算法导论-红黑树C++实现

红黑树的定义：
一棵二叉查找树如果满足下面的红黑性质，则为一棵红黑树：
1）每个节点或是红的，或是黑的。
2）根节点是黑的。
3）每个叶节点（NIL）是黑节点。
4）如果一个节点是红的，则它的两个儿子都是黑的。
5）对每个节点，从该节点到其子孙节点的所有路径上包含相同节点数目的黑节点。

C++代码实现：
BRTreeNode.h

#ifndef BRTREENODE_H_INCLUDED #define BRTREENODE_H_INCLUDED #include<iostream> using namespace std; class BRTree; class BRTreeNode { private: 	friend class BRTree; 	int key; 	bool color; 	BRTreeNode* left; 	BRTreeNode* right; 	BRTreeNode* parent; public: 	BRTreeNode():key(-1),color(0),left(NULL),right(NULL),parent(NULL){} 	BRTreeNode(BRTreeNode* node):key(node->key),color(node->color),left(node->left),right(node->right),parent(node->parent) 	{} 	BRTreeNode(int num,bool flag):key(num),color(flag),left(NULL),right(NULL),parent(NULL){} 	~BRTreeNode() 	{  	} 	int Getkey() 	{ 		return key; 	} 	bool Getcolor() 	{ 		return this->color; 	} 	BRTreeNode* GetLeft() 	{ 		return this->left; 	} 	BRTreeNode* Getright() 	{ 		return this->right; 	} 	BRTreeNode* Getparent() 	{ 		return this->parent; 	} 	void Inorder() 	{ 		if(this!=NULL) 		{ 			this->left->Inorder(); 			cout<<this->key<<" "; 			this->right->Inorder(); 		} 	} 	void Preorder() 	{ 		if(this!=NULL) 		{ 			cout<<this->key<<" "; 			this->left->Preorder(); 			this->right->Preorder(); 		} 	} 	void Postorder() 	{ 		if(this!=NULL) 		{ 			this->left->Postorder(); 			this->right->Postorder(); 			cout<<this->key<<" "; 		} 	}  	void MakeEmpty() 	{ 		if(this!=NULL) 		{ 			this->left->MakeEmpty(); 			this->right->MakeEmpty(); 			delete this; 		} 	} 	int GetHeight() 	{ 		int L,R; 		if(this==NULL) 		{ 			return 0; 		} 		L=this->left->GetHeight(); 		R=this->right->GetHeight(); 		return 1+(L>R? L:R); 	} };   #endif // BRTREENODE_H_INCLUDED

