数据结构--可迭代红黑树模板类（C++）

一、结点类与红黑树类：

（一）结点类基本数据成员：

1.左右子结点指针域

2.父结点指针域，方便回访父结点

3.有序前驱 / 后继指针域，迭代访问元素，提供一种顺序存储的假象

4.结点颜色，利用红黑规则，保持树的平衡。

（二）结点类的基本成员函数：

两个重载的构造函数，构造红色的新结点

（三）红黑树类基本数据成员：

1.头结点：保存一个据点，用来维系根节点与公用空结点

2.根结点：是红黑树的起始位置

3.空结点：作为所有空指针域的指向，一棵树只有一个

4.全局前驱、后继结点：用来使红黑树线索化，变得可迭代

（四）红黑树类基本成员函数（面向内部）：

1.中序递归构造线索

2.结点左旋、右旋操作

3.插入后修正红黑树

4.移除后修正红黑树

5.移植（替换）结点

6.子树最大、最小结点

（五）红黑树类基本成员函数（面向用户）：

1.构造函数，构造空树

2.空树判断

3.插入元素

4.移除元素

5.搜索元素

6.获取起始、终止迭代器、元素最大值、元素最小值

7.递归遍历

8.迭代器遍历

 1 class RBTree;
 2 enum Color{RED=0,BLACK=1};
 3 template<typename T>
 4 class RBnode{
 5     friend class RBTree<T>;
 6     public:
 7         typedef RBnode<T>* rb_iterator;
 8     private:
 9         typedef RBnode<T>* Nodeptr;
10     public:
11         Nodeptr left,right,parent;
12         Nodeptr prior,next;
13         Color color;
14     public:
15         T val;
16     public://新结点都是红结点
17         RBnode(T value){left=right=parent=this;val=value;color=RED;}
18         RBnode(T value, Nodeptr l, Nodeptr r):val(value),left(l),right(r){parent=this,color=RED;}
19 };
20 template<typename T>
21 class RBTree{
22     friend class RBnode<T>;
23     private:
24         typedef RBnode<T>* Nodeptr;
25     public:
26         typedef RBnode<T>* rb_iterator;
27     private:
28         Nodeptr header;
29         Nodeptr root;
30         Nodeptr nlnode;
31         Nodeptr _prior;
32         Nodeptr _next;
33     public:
34         RBTree(){
35             header=new RBnode<T>(0);
36             nlnode=new RBnode<T>(-1);
37             nlnode->color = header->color = BLACK;
38             root=nlnode;
39             root->parent=header;
40             root->left=root->right=nlnode;
41             header->left=nlnode;
42             header->right=root;
43             nlnode->parent=nlnode;
44             header->next = nlnode;
45             header->prior = nlnode;
46         }
47     public:
48         bool isEmpyty();
49         void Insert(T x);
50         void Insert(Nodeptr);
51         bool remove(T x);
52         bool remove(Nodeptr x);
53         Nodeptr search(T x);
54         T getMax();
55         T getMin();
56         rb_iterator begin(){return header->next;}
57         rb_iterator end(){return header;}
58         void inorderWalk(Nodeptr p) const ;
59         void LORvisit();
60         void Iterator_visit(rb_iterator start, rb_iterator over) {
61             rb_iterator temp = start;
62             while(temp != over){
63                 cout << temp->val << ' ';
64                 temp = temp->next;
65             }
66         }
67     private:
68         void LOR();
69         void LOR(Nodeptr c);
70         void LeftRotate(Nodeptr x);
71         void RightRotate(Nodeptr x);
72         void Fix_up_insert(Nodeptr x);
73         void Fix_up_remove(Nodeptr x);
74         void Transplante(Nodeptr old, Nodeptr neo);
75         Nodeptr BranchMax(Nodeptr x);
76         Nodeptr BranchMin(Nodeptr x);
77         void LORvisit(Nodeptr c);
78 };

二、功能函数实现

（一）空树判断：

1 template<typename T>
2 bool RBTree<T>::isEmpyty(){
3     return root == nlnode;
4 }

