AVL树的平衡

 

一.左旋和右旋（以左旋为例）

（1）左旋情况一：newroot左孩子为空

（2）左旋情况二：newroot左孩子不为空

 

二.思路图

 三.双旋转

 代码实现：

typedef int KeyType;
typedef struct AVLNode
{
	struct AVLNode* leftchild;
	struct AVLNode* parent;
	struct AVLNode* rightchild;
	int balance;//-1 0 1;
	KeyType key;
}AVLNode;

typedef struct
{
	AVLNode* root;
	int cursize;
}AVLTree;

//左旋
static AVLNode* RotateLeft(AVLTree* ptree, AVLNode* ptr)
{
	AVLNode* newroot = ptr->rightchild;//旋转点1.1
	newroot->parent = ptr->parent;//修改旋转点父节点2.1
	ptr->rightchild = newroot->leftchild;//1.2
	if (newroot->leftchild != NULL)
	{
		newroot->leftchild->parent = ptr;//2.2
	}
	newroot->leftchild = ptr;//1.3
	if (ptr == ptree->root)
	{
		ptree->root = newroot;
	}
	else
	{
		if (ptr == ptr->parent->leftchild)
		{
			ptr->parent->leftchild = newroot;
		}
		else
		{
			ptr->parent->rightchild = newroot;
		}
	}
	ptr->parent = newroot;//2.3
	return newroot;
}

//右旋
static AVLNode* RotateRight(AVLTree* ptree, AVLNode* ptr)
{
	AVLNode* newroot = ptr->leftchild;
	newroot->parent = ptr->parent;
	ptr->leftchild = newroot->rightchild;
	if (newroot->rightchild != NULL)
	{
		newroot->rightchild->parent = ptr;
	}
	newroot->rightchild = ptr;
	if (ptr == ptree->root)
	{
		ptree->root = newroot;
	}
	else
	{
		if (ptr->parent->leftchild == ptr)
		{
			ptr->parent->leftchild = newroot;
		}
		else
		{
			ptr->parent->rightchild = newroot;
		}
	}
	ptr->parent = newroot;
	return newroot;
}

四.左平衡和右平衡（以左平衡为例）

情况一（插入m节点，A,B平衡因子发生变化）

情况二（插入m节点，A,B,E平衡因子发生变化）

情况三（插入m节点，A,B,E平衡因子发生变化）

代码实现：

//左平衡
static void LeftBalance(AVLTree* ptree, AVLNode* ptr)
{
	AVLNode* subleft = ptr->leftchild, * subright = NULL;
	switch (subleft->balance)
	{
	case 0:
		fprintf(stderr, "left balance\n");
		break;
	case -1:
		ptr->balance = 0;
		subleft->balance = 0;
		RotateRight(ptree, ptr);
		break;
	case 1:
		subright = subleft->rightchild;
		switch (subright->balance)
		{
		case 0:
			ptr->balance = 0;
			subleft->balance = 0;
			break;
		case 1:
			ptr->balance = 0;
			subleft->balance = -1;
			break;
		case -1:
			ptr->balance = 1;
			subleft->balance = 0;
			break;
		}
		subright->balance = 0;
		RotateLeft(ptree, ptr->leftchild);
		RotateRight(ptree, ptr);
		break;
	}
}

//右平衡
static void RightBalance(AVLTree* ptree, AVLNode* ptr)
{
	AVLNode* subleft =NULL, * subright = ptr->rightchild;
	switch (subright->balance)
	{
	case 0:
		fprintf(stderr, "right balance\n");
		break;
	case 1:
		ptr->balance = 0;
		subright->balance = 0;
		RotateLeft(ptree, ptr);
		break;
	case -1:
		subleft = subright->leftchild;
		switch (subleft->balance)
		{
		case 0:
			ptr->balance = 0;
			subright->balance = 0;
			break;
		case 1:
			ptr->balance = -1;
			subright->balance = 0;
			break;
		case -1:
			ptr->balance = 0;
			subright->balance = 1;
			break;
		}
		subleft->balance = 0;
		RotateRight(ptree, ptr->rightchild);
		RotateLeft(ptree, ptr);
		
		break;
	}
}