BRTree.h

#ifndef BRTREE_H_INCLUDED #define BRTREE_H_INCLUDED #define maxSize 30 #define maxWidth 30 #include"BRTreeNode.h" class BRTree { private: 	BRTreeNode* root; 	BRTreeNode* nil; public: 	BRTree():nil(new BRTreeNode()) 	{ 		nil->color=0; 		nil->key=-1; 		nil->left=nil->right=nil->parent=NULL; 		root=nil; 	} 	~BRTree() 	{ 		MakeEmpty(root); 		delete nil; 	} 	//清空以node为根节点的树 	void MakeEmpty(BRTreeNode*node) 	{ 		if(node!=nil) 		{ 			MakeEmpty(node->left); 			MakeEmpty(node->right); 			delete node; 		} 	} 	int Getkey(BRTreeNode* node) 	{ 		return node->Getkey(); 	} 	bool Getcolor(BRTreeNode* node) 	{ 		return node->Getcolor(); 	} 	BRTreeNode* Getroot() 	{ 		return root; 	} 	BRTreeNode* GetParent(BRTreeNode*node) 	{ 		return node->parent; 	} 	int GetHeight(BRTreeNode* node) 	{ 		int L,R; 		if(node==nil) 			return 0; 		L=GetHeight(node->left); 		R=GetHeight(node->right); 		return 1+(L>R? L:R); 	}     int GetBlackHeight(BRTreeNode* node) 	{ 		int L,R; 		if(node==nil) return 0; 		L=GetHeight(node->left); 		R=GetHeight(node->right); 		if(node->Getcolor()) return(L>R? L:R); 		else return 1+(L>R? L:R); 	} 	void Inorder(BRTreeNode*node) 	{ 		if(node!=nil) 		{ 			Inorder(node->left); 			cout<<node->key<<" "; 			Inorder(node->right); 		} 	} 	void Preorder(BRTreeNode*node) 	{ 		if(node!=nil) 		{ 			cout<<node->key<<" "; 			Preorder(node->left); 			Preorder(node->right); 		} 	} 	void Posetorder(BRTreeNode*node) 	{ 		if(node!=nil) 		{ 			Posetorder(node->left); 			Posetorder(node->right); 			cout<<node->key<<" "; 		} 	} 	//层次法打印树 void DispTree(BRTreeNode*BT) {     BRTreeNode stack[maxSize],p;     int level[maxSize][2],top,n,i,width=4;     if(BT!=NULL)     {         cout<<"Display a tree by hollow means."<<endl;         top=1;         stack[top]=BT;//push root point to stack.         level[top][0]=width;         while(top>0)         {             p=stack[top];             n=level[top][0];             for(i=1;i<=n;i++)                 cout<<" ";             //输出信息             if(p.key==0)             {                 cout<<")";             }             else{             if(p.key==-1) cout<<"Nil";             else if(p.left&&p.right) cout<<"("<<p.key;             else cout<<p.key;             if(p.Getcolor()) cout<<"R,";             else cout<<"B,";             }             for(i=n+1;i<maxWidth;i+=2)                 cout<<"--";             cout<<endl;             top--;             if(p.right!=NULL)             {                 //插入一个括号节点，key值为0                 top++;                 BRTreeNode* tmp=new BRTreeNode();                 tmp->key=0;                 stack[top]=tmp;                 level[top][0]=n+width;                 level[top][1]=2;                 top++;                 stack[top]=p.right;                 level[top][0]=n+width;                 level[top][1]=2;              }             if(p.left!=NULL)             {                 top++;                 stack[top]=p.left;                 level[top][0]=n+width;                 level[top][1]=1;             }         }     } } 	//左旋节点node 	bool LeftRotate(BRTreeNode* node) 	{ 		BRTreeNode*y; 		if(node->right==nil) 		{ 			cout<<"can't left rotate!"<<endl; 			return 0; 		} 		y=node->right; 		node->right=y->left; 		if(y->left!=nil) 		{ 			y->left->parent=node; 		} 		y->parent=node->parent; 		if(node->parent==nil) 		{ 			root=y; 		} 		else if(node->parent->left==node) 		{ 			node->parent->left=y; 		} 		else 		{ 			node->parent->right=y; 		} 		y->left=node; 		node->parent=y; 		return 1; 	} 	//右旋节点 	bool RightRotate(BRTreeNode* node) 	{ 		if(node->left==nil) 		{ 			cout<<"can't rightrotate!"<<endl; 			return 0; 		} 		BRTreeNode* x; 		x=node->left; 		node->left=x->right; 		if(x->right!=nil) 		{ 			x->right->parent=node; 		} 		x->parent=node->parent; 		if(node->parent==nil) 		{ 			root=x; 		} 		else if(node->parent->left==node) 		{ 			node->parent->left=x; 		} 		else 		{ 			node->parent->right=x; 		} 		node->parent=x; 		x->right=node; 		return 1; 	} 	void Insert(int num) 	{ 		BRTreeNode* node=new BRTreeNode(num,1); 		node->left=nil; 		node->right=nil; 		node->parent=nil; 		BRTreeNode* p=root,*q=nil; 		if(root==nil) 		{ 			node->color=0; 			root=node; 			root->left=root->right=root->parent=nil; 			return ; 		} 		while(p!=nil) 		{ 			if(p->key==num) 			{ 				cout<<num<<"  has exist!"