（二）插入结点：先把传入的元素进行封装，变成结点，再插入

template<typename T>
void RBTree<T>::Insert(T x){
    Nodeptr n=new RBnode<T>(x, nlnode, nlnode);
    Insert(n);
}
template<typename T>
void RBTree<T>::Insert(Nodeptr x){
    Nodeptr first,second;
    first = second = root;
    if(root == nlnode){
        root = x;
        header->right = x;
        x->parent = header;
        x->color = BLACK;
        return;
    }
    while(first!=nlnode){
        second = first;
        if(first->val > x->val){
            first = first->left;
        }else if(first->val < x->val){
            first = first->right;
        }else{
            return ;
        }
    }
    x->parent = second;
    if(second->val > x->val){
        second->left = x;
    }else{
        second->right = x;
    }
    Fix_up_insert(x);
    LOR();
}

（三）左旋与右旋

 1 template<typename T>
 2 void RBTree<T>::LeftRotate(Nodeptr x){
 3     if(x->right == nlnode)//无右子树不可左旋,避免错误操作将树旋空
 4         return;
 5     Nodeptr x_r=x->right;
 6     x->right = x_r->left;
 7     if(x_r->left!=nlnode)//避免破坏空节点的特性：父结点指向自身
 8         x_r->left->parent = x;
 9     x_r->parent = x->parent;
10     if(x_r->parent == header){//根节点
11         root = x_r;
12     }else if(x->parent->left == x){//更新父结点
13         x->parent->left = x_r;
14     }else if(x->parent->right == x){
15         x->parent->right = x_r;
16     }
17     x_r->left = x;
18     x->parent = x_r;
19 }
20 template<typename T>
21 void RBTree<T>::RightRotate(Nodeptr x){
22     if(x->left == nlnode)//无右子树不可左旋,避免错误操作将树旋空
23         return;
24     Nodeptr x_l=x->left;
25     x->left = x_l->right;
26     if(x_l->right!=nlnode)//避免破坏空节点的特性：父结点指向自身
27         x_l->right->parent = x;
28     x_l->parent = x->parent;
29     if(x_l->parent == header){//根节点
30         root = x_l;
31     }else if(x->parent->right == x){//更新父结点
32         x->parent->right = x_l;
33     }else if(x->parent->left == x){
34         x->parent->left = x_l;
35     }
36     x_l->right = x;
37     x->parent = x_l;
38 }

（四）插入后修正

 1 template<typename T>
 2 void RBTree<T>::Fix_up_insert(Nodeptr x){
 3     while(x->parent->color==RED){//首先满足没有连续的红色结点
 4         if(x->parent == x->parent->parent->left){
 5             if(x->parent->parent->right->color == RED){//case 1: son --red,dad&dad's brother --red
 6                 x->parent->parent->right->color = x->parent->color = BLACK;
 7                 x->parent->parent->color = RED;
 8                 x = x->parent->parent;
 9             }
10             else{
11                 if(x == x->parent->right){//case 2:inner side,son --red,dad --red
12                     x = x->parent;
13                     LeftRotate(x);
14                 }
15                 x->parent->parent->color = RED;//case 3:outer side,son --red,dad --red
16                 x->parent->color = BLACK;
17                 x = x->parent;
18                 RightRotate(x->parent->parent);
19             }
20         }
21         else{
22             if(x->parent->parent->left->color == RED){//case 1: son --red,dad&dad's brother --red
23                 x->parent->parent->left->color = x->parent->color = BLACK;
24                 x->parent->parent->color = RED;
25                 x = x->parent->parent;
26             }
27             else{
28                 if(x == x->parent->left){//case 2:inner side,son --red,dad --red
29                     x = x->parent;
30                     LeftRotate(x);
31                 }
32                 x->parent->parent->color = RED;//case 3:outer side,son --red,dad --red
33                 x->parent->color = BLACK;
34                 x = x->parent;
35                 RightRotate(x->parent->parent);
36             }
37         }
38     }
39     root->color=BLACK;
40 }

