算法导论红黑树的C++实现

按照算法导论里的红黑树伪代码用C++实现了一下，
并附带一些测试代码。

#include <iostream>
#include <utility>
using namespace std;
enum Color{RED,BLACK};//颜色标记
template<class T>
class Binary_Tree_Node//红黑树节点
{
public:
Binary_Tree_Node()
{
parent=NULL;
leftchild=NULL;
rightchild=NULL;
C=BLACK;
}
Binary_Tree_Node<T> * parent;//*/父节点*/
Binary_Tree_Node<T> * leftchild;//左子树
Binary_Tree_Node<T> * rightchild;//后子树
T Key;//键值
Color C;//颜色标记

};
template<class T>
class Binary_Tree//红黑树结构
{
public:
Binary_Tree()
{
root =NULL;
}
Binary_Tree_Node<T> * root;//根节点
};
template<class T>
void Inorder_Tree_Walk( Binary_Tree_Node<T> * A)//顺序打印树
{
if (A!=NULL)
{
Inorder_Tree_Walk(A->leftchild);
cout<<A->Key<<"  ";
Inorder_Tree_Walk(A->rightchild);
}
}
template<class T>
Binary_Tree_Node<T> * Tree_Search( Binary_Tree_Node<T> * A,const T & Search_Key)//递归查找
{
if (A==NULL||A->Key==Search_Key)
{
return A;
}
if (A->Key<Search_Key)
{
return Tree_Search(A->rightchild,Search_Key);
}
else
{
return Tree_Search(A->leftchild,Search_Key);
}
}
template<class T>
Binary_Tree_Node<T> * Interative_Tree_Search( Binary_Tree_Node<T> * A,const T   & Search_Key )//非递归查找
{
Binary_Tree_Node<T> * temp=A;
while(temp!=NULL&& temp->Key!=Search_Key)
{

if (temp->Key<Search_Key)
{
temp=temp->leftchild;
}
else
{
temp=temp->rightchild;
}
}
return temp;
}
template<class T>
Binary_Tree_Node<T> * Tree_Min(Binary_Tree_Node<T> * A)//求节点下的最小值
{
Binary_Tree_Node<T> * temp=A;
Binary_Tree_Node<T> * tempRt=NULL;
while (temp!=NULL)
{
tempRt=temp;
temp=temp->leftchild;
}
return tempRt;
}
template<class T>
Binary_Tree_Node<T> * Tree_Max(Binary_Tree_Node<T> * B)//求节点下的最大值
{
Binary_Tree_Node<T> * temp=B;
Binary_Tree_Node<T> * tempRt=NULL;
while(temp!=NULL)
{
tempRt=temp;
temp=temp->rightchild;
}
return tempRt;
}
template<class T>
Binary_Tree_Node<T> * Successor(Binary_Tree_Node<T> * A)//求比节点的大的后一个值
{
Binary_Tree_Node<T> * temp=A;
if (temp!=NULL)
{
if (temp->rightchild!=NULL)
{
return Tree_Min(temp->rightchild);
}
Binary_Tree_Node<T> * y=temp->parent;
while(y!=NULL && temp==y->rightchild)
{
temp=y;
y=y->parent;
}
return y;
}
else
{
return temp;
}
}
template<class T>
Binary_Tree_Node<T> * Predecessor(Binary_Tree_Node<T> * A)//求比节点小的前一个值
{
Binary_Tree_Node<T> * temp=A;
if (temp!=NULL)
{
if (temp->leftchild!=NULL)
{
return Tree_Max(temp->leftchild);
}
Binary_Tree_Node<T> * y=temp->parent;
while(y!=NULL && temp==y->leftchild)
{
temp=y;
y=y->parent;
}
return y;
}
else
{
return temp;
}
}
template<class T>
void RB_Tree_Insert(Binary_Tree<T> & Tree,const T & InsertKey)//红黑树插入
{
Binary_Tree_Node<T> * y=NULL;
Binary_Tree_Node<T> * x=Tree.root;
while(x!=NULL)
{
y=x;
if (x->Key<InsertKey)
{
x=x->rightchild;
}
else
{
x=x->leftchild;
}
}
Binary_Tree_Node<T> * NewNode=new Binary_Tree_Node<T>;
NewNode->Key=InsertKey;
NewNode->parent=y;
if (y==NULL)
{
Tree.root=NewNode;
}
else
{
if (y->Key<InsertKey)
{
y->rightchild=NewNode;
}
else
{
y->leftchild=NewNode;
}
}
NewNode->C=RED;
RB_Tree_Insert_Fixup(Tree,NewNode);//插入后修复红黑树属性