<<endl; 				return ; 			} 			else if(p->key>num) 			{ 				q=p; 				p=p->left; 			} 			else 			{ 				q=p; 				p=p->right; 			} 		} 		if(q->key>num) 		{ 			q->left=node; 			node->parent=q; 		} 		else 		{ 			q->right=node; 			node->parent=q; 		} 		RBInsertAdjust(node); 	} 	void RBInsertAdjust(BRTreeNode* node) 	{ 		BRTreeNode* y; 		while(node->parent->color==1) 		{ 			if(node->parent==node->parent->parent->left) 			{ 				y=node->parent->parent->right; 				if(y->color==1) 				{ 					node->parent->color=0; 					y->color=0; 					y->parent->color=1; 					node=node->parent->parent; 				} 				//此时y的颜色是黑色 				else 				{ 					//第二种情况 					if(node==node->parent->right) 					{ 						node=node->parent; 						LeftRotate(node); 					} 					//第三种情况 					node->parent->color=0; 					node->parent->parent->color=1; 					RightRotate(node->parent->parent); 				} 			} 			else 			{ 				y=node->parent->parent->left; 				if(y->color==1) 				{ 					node->parent->color=0; 					y->color=0; 					y->parent->color=1; 					node=node->parent->parent; 				} 				else 				{ 					if(node==node->parent->left) 					{ 						node=node->parent; 						RightRotate(node); 					} 					node->parent->color=0; 					node->parent->parent->color=1; 					LeftRotate(node->parent->parent); 				} 			} 		} 		root->color=0; 	} 	BRTreeNode* Search(int num) 	{ 		BRTreeNode* p=root; 		while(p!=nil) 		{ 			if(p->key==num) 			{ 				return p; 			} 			else if(p->key>num) 			{ 				p=p->left; 			} 			else 			{ 				p=p->right; 			} 		} 		cout<<"there is no "<<num<<" in this tree!"<<endl; 		return nil; 	} 	//获取以node节点为根节点的树的最小元素，并返回该最小值 	int Minnum(BRTreeNode*node) 	{ 		BRTreeNode*p=node; 		while(p->left!=nil) 		{ 			p=p->left; 		} 		return p->key; 	} 	//获取以node节点为根节点的树的最da元素，并返回该最da值 	int Maxnum(BRTreeNode*node) 	{ 		BRTreeNode*p=node; 		while(p->right!=nil) 		{ 			p=p->right; 		} 		return p->key; 	} 	//获取以node节点为根节点的树的最小元素，并返回该节点 	BRTreeNode* MinNum(BRTreeNode*node) 	{ 		BRTreeNode*p=node; 		while(p->left!=nil) 		{ 			p=p->left; 		} 		return p; 	} 	//获取以node节点为根节点的树的最大元素 	BRTreeNode* MaxNum(BRTreeNode*node) 	{ 		BRTreeNode*p=node; 		while(p->right!=nil) 		{ 			p=p->right; 		} 		return p; 	} 	BRTreeNode*InorderSuccessor(BRTreeNode*node) 	{ 		if(node->right!=nil) 		{ 			return MinNum(node->right); 		} 		else 		{ 			BRTreeNode*p=GetParent(node); 			while(p&&node==p->right) 			{ 				node=p; 				p=GetParent(node); 			} 			return p; 		} 	} 	//中序遍历的前趋 	BRTreeNode*InordePredecessor(BRTreeNode*node) 	{ 		if(node->left!=nil) 		{ 			return MaxNum(node->left); 		} 		else 		{ 			BRTreeNode*p=GetParent(node); 			while(p&&node==p->left) 			{ 				node=p; 				p=GetParent(node); 			} 			return p; 		} 	} 	bool Delete(int num) 	{ 		BRTreeNode*z,*y,*x;         //寻找key值为num的节点p         z=Search(num); 		//如果没有该节点则返回0         if(z==nil)         {             return 0;         } 		if(z->left==nil||z->right==nil) 		{ 			y=z; 		} 		else 			y=InorderSuccessor(z); 		if(y->left!=nil) 			x=y->left; 		else 			x=y->right; 		x->parent=y->parent; 		if(x->parent==nil) 			root=x; 		else if(y=y->parent->left) 			y->parent->left=x; 		else 			y->parent->right=x; 		if(y!=z) 		{ 			z->key=y->key; 		} 		if(y->color==0) 		{ 			RBTreeFixup(x); 		} 		return 1; 	} 	void RBTreeFixup(BRTreeNode* x) 	{ 		BRTreeNode*w; 		while(x!=root&&x->color==0) 		{ 			if(x==x->parent->left) 			{ 				w=x->parent->right; 				if(w->color==1) 				{ 					w->color=0; 					x->parent->color=1; 					LeftRotate(x->parent); 					w=x->parent->right; 				} 				if(w->left->color==0&&w->right->color==0) 				{ 					w->color=1; 					x=x->parent; 				} 				else 				{ 					if(w->right->color==0) 					{ 						w->color=1; 						RightRotate(w); 						w=x->parent->right; 					} 					w->color=x->parent->color; 					x->parent->color=0; 					w->right->color=0; 					LeftRotate(x->parent); 					x=root; 				} 			} 			else 			{ 				w=x->parent->left; 				if(w->color==1) 				{ 					w->color=0; 					x->parent->color=1; 					RightRotate(x->parent); 					w=x->parent->left; 				} 				if(w->right->color==0&&w->left->color==0) 				{ 					w->color=1; 					x=x->parent; 				} 				else 				{ 					if(w->left->color==0) 					{ 						w->color=1; 						LeftRotate(w); 						w=x->parent->left; 					} 					w->color=x->parent->color; 					x->parent->color=0; 					w->left->color=0; 					RightRotate(x->parent); 					x=root; 				} 			} 		} 		x->color=0; 	} };  #endif // BRTREE_H_INCLUDED

测试程序

#include <iostream> #include"BRTree.h" #include "BRTreeNode.h" using namespace std;  int main() {     BRTree tree;     cout<<"Insert 9 numbers:"<<endl;     int a[9]={8,11,17,15,6,1,22,25,27};     int i;     for(i=0;i<9;i++)     {         tree.Insert(a[i]);     }     tree.DispTree(tree.Getroot());     cout<<"Delete 11:"<<endl;     tree.Delete(11);     tree.DispTree(tree.Getroot());     cout << "blackHeight:" <<tree.GetBlackHeight(tree.Getroot())<<endl;      return 0; }

运行结果：




参考：
教你透彻了解红黑树-http://blog.csdn.net/v_JULY_v/article/details/6105630