（五）寻找元素：

 1 template<typename T>
 2 RBnode<T>* RBTree<T>::search(T x){
 3     Nodeptr temp = root;
 4     while(temp!=nlnode){
 5         if(temp->val > x){
 6             temp = temp->left;
 7         }else if(temp->val < x){
 8             temp = temp->right;
 9         }else{
10             return temp;
11         }
12     }
13     return nlnode;
14 }

（六）移植(替换)结点：

 1 template<typename T>
 2 void RBTree<T>::Transplante(Nodeptr old, Nodeptr neo){
 3     if(old->parent == header){
 4         header->right = neo;
 5         root = neo;
 6     }else if(old->parent->left == old){
 7         old->parent->left = neo;
 8     }else if(old->parent->right == old){
 9         old->parent->right = neo;
10     }
11     neo->parent = old->parent;
12 }

（七）子树最大最小结点：

 1 template<typename T>
 2 RBnode<T>* RBTree<T>::BranchMax(Nodeptr x){
 3     if(x == nlnode)
 4         return x;
 5     Nodeptr temp=x;
 6     while(temp->right!=nlnode){
 7         temp=temp->right;
 8     }
 9     return temp;
10 }
11 template<typename T>
12 RBnode<T>* RBTree<T>::BranchMin(Nodeptr x){
13     if(x == nlnode)
14         return x;
15     Nodeptr temp=x;
16     while(temp->left!=nlnode){
17         temp=temp->left;
18     }
19     return temp;
20 }

（八）移除结点：

 1 template<typename T>
 2 bool RBTree<T>::remove(T x){
 3     Nodeptr target = search(x);
 4     if(target == nlnode){
 5         LOR();
 6         return false;}
 7     return remove(target);
 8 }
 9 template<typename T>
10 bool RBTree<T>::remove(Nodeptr x){
11     Nodeptr a = x;
12     Nodeptr b = nlnode;
13     Color a_OriCo = a->color;
14     if(x->left==nlnode){//case 1:with one kid or no one
15         b = x->right;
16         Transplante(x, x->right);
17     }else if(x->right==nlnode){
18         b = x->left;
19         Transplante(x, x->left);
20     }else{
21         Nodeptr a=BranchMin(x->right);
22         a_OriCo = a->color;
23         b = a->right;
24         if(a->parent == x){//case 2:replace node is son of x
25             b->parent = a;//case nlnode
26         }else{
27             Transplante(a, a->right);//a break away from there
28             a->right = x->right;
29             a->right->parent = a;
30         }
31         Transplante(x, a);//用新结点分支替换旧结点分支
32         a->left = x->left;
33         a->left->parent = a;
34         a->color = x->color;
35     }
36     delete x;
37     if(a_OriCo == BLACK){//case 3:违背红黑规则，路径黑结点数不同
38         Fix_up_remove(b);
39     }
40     LOR();//构建迭代联系，懒得写就直接从头构建了，这里应该仿造双链表删除结点来写
41 }