}
template<class T>
void RB_Tree_Insert_Fixup(Binary_Tree<T> & Tree,Binary_Tree_Node<T> * NewNode)
{
Binary_Tree_Node<T> * Z=NULL;
/*Binary_Tree_Node<T> Nil;*/
Z=NewNode;
while(Z->parent!=NULL&&Z->parent->C==RED)
{
Binary_Tree_Node<T> * y=NULL;
if (Z->parent==Z->parent->parent->leftchild)
{
y=Z->parent->parent->rightchild;
if (y!=NULL&&y->C==RED)
{
y->C=BLACK;
Z->parent->C=BLACK;
Z->parent->parent->C=RED;
Z=Z->parent->parent;
continue;
}
else
{

if (Z==Z->parent->rightchild)
{
Z=Z->parent;
Left_Roation(Tree,Z);
continue;
}
else
{
Z->parent->C=BLACK;
Z->parent->parent->C=RED;
Right_Roation(Tree,Z->parent->parent);
}
}
}
else
{
y=Z->parent->parent->leftchild;
if (y!=NULL&&y->C==RED)
{
y->C=BLACK;
Z->parent->C=BLACK;
Z->parent->parent->C=RED;
Z=Z->parent->parent;
continue;
}
else
{
if (Z==Z->parent->leftchild)
{
Z=Z->parent;
Right_Roation(Tree,Z);
continue;
}
else
{
Z->parent->C=BLACK;
Z->parent->parent->C=RED;
Left_Roation(Tree,Z->parent->parent);
}
}
}
}
Tree.root->C=BLACK;
}
template<class T>
void Tree_Insert(Binary_Tree<T> & Tree,const T & InsertKey)//普通二叉树插入
{
Binary_Tree_Node<T> * y=NULL;
Binary_Tree_Node<T> * x=Tree.root;
while(x!=NULL)
{
y=x;
if (x->Key<InsertKey)
{
x=x->rightchild;
}
else
{
x=x->leftchild;
}
}
Binary_Tree_Node<T> * NewNode=new Binary_Tree_Node<T>;
NewNode->Key=InsertKey;
NewNode->parent=y;
if (y==NULL)
{
Tree.root=NewNode;
}
else
{
if (y->Key<InsertKey)
{
y->rightchild=NewNode;
}
else
{
y->leftchild=NewNode;
}
}
return ;
}
template<class T>
void RB_Tree_Delete(Binary_Tree<T> & Tree,Binary_Tree_Node<T> * DeleteNode)//红黑树删除
{
Binary_Tree_Node<T> * tempDeleteNode=DeleteNode;
Binary_Tree_Node<T> * y=NULL;
Binary_Tree_Node<T> * x=NULL;
Binary_Tree_Node<T> Nil;//本地临时的Nil
if (tempDeleteNode!=NULL)
{
if (tempDeleteNode->leftchild==NULL
||tempDeleteNode->rightchild==NULL)
{
y=tempDeleteNode;
}
else
{
y=Successor(tempDeleteNode);
}
if (y->leftchild!=NULL)
{
x=y->leftchild;
}
else
{
x=y->rightchild;
}
if (x==NULL)
{
x=&Nil;//x为null 则赋值为nil的指针;.
}
x->parent=y->parent;
if (y->parent==NULL)
{
Tree.root=x;
}
else if (y==y->parent->leftchild)
{
y->parent->leftchild=x;
}
else
{
y->parent->rightchild=x;
}
if (y!=DeleteNode)
{
DeleteNode->Key=y->Key;
}
if (y->C==BLACK)
{
RB_Tree_Delete_FixUp(Tree,x);//修复红黑树属性
}
if (Nil.parent!=NULL)//将临时插入的nil还原为null指针
{
if (&Nil==Nil.parent->leftchild)
{
Nil.parent->leftchild=NULL;
}
else if (&Nil==Nil.parent->rightchild)
{
Nil.parent->rightchild=NULL;
}
}
if (Tree.root==&Nil)
{
Tree.root=NULL;
}
delete y;
return;

