C++ Red-Black Tree (3) -------- Double Rotation of Red-Black Tree

1. The previous article

     C++ Red-Black Tree (1) -------- Creation of Red-Black Tree and Inserting Node

    C++ Red-Black Tree (2) -------- Single Rotation of Red-Black Tree

 

2. The problem of single rotation of the red-black tree:

      Single rotation cannot achieve the balance of the red-black tree, and cannot change the depth of the node, as shown in the figure below

 

3. The result of double rotation is as follows:

  

4. Take the following figure as an example, do a double rotation on k3 in the figure below

  

Code:

#include <iostream>

using namespace std;

template < class T>
class RedBlackTree;  //红黑树

template <class T>
class RedBlackTreeNode; //红黑树节点


template <class T>
class RedBlackTree
{
	typedef RedBlackTreeNode<T> Node;

public:
	enum { BLACK, RED };

	RedBlackTree(const T &negInfo);  //构造函数主要初始化私有成员 header 和 nullNode
	~RedBlackTree();

	void insert(const T & x); //红黑树插入元素

	void rotateWithLeftChild(Node * & k2) const; //带着左孩子旋转即向右转 k2是旋转前的根节点

	void rotateWithRightChild(Node * &k1) const; //带着右孩子旋转即向左转 k1是旋转前的根节点

	void doubleRotateWithLeftChild(Node * &k3) const;//带着左孩子向右双旋转

	void doubleRotateWithRightChild(Node * &k1) const;//带着右孩子向左双旋转

//private:
	Node *header; //header 的左子节点和右子节点初始化指向nullNode,将来右子节点会指向根节点，
				  //header节点的元素是个无效值
	Node *nullNode; //空节点

	Node *current; //当前节点
	Node *parent; //当前节点的父节点
	Node *grand; //当前节点的祖父节点
	Node *great; //当前节点的曾祖父节点

};


template <class T>
RedBlackTree<T>::RedBlackTree(const T &negInfo)
{
	nullNode = new Node();
	nullNode->left = nullNode->right = NULL;

	header = new Node(negInfo);
	header->left = header->right = nullNode; //header的左右节点初始化为nullNode
}

template <class T >
RedBlackTree<T>::~RedBlackTree()
{
	delete header;
	delete nullNode;
}

template <class T>
void RedBlackTree<T>::insert(const T &x)
{
	current = parent = grand = great = header; // 刚开始都指向头结点
	nullNode->element = x;  //空节点的元素等于新元素

	while (current->element != x)  //红黑树不允许有重复的节点
	{
		great = grand;        //一辈一辈往下循环
		grand = parent;
		parent = current;

		current = x > current->element ? current->right : current->left; //左大、右小
	}

	if (current != nullNode)
	{
		cout << "有重复元素了" << endl;

		return;
	}

	current = new Node(x, nullNode, nullNode);

	if (x < parent->element)
		parent->left = current;
	else
		parent->right = current;

	return;
}

template <class T>
void RedBlackTree<T>::rotateWithLeftChild(Node * & k2) const  //k2是旋转前的根节点
{
	Node * k1 = k2->left;

	k2->left = k1->right;
	k1->right = k2;

	k2 = k1;

}

template <class T>
void RedBlackTree<T>::rotateWithRightChild(Node * &k1) const //k1是旋转前的根节点
{
	Node *k2 = k1->right;

	k1->right = k2->left;
	k2->left = k1;
	k1 = k2;

}

template <class T>
void RedBlackTree<T>::doubleRotateWithLeftChild(Node * &k3) const
{
	rotateWithRightChild(k3->left);  //先把k3的左子节点向左旋转
	rotateWithLeftChild(k3);  //再把整个k3向右旋转
}

template <class T>
void RedBlackTree<T>::doubleRotateWithRightChild(Node * &k1)const
{
	rotateWithLeftChild(k1->right); //先把k1的右子节点向右旋转
	rotateWithRightChild(k1); //再把k1整体向左旋转
}


template <class T>
class RedBlackTreeNode
{
	friend  RedBlackTree<T>;

public:
	RedBlackTreeNode(const T & ele = T(),
		RedBlackTreeNode* lf = NULL,
		RedBlackTreeNode *rg = NULL,
		int c = RedBlackTree<T>::BLACK) :element(ele), left(lf), right(rg), color(c)
	{};//红黑树节点构造函数
//private:
	RedBlackTreeNode *left;  //左子节点
	RedBlackTreeNode *right; //右子节点
	T element;				 //元素
	int color;				//节点颜色

};

void insert_test(void)
{
	cout << "insert_test" << endl;
	const int NEG_INFO = -9999;

	RedBlackTree<int> redBlackTree(NEG_INFO);

	redBlackTree.insert(30);
	redBlackTree.insert(15);
	redBlackTree.insert(70);
	redBlackTree.insert(20);

	cout << "原始数据:" << endl;
	cout << redBlackTree.header->right->element << endl;
	cout << redBlackTree.header->right->left->element << endl;
	cout << redBlackTree.header->right->right->element << endl;
	cout << redBlackTree.header->right->left->right->element << endl;
}

void single_rotate_test(void)
{
	cout << "single_rotate_test" << endl;
	const int NEG_INFO = -9999;
	RedBlackTree<int> redBlackTree(NEG_INFO);

	redBlackTree.insert(30);
	redBlackTree.insert(15);
	redBlackTree.insert(70);
	redBlackTree.insert(20);

	cout << "原始数据:" << endl;
	cout << redBlackTree.header->right->element << endl;
	cout << redBlackTree.header->right->left->element << endl;
	cout << redBlackTree.header->right->right->element << endl;
	cout << redBlackTree.header->right->left->right->element << endl;

	cout << "向右转:" << endl;
	redBlackTree.rotateWithLeftChild(redBlackTree.header->right);
	cout << redBlackTree.header->right->element << endl;
	cout << redBlackTree.header->right->right->element << endl;
	cout << redBlackTree.header->right->right->left->element << endl;
	cout << redBlackTree.header->right->right->right->element << endl;

	cout << "向左转:" << endl;
	redBlackTree.rotateWithRightChild(redBlackTree.header->right);
	cout << redBlackTree.header->right->element << endl;
	cout << redBlackTree.header->right->left->element << endl;
	cout << redBlackTree.header->right->right->element << endl;
	cout << redBlackTree.header->right->left->right->element << endl;
}

void double_rotate_test(void)
{
	cout << "double_rotate_test" << endl;
	const int NEG_INFO = -9999;
	RedBlackTree<int> tree(NEG_INFO);

	tree.insert(12);
	tree.insert(8);
	tree.insert(16);
	tree.insert(4);
	tree.insert(10);
	tree.insert(14);
	tree.insert(2);
	tree.insert(6);
	tree.insert(5);

	cout << "双旋转前:" << tree.header->right->left->left->right->left->element << endl;
	cout << "双旋转前:" << tree.header->right->right->left->element << endl;
	cout << "双旋转前:" << tree.header->right->left->right->element << endl;

	tree.doubleRotateWithLeftChild(tree.header->right->left);
	cout << "双旋转后:" << tree.header->right->left->left->left->element << endl;
	cout << "双旋转后:" << tree.header->right->left->left->right->element << endl;
}

int main()
{
	//insert_test();
	//single_rotate_test();
	double_rotate_test();


	return 0;
}

operation result: