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【C++】 红黑树实现

2024-07-06 20:19:23   226人阅读

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【C++】红黑树实现

 

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。

 

关于更多红黑树的知识请参见百度百科：红黑树

 

 

 

C++：BRTreeNode.h

 

 1 #ifndef BRTREENODE_H_INCLUDED
 2 #define BRTREENODE_H_INCLUDED
 3 #include<iostream>
 4 using namespace std;
 5 class BRTree;
 6 class BRTreeNode
 7 {
 8 private:
 9     friend class BRTree;
10     int key;
11     bool color;
12     BRTreeNode* left;
13     BRTreeNode* right;
14     BRTreeNode* parent;
15 public:
16     BRTreeNode():key(-1),color(0),left(NULL),right(NULL),parent(NULL){}
17     BRTreeNode(BRTreeNode* node):key(node->key),color(node->color),left(node->left),right(node->right),parent(node->parent)
18     {}
19     BRTreeNode(int num,bool flag):key(num),color(flag),left(NULL),right(NULL),parent(NULL){}
20     ~BRTreeNode()
21     {
22 
23     }
24     int Getkey()
25     {
26         return key;
27     }
28     bool Getcolor()
29     {
30         return this->color;
31     }
32     BRTreeNode* GetLeft()
33     {
34         return this->left;
35     }
36     BRTreeNode* Getright()
37     {
38         return this->right;
39     }
40     BRTreeNode* Getparent()
41     {
42         return this->parent;
43     }
44     void Inorder()
45     {
46         if(this!=NULL)
47         {
48             this->left->Inorder();
49             cout<<this->key<<" ";
50             this->right->Inorder();
51         }
52     }
53     void Preorder()
54     {
55         if(this!=NULL)
56         {
57             cout<<this->key<<" ";
58             this->left->Preorder();
59             this->right->Preorder();
60         }
61     }
62     void Postorder()
63     {
64         if(this!=NULL)
65         {
66             this->left->Postorder();
67             this->right->Postorder();
68             cout<<this->key<<" ";
69         }
70     }
71 
72     void MakeEmpty()
73     {
74         if(this!=NULL)
75         {
76             this->left->MakeEmpty();
77             this->right->MakeEmpty();
78             delete this;
79         }
80     }
81     int GetHeight()
82     {
83         int L,R;
84         if(this==NULL)
85         {
86             return 0;
87         }
88         L=this->left->GetHeight();
89         R=this->right->GetHeight();
90         return 1+(L>R? L:R);
91     }
92 };
93 
94 
95 #endif // BRTREENODE_H_INCLUDED

 

BRTree.h

 

