree_node *B = A->Left;

	A->Left = B->Right;
	B->Right = A;
	A->Hight = max(GetHight(A->Left), GetHight(A->Right)) + 1;
	B->Hight = max(GetHight(B->Left), GetHight(B->Right)) + 1;

	return B;
}

Tree_node *SingleLeftRightRotation(Tree_node *A)
{
	A->Left = SingleRightRotation(A->Left);
	return SingleLeftRotation(A);
}

Tree_node *SingleRightRotation(Tree_node *A)
{
	Tree_node *B = A->Right;

	A->Right = B->Left;
	B->Left = A;
	A->Hight = max(GetHight(A->Left), GetHight(A->Right)) + 1;
	B->Hight = max(GetHight(B->Left), GetHight(B->Right)) + 1;

	return B;
}

Tree_node *SingleRightLeftRotation(Tree_node *A)
{
	A->Right = SingleLeftRotation(A->Right);
	return SingleRightRotation(A);
}