【数据结构】AVL树的实现

在上一篇博客中我们对AVL树进行了初步的介绍和插入算法分析，这次对AVL树进行代码实现：

【数据结构】AVL树介绍

代码如下：

#include
using namespace std;
template< class K, class V>
struct AVLTreeNode
{
	AVLTreeNode(const K& key, const V& value)
	:_pLeft(NULL)
	, _pRight(NULL)
	, _pParent(NULL)
	, _key(key)
	, _value(value)
	, _bf(0)
	{}
	AVLTreeNode* _pLeft;
	AVLTreeNode* _pRight;
	AVLTreeNode* _pParent;
	K _key;
	V _value;
	int _bf;
};


template
class AVLTree
{
public:
	
	typedef AVLTreeNode Node;
	typedef Node* pNode;
	AVLTree()
		:_pRoot(NULL)
	{}
	
	bool Insert(const K& key, const V& value)
	{

		if (_pRoot == NULL)
		{
			_pRoot = new Node(key, value);
			return true;
		}
		pNode  pParent = NULL;
		pNode cur = _pRoot;
		while (cur)
		{
			if (cur->_key == key)
				return false;
			else if (cur->_key > key)
			{
				pParent = cur;
				cur = cur->_pLeft;

			}
			else
			{
				pParent = cur;
				cur = cur->_pRight;
			}

		}
		pNode pNewNode = new Node(key, value);
		if (pParent->_key > key)
		{
			pParent->_pLeft = pNewNode;
			pNewNode->_pParent = pParent;
		}
		else
		{
			pParent->_pRight = pNewNode;
			pNewNode->_pParent = pParent;
		}
		while (pParent)
		{
			if (pParent->_pLeft == pNewNode)
				pParent->_bf--;
			else 
				pParent->_bf++;
			if (pParent->_bf == 0)
				return true;
			else if (pParent->_bf == 1 || pParent->_bf == -1)
			{
				pNewNode = pParent;
				pParent = pParent->_pParent;
			}
			else if (pParent->_bf == 2 || pParent->_bf == -2)
			{
				if (pParent->_bf == 2)//左边的结点比较多  
				{
					if (pNewNode->_bf == 1)
					{
						_RotateL(pParent);//  
						return true;
					}
					else
					{
						_RotateRL(pParent);//右左旋转  
						return true;
					}
				}
				if (pParent->_bf == -2)
				{
					if (pNewNode->_bf == -1)
					{
						_RotateR(pParent);
						return true;
					}
					else
					{
						_RotateLR(pParent);
						return true;
					}
				}
			}
		}
		return true;
	}
	
	
	void InOrder()
	{
		_InOrder(_pRoot);
	}

	bool IsBalance()
	{
		return _IsBalance(_pRoot);
	}
	int Height()
	{
		return _Height(_pRoot);
	}
	bool IsBalance2()
	{
		int depth = 0;
		return _IsBalance2(_pRoot, depth);
	}
private:
	bool _IsBalance2(pNode pRoot, int depth)
	{
		if (NULL == pRoot)
		{
			depth = 0;
			return true;
		}
		int leftDepth = 0;
		int rightDepth = 0;
		if (_IsBalance2(pRoot->_pLeft, leftDepth) == false)
		{
			return false;
		}
		if (_IsBalance2(pRoot->_pRight, rightDepth) == false)
		{
			return false;
		}
		if (rightDepth - leftDepth != pRoot->_bf)
		{
			cout << "bf异常" << pRoot->_bf << endl;
		}
		depth = leftDepth > rightDepth ? (leftDepth + 1) : (rightDepth + 1);
		return true;