（九）删除后修正

 1 template<typename T>
 2 void RBTree<T>::Fix_up_remove(Nodeptr x){
 3     Nodeptr z = nlnode;
 4     while(x!=root&&x->color==BLACK){
 5         if(x == x->parent->left){
 6             z=x->parent->right;
 7             if(z->color == RED){//case 1:x's brather --red
 8                 z->color=BLACK;
 9                 x->parent->color = RED;
10                 LeftRotate(x->parent);//利用红色来保持黑一致
11                 z = x->parent->right;//update x's brother
12             }//case 2:x&x's brother sons color same
13             if(z->left->color==BLACK && z->right->color==BLACK){
14                 z->color = RED;//保持与x颜色一致，因为是兄弟结点
15                 x = x->parent;//向上调整
16             }
17             else {
18                 if(z->right->color==BLACK) {//z:x's brother
19                     z->color = RED;//case 3:z left--red,right--black
20                     z->left->color = BLACK;
21                     RightRotate(z);
22                     z = x->parent->right;
23                 }
24                 //case 4:adjust x and z
25                 //将树平衡高度，保持了原父结点位置的颜色
26                 z->color = x->parent->color;
27                 x->parent->color = BLACK;
28                 z->right->color = BLACK;
29                 LeftRotate(x->parent);
30                 break;
31             }
32         }
33         else {
34             z=x->parent->left;
35             if(z->color == RED){//case 1:x's brather --red
36                 z->color=BLACK;
37                 x->parent->color = RED;
38                 this->RightRotate(x->parent);//利用红色来保持黑一致
39                 z = x->parent->left;//update x's brother
40             }//case 2:x&x's brother sons color same
41             if(z->right->color==BLACK && z->left->color==BLACK){
42                 z->color = RED;//保持与x颜色一致，因为是兄弟结点
43                 x = x->parent;//向上调整
44             }
45             else {
46                 if(z->left->color==BLACK) {//z:x's brother
47                     z->color = RED;//case 3:z left--red,right--black
48                     z->right->color = BLACK;
49                     LeftRotate(z);
50                     z = x->parent->left;
51                 }
52                 //case 4:adjust x and z
53                 //将树平衡高度，保持了原父结点位置的颜色
54                 z->color = x->parent->color;
55                 x->parent->color = BLACK;
56                 z->left->color = BLACK;
57                 RightRotate(x->parent);
58                 break;
59             }
60         }
61     }
62     root->color = BLACK;//保持根为黑
63 }

（十）获取最大最小元素：

1 template<typename T>
2 T RBTree<T>::getMax(){
3     return header->prior->val;
4 }
5 template<typename T>
6 T RBTree<T>::getMin(){
7     return header->next->val;
8 }

（十一）迭代构造线索

 1 template<typename T>
 2 void RBTree<T>::LOR(){
 3     _prior = _next = header;
 4     LOR(root);
 5     _next->next=header;
 6     header->prior=_next;
 7 }
 8 template<typename T>
 9 void RBTree<T>::LOR(Nodeptr c){
10     if(c->left != nlnode){
11         LOR(c->left);
12     }
13     _prior = _next;
14     _next = c;
15     _prior->next=_next;
16     _next->prior=_prior;
17     if(c->right != nlnode){
18         LOR(c->right);
19     }
20 }

（十二）递归遍历与迭代遍历：

 1 template<typename T>
 2 void RBTree<T>::LORvisit(){
 3     LORvisit(root);
 4     cout << endl;
 5 }
 6 template<typename T>
 7 void RBTree<T>::LORvisit(Nodeptr c){
 8     if(c->left != nlnode){
 9         LORvisit(c->left);
10     }
11     cout << c->val << ' ';
12     if(c->right != nlnode){
13         LORvisit(c->right);
14     }
15 }
16 void Iterator_visit(rb_iterator start, rb_iterator over) {
17      rb_iterator temp = start;
18      while(temp != over){
19           cout << temp->val << ' ';
20           temp = temp->next;
21      }
22 }

三、红黑树测试：

 1 #include <iostream>
 2 #include <stdlib.h>
 3 #include "templateRBTree.h"
 4 using namespace std;
 5 
 6 int main()
 7 {
 8     RBTree<int> rb;
 9     for(int i=0;i < 10;++i)
10         rb.Insert(rand()%20);
11     cout << "create RBTree: ";
12     rb.LORvisit();
13     RBTree<int>::rb_iterator itr=rb.begin();
14     cout << "visit tree by iterator: " << endl;
15     rb.Iterator_visit(itr, rb.end());
16     cout << endl;
17     cout << "the max of tree: " << rb.getMax() << endl;
18     cout << "the min of tree: " << rb.getMin() << endl;
19     for(int i=0;i<10;++i)
20         rb.remove(i);
21     cout << "remove x<10: ";
22     rb.LORvisit();
23     cout << "the max of tree: " << rb.getMax() << endl;
24     cout << "the min of tree: " << rb.getMin() << endl;
25     itr=rb.begin();
26     cout << "visit tree by iterator: " << endl;
27     rb.Iterator_visit(itr, rb.end());
28     return 0;
29 }