  1 #ifndef BRTREE_H_INCLUDED
  2 #define BRTREE_H_INCLUDED
  3 #define maxSize 30
  4 #define maxWidth 30
  5 #include"BRTreeNode.h"
  6 class BRTree
  7 {
  8 private:
  9     BRTreeNode* root;
 10     BRTreeNode* nil;
 11 public:
 12     BRTree():nil(new BRTreeNode())
 13     {
 14         nil->color=0;
 15         nil->key=-1;
 16         nil->left=nil->right=nil->parent=NULL;
 17         root=nil;
 18     }
 19     ~BRTree()
 20     {
 21         MakeEmpty(root);
 22         delete nil;
 23     }
 24     //清空以node为根节点的树
 25     void MakeEmpty(BRTreeNode*node)
 26     {
 27         if(node!=nil)
 28         {
 29             MakeEmpty(node->left);
 30             MakeEmpty(node->right);
 31             delete node;
 32         }
 33     }
 34     int Getkey(BRTreeNode* node)
 35     {
 36         return node->Getkey();
 37     }
 38     bool Getcolor(BRTreeNode* node)
 39     {
 40         return node->Getcolor();
 41     }
 42     BRTreeNode* Getroot()
 43     {
 44         return root;
 45     }
 46     BRTreeNode* GetParent(BRTreeNode*node)
 47     {
 48         return node->parent;
 49     }
 50     int GetHeight(BRTreeNode* node)
 51     {
 52         int L,R;
 53         if(node==nil)
 54             return 0;
 55         L=GetHeight(node->left);
 56         R=GetHeight(node->right);
 57         return 1+(L>R? L:R);
 58     }
 59     int GetBlackHeight(BRTreeNode* node)
 60     {
 61         int L,R;
 62         if(node==nil) return 0;
 63         L=GetHeight(node->left);
 64         R=GetHeight(node->right);
 65         if(node->Getcolor()) return(L>R? L:R);
 66         else return 1+(L>R? L:R);
 67     }
 68     void Inorder(BRTreeNode*node)
 69     {
 70         if(node!=nil)
 71         {
 72             Inorder(node->left);
 73             cout<<node->key<<" ";
 74             Inorder(node->right);
 75         }
 76     }
 77     void Preorder(BRTreeNode*node)
 78     {
 79         if(node!=nil)
 80         {
 81             cout<<node->key<<" ";
 82             Preorder(node->left);
 83             Preorder(node->right);
 84         }
 85     }
 86     void Posetorder(BRTreeNode*node)
 87     {
 88         if(node!=nil)
 89         {
 90             Posetorder(node->left);
 91             Posetorder(node->right);
 92             cout<<node->key<<" ";
 93         }
 94     }
 95     //层次法打印树
 96 void DispTree(BRTreeNode*BT)
 97 {
 98     BRTreeNode stack[maxSize],p;
 99     int level[maxSize][2],top,n,i,width=4;
100     if(BT!=NULL)
101     {
102         cout<<"Display a tree by hollow means."<<endl;
103         top=1;
104         stack[top]=BT;//push root point to stack.
105         level[top][0]=width;
106         while(top>0)
107         {
108             p=stack[top];
109             n=level[top][0];
110             for(i=1;i<=n;i++)
111                 cout<<" ";
112             //输出信息
113             if(p.key==0)
114             {
115                 cout<<")";
116             }
117             else{
118             if(p.key==-1) cout<<"Nil";
119             else if(p.left&&p.right) cout<<"("<<p.key;
120             else cout<<p.key;
121             if(p.Getcolor()) cout<<"R,";
122             else cout<<"B,";
123             }
124             for(i=n+1;i<maxWidth;i+=2)
125                 cout<<"--";
126             cout<<endl;
127             top--;
128             if(p.right!=NULL)
129             {
130                 //插入一个括号节点，key值为0
131                 top++;
132                 BRTreeNode* tmp=new BRTreeNode();
133                 tmp->key=0;
134                 stack[top]=tmp;
135                 level[top][0]=n+width;
136                 level[top][1]=2;
137                 top++;
138                 stack[top]=p.right;
139                 level[top][0]=n+width;
140                 level[top][1]=2;
141 
142             }
143             if(p.left!=NULL)
144             {
145                 top++;
146                 stack[top]=p.left;
147                 level[top][0]=n+width;
148                 level[top][1]=1;
149             }
150         }
151     }
152 }
153     //左旋节点node
154     bool LeftRotate(BRTreeNode* node)
155     {
156         BRTreeNode*y;
157         if(node->right==nil)
158         {
159             cout<<"can‘t left rotate!"<<endl;
160             return 0;
161         }
162         y=node->right;
163         node->right=y->left;
164         if(y->left!=nil)
165         {
166             y->left->parent=node;
167         }
168         y->parent=node->parent;
169         if(node->parent==nil)
170         {
171             root=y;
172         }
173         else if(node->parent->left==node)
174         {
175             node->parent->left=y;
176         }
177         else
178         {
179             node->parent->right=y;
180         }
181         y->left=node;
182         node->parent=y;
183         return 1;
184     }
185     //右旋节点
186     bool RightRotate(BRTreeNode* node)
187     {
188         if(node->left==nil)
189         {
190             cout<<"can‘t rightrotate!"<<endl;
191             return 0;
192         }
193         BRTreeNode* x;
194         x=node->left;
195         node->left=x->right;
196         if(x->right!=nil)
197         {
198             x->right->parent=node;
199         }
200         x->parent=node->parent;
201         if(node->parent==nil)
202         {
203             root=x;
204         }
205         else if(node->parent->left==node)
206         {
207             node->parent->left=x;
208         }
209         else
210         {
211             node->parent->right=x;
212         }
213         node->parent=x;
214         x->right=node;
215         return 1;
216     }
217     void Insert(int num)
218     {
219         BRTreeNode* node=new BRTreeNode(num,1);
220         node->left=nil;
221         node->right=nil;
222         node->parent=nil;
223         BRTreeNode* p=root,*q=nil;
224         if(root==nil)
225         {