	}
	bool _IsBalance(pNode pRoot)
	{
		if (pRoot == NULL)
			return true;
		else
		{
			int height = abs(_Height(pRoot->_pRight) - _Height(pRoot->_pLeft));
			return (height < 2) && _IsBalance(pRoot->_pLeft) && _IsBalance(pRoot->_pRight);
		}
	}
	int _Height(pNode pRoot)
	{
		int treeheight = 0;
		if (pRoot == NULL)
			return 0;
		else
		{
			int lefttreeheight = _Height(pRoot->_pLeft);
			int righttreeheight = _Height(pRoot->_pRight);
			treeheight = lefttreeheight > righttreeheight ? lefttreeheight + 1 : righttreeheight + 1;
		}
		return treeheight;
		
	}

	void _RotateL(pNode pParent)
	{
		pNode subR = pParent->_pRight;
		pNode subRL = subR->_pLeft;
		pParent->_pRight = subRL;
		if (subRL)
			subRL->_pParent = pParent;
		pNode ppParent = pParent->_pParent;
		subR->_pLeft = pParent;
		pParent->_pParent = subR;
		if (ppParent == NULL)
		{
			_pRoot = subR;
			subR->_pParent = NULL;
		}
		else
		{
			if (ppParent->_pLeft == pParent)
			{
				ppParent->_pLeft = subR;
				
			}
			else
			{
				ppParent->_pRight = subR;
				
			}
			subR->_pParent = ppParent;

		}
		pParent->_bf = subR->_bf = 0;
		
	}
	
	void _RotateR(pNode pParent)
	{
		pNode subL = pParent->_pLeft;
		pNode subLR = subL->_pRight;
		pParent->_pLeft = subLR;
		if (subLR)
			subLR->_pParent = pParent;
		pNode ppParent = pParent->_pParent;
		subL->_pRight = pParent;
		pParent->_pParent = subL;
		if (ppParent == NULL)
		{
			_pRoot = subL;
			subL->_pParent = NULL;
		}
		else
		{
			if (ppParent->_pLeft == pParent  )

			{
				ppParent->_pLeft = subL;
				subL->_pParent = ppParent;
			}
			else
			{
				ppParent->_pRight = subL;
				subL->_pParent = ppParent;
			}
		}
		pParent->_bf = subL->_bf = 0;
	}
	
	void _RotateRL(pNode pParent)
	{
		pNode subR = pParent->_pRight;
		pNode subRL = subR->_pLeft;
		int bf = subRL->_bf;
		_RotateR(subR);
		_RotateL(pParent);
		if (bf == 0)
		{
			pParent->_bf = subR->_bf = 0;
		}
		else if (bf == -1)
		{
			subR->_bf = 0;
			pParent->_bf = -1;
		}
		else
		{
			subR->_bf = -1;
			pParent->_bf = 0;
			
		}
		subRL->_bf = 0;

	}
	void _RotateLR(pNode pParent)
	{
		pNode subL = pParent->_pLeft;
		pNode subLR = subL->_pRight;
		int bf = subLR->_bf;
		_RotateL(subL);
		_RotateR(pParent);
		if (bf == 0)
		{
			subL->_bf=pParent->_bf   = 0;
		}
		else if (bf == -1)
		{
			subL->_bf = -1;
			pParent->_bf = 0;
			
		}
		else
		{
			subL->_bf = 0;
			pParent->_bf = -1;
			
		}
		subLR->_bf = 0;
	}
	
	void _InOrder(pNode pRoot)
	{
	
		if (pRoot)
		{
			_InOrder(pRoot->_pLeft);
			cout << pRoot->_key << " ";
			_InOrder(pRoot->_pRight);
		}
	
	}
private:
	pNode _pRoot;
};
int main()
{
	
	int a[] = { 18, 14, 20, 12, 16, 15 };
	AVLTree< int, int> bst;
	for (int i = 0; i < sizeof(a) / sizeof(*a); ++i)
	{
		bst.Insert(a[i], i);
	}
	bst.InOrder();
	cout << endl;
	cout << bst.Height() << endl;
	if (bst.IsBalance())
		cout << "平衡" << endl;
	else
		cout << "不平衡" << endl;
	if(bst.IsBalance2())
		cout<<"平衡"<