}
else
{
return ;
}
}
template<class T>
void RB_Tree_Delete_FixUp(Binary_Tree<T> & Tree,Binary_Tree_Node<T> * x)
{
while(x!=Tree.root&&x->C==BLACK)
{
Binary_Tree_Node<T> * w=NULL;
if (x==x->parent->leftchild)
{
w=x->parent->rightchild;
if (w!=NULL&&w->C==RED)
{
w->C=BLACK;
x->parent->C=RED;
Left_Roation(Tree,x->parent);
w=x->parent->rightchild;
}
if (w==NULL||(w!=NULL&&(w->leftchild==NULL||w->leftchild->C==BLACK)
&&(w->
4000
rightchild==NULL||w->rightchild->C==BLACK)))
{
if (w!=NULL)
{
w->C=RED;
}
x=x->parent;
continue;
}
else if(w->rightchild==NULL||w->rightchild->C==BLACK)
{
w->C=RED;
w->leftchild->C=BLACK;
Right_Roation(Tree,w);
w=x->parent->rightchild;
}
w->C=x->parent->C;
x->parent->C=BLACK;
w->rightchild->C=BLACK;
Left_Roation(Tree,x->parent);
x=Tree.root;
}
else
{
w=x->parent->leftchild;
if (w!=NULL&&w->C==RED)
{
w->C=BLACK;
x->parent->C=RED;
Right_Roation(Tree,x->parent);
w=x->parent->leftchild;
}
if (w==NULL||(w!=NULL&&(w->leftchild==NULL||w->leftchild->C==BLACK)
&&(w->rightchild==NULL||w->rightchild->C==BLACK)))
{
if (w!=NULL)
{
w->C=RED;
}
x=x->parent;
continue;
}
else if (w->leftchild==NULL||w->leftchild->C==BLACK)
{
w->C=RED;
w->rightchild->C=BLACK;
Left_Roation(Tree,w);
w=x->parent->leftchild;
}
w->C=x->parent->C;
x->parent->C=BLACK;
w->leftchild->C=BLACK;
Right_Roation(Tree,x->parent);
x=Tree.root;
}
}
x->C=BLACK;
return;
}
template<class T>
void Tree_Delete(Binary_Tree<T> & Tree,Binary_Tree_Node<T> * DeleteNode)//普通二叉树删除
{
Binary_Tree_Node<T> * tempDeleteNode=DeleteNode;
Binary_Tree_Node<T> * y=NULL;
Binary_Tree_Node<T> * x=NULL;
if (tempDeleteNode!=NULL)
{
if (tempDeleteNode->leftchild==NULL
||tempDeleteNode->rightchild==NULL)
{
y=tempDeleteNode;
}
else
{
y=Successor(tempDeleteNode);
}
if (y->leftchild!=NULL)
{
x=y->leftchild;
}
else
{
x=y->rightchild;
}
if (x!=NULL)
{
x->parent=y->parent;
}
if (y->parent==NULL)
{
Tree.root=x;
}
else if (y==y->parent->leftchild)
{
y->parent->leftchild=x;
}
else
{
y->parent->rightchild=x;
}
if (y!=DeleteNode)
{
DeleteNode->Key=y->Key;
}
delete y;
return;

}
else
{
return ;
}
}
template<class T>
void Left_Roation(Binary_Tree<T> & Tree,Binary_Tree_Node<T> * Node)//左旋
{
Binary_Tree_Node<T> * y=NULL;
y=Node->rightchild;
if (y!=NULL)
{
if (y->leftchild!=NULL)
{
Node->rightchild=y->leftchild;
y->leftchild->parent=Node;
}
else
{
Node->rightchild=NULL;
}
y->parent=Node->parent;
if (Node->parent==NULL)
{
Tree.root=y;
}
else
{
if (Node->parent->leftchild==Node)
{
Node->parent->leftchild=y;
}
else
{
Node->parent->rightchild=y;
}
}
y->leftchild=Node;
Node->parent=y;
}
return;
}
template<class T>
void Right_Roation(Binary_Tree<T> & Tree,Binary_Tree_Node<T> * Node)//右旋
{
Binary_Tree_Node<T> * y=NULL;
y=Node->leftchild;
if (y!=NULL)
{
if (y->rightchild!=NULL)
{
Node->leftchild=y->rightchild;
y->rightchild->parent=Node;
}
else
{
Node->leftchild=NULL;
}
y->parent=Node->parent;
if (Node->parent==NULL)
{
Tree.root=y;
}
else
{
if (Node->parent->leftchild==Node)
{
Node->parent->leftchild=y;
}
else
{
Node->parent->rightchild=y;
}
}
y->rightchild=Node;
Node->parent=y;
}
return;
}
#include <algorithm>
int * randIntGernate(int Num,bool output=true)//生成随机测试数组
{
if (Num<=0)
{
return NULL;
}
int * RT=new int[Num];
for (int i=0;i<Num;i++)
{
RT[i]=i;
}
random_shuffle(RT,RT+Num);
//
if (output)
{
cout<<"gernate rand "<<Num<<" Int array:"
<<endl;
for (int i=0;i<Num;i++)
{
cout<<RT[i]<<" ";
}
cout<<endl;
}

//
return RT;
}

#include <utility>
typedef pair<int,int> count_Pair;
template<class T>
void count_Path_Color(Binary_Tree_Node<T> * Node,count_Pair PathCount=count_Pair(0,0))
//打印红黑树的节点分布情况,检测红黑树是否正确
{
if (Node!=NULL)
{
if (Node->C==RED)
{
PathCount.first++;
}
else
{
PathCount.second++;
}
count_Path_Color(Node->leftchild,PathCount);
count_Path_Color(Node->rightchild,PathCount);
}
else
{
PathCount.second++;
cout<<"RED:  "<<PathCount.first<<"  BLACK:  "<<PathCount.second<<endl;
}
}
#include <string>
template<class T>
void Print_Tree(Binary_Tree_Node<T> * Node, string s ="")//递归打印一颗树
{
cout<<s;
if (Node!=NULL)
{
if (Node->leftchild==NULL&&Node->rightchild==NULL)
{
cout<<Node->Key<<"_"<<(Node->C==RED?'R':'B')<<endl;//leaf
return;
}
cout<<Node->Key<<"_"<<(Node->C==RED?'R':'B')<<" :[";
Inorder_Tree_Walk(Node);
cout<<"]"<<endl;
//
Print_Tree(Node->leftchild,s+"|  ");
Print_Tree(Node->rightchild,s+"   ");
}
else
{
cout<<"NULL_B\r\n";
}
}
void doTest(bool output=true)//测试
{
while(1)
{
cout<<"How many nodes do you want the RB_Tree to have"<<endl;
int num;
cin>>num;
int * arrayInt=randIntGernate(num,output);//随机化一个数组,填充红黑树
Binary_Tree<int> tttt;
for (int i=0;i<num;i++)
{
RB_Tree_Insert(tttt,arrayInt[i]);
}
delete [] arrayInt;
Print_Tree(tttt.root);
cout<<endl;
count_Path_Color(tttt.root);
while(1)
{
cout<<"Please chose an operator \r\n0:search\r\n1:delete\r\n2:insert\r\n-1:new RB_Tree\r\n";
int a;
cin>>a;
if (a==-1)//新的树
{
break;
}
if (a==0)//查询
{
cout<<"please input the number to be searched:"<<endl;
int number;
cin>>number;
Binary_Tree_Node<int> * find=Tree_Search(tttt.root,number);
if (find!=NULL)
{
cout<<"find "<<number<<endl;
}
else
{
cout<<"can not find "<<number<<endl;
}
}
if (a==1)//删除
{
cout<<"please input the number to be deleted:"<<endl;
int number;
cin>>number;
Binary_Tree_Node<int> * find=Tree_Search(tttt.root,number);
if (find==NULL)
{
cout<<number<<" not exist"<<endl;
}
cout<<"before delete"<<endl;
Print_Tree(tttt.root);
cout<<endl;
count_Path_Color(tttt.root);
cout<<endl;
RB_Tree_Delete(tttt,find);
cout<<"after delete "<<endl;
Print_Tree(tttt.root);
cout<<endl;
count_Path_Color(tttt.root);
cout<<endl;
}
else if (a==2)//插入
{

cout<<endl;
cout<<"Please input the number to be inserted:"<<endl;
int Num;
cin>>Num;
cout<<"before insert "<<endl;
Print_Tree(tttt.root);
cout<<endl;
count_Path_Color(tttt.root);
cout<<endl;
RB_Tree_Insert(tttt,Num);
cout<<"after insert:"<<Num<<endl;
Print_Tree(tttt.root);
cout<<endl;
count_Path_Color(tttt.root);
cout<<endl;
}
}

}

}