226             node->color=0;
227             root=node;
228             root->left=root->right=root->parent=nil;
229             return ;
230         }
231         while(p!=nil)
232         {
233             if(p->key==num)
234             {
235                 cout<<num<<"  has exist!"<<endl;
236                 return ;
237             }
238             else if(p->key>num)
239             {
240                 q=p;
241                 p=p->left;
242             }
243             else
244             {
245                 q=p;
246                 p=p->right;
247             }
248         }
249         if(q->key>num)
250         {
251             q->left=node;
252             node->parent=q;
253         }
254         else
255         {
256             q->right=node;
257             node->parent=q;
258         }
259         RBInsertAdjust(node);
260     }
261     void RBInsertAdjust(BRTreeNode* node)
262     {
263         BRTreeNode* y;
264         while(node->parent->color==1)
265         {
266             if(node->parent==node->parent->parent->left)
267             {
268                 y=node->parent->parent->right;
269                 if(y->color==1)
270                 {
271                     node->parent->color=0;
272                     y->color=0;
273                     y->parent->color=1;
274                     node=node->parent->parent;
275                 }
276                 //此时y的颜色是黑色
277                 else
278                 {
279                     //第二种情况
280                     if(node==node->parent->right)
281                     {
282                         node=node->parent;
283                         LeftRotate(node);
284                     }
285                     //第三种情况
286                     node->parent->color=0;
287                     node->parent->parent->color=1;
288                     RightRotate(node->parent->parent);
289                 }
290             }
291             else
292             {
293                 y=node->parent->parent->left;
294                 if(y->color==1)
295                 {
296                     node->parent->color=0;
297                     y->color=0;
298                     y->parent->color=1;
299                     node=node->parent->parent;
300                 }
301                 else
302                 {
303                     if(node==node->parent->left)
304                     {
305                         node=node->parent;
306                         RightRotate(node);
307                     }
308                     node->parent->color=0;
309                     node->parent->parent->color=1;
310                     LeftRotate(node->parent->parent);
311                 }
312             }
313         }
314         root->color=0;
315     }
316     BRTreeNode* Search(int num)
317     {
318         BRTreeNode* p=root;
319         while(p!=nil)
320         {
321             if(p->key==num)
322             {
323                 return p;
324             }
325             else if(p->key>num)
326             {
327                 p=p->left;
328             }
329             else
330             {
331                 p=p->right;
332             }
333         }
334         cout<<"there is no "<<num<<" in this tree!"<<endl;
335         return nil;
336     }
337     //获取以node节点为根节点的树的最小元素，并返回该最小值
338     int Minnum(BRTreeNode*node)
339     {
340         BRTreeNode*p=node;
341         while(p->left!=nil)
342         {
343             p=p->left;
344         }
345         return p->key;
346     }
347     //获取以node节点为根节点的树的最da元素，并返回该最da值
348     int Maxnum(BRTreeNode*node)
349     {
350         BRTreeNode*p=node;
351         while(p->right!=nil)
352         {
353             p=p->right;
354         }
355         return p->key;
356     }
357     //获取以node节点为根节点的树的最小元素，并返回该节点
358     BRTreeNode* MinNum(BRTreeNode*node)
359     {
360         BRTreeNode*p=node;
361         while(p->left!=nil)
362         {
363             p=p->left;
364         }
365         return p;
366     }
367     //获取以node节点为根节点的树的最大元素
368     BRTreeNode* MaxNum(BRTreeNode*node)
369     {
370         BRTreeNode*p=node;
371         while(p->right!=nil)
372         {
373             p=p->right;
374         }
375         return p;
376     }
377     BRTreeNode*InorderSuccessor(BRTreeNode*node)
378     {
379         if(node->right!=nil)
380         {
381             return MinNum(node->right);
382         }
383         else
384         {
385             BRTreeNode*p=GetParent(node);
386             while(p&&node==p->right)
387             {
388                 node=p;
389                 p=GetParent(node);
390             }
391             return p;
392         }
393     }
394     //中序遍历的前趋
395     BRTreeNode*InordePredecessor(BRTreeNode*node)
396     {
397         if(node->left!=nil)
398         {
399             return MaxNum(node->left);
400         }
401         else
402         {
403             BRTreeNode*p=GetParent(node);
404             while(p&&node==p->left)
405             {
406                 node=p;
407                 p=GetParent(node);
408             }
409             return p;
410         }
411     }
412     bool Delete(int num)
413     {
414         BRTreeNode*z,*y,*x;
415         //寻找key值为num的节点p
416         z=Search(num);
417         //如果没有该节点则返回0
418         if(z==nil)
419         {
420             return 0;
421         }
422         if(z->left==nil||z->right==nil)
423         {
424             y=z;
425         }
426         else
427             y=InorderSuccessor(z);
428         if(y->left!=nil)
429             x=y->left;
430         else
431             x=y->right;
432         x->parent=y->parent;
433         if(x->parent==nil)
434             root=x;
435         else if(y=y->parent->left)
436             y->parent->left=x;
437         else
438             y->parent->right=x;
439         if(y!=z)
440         {
441             z->key=y->key;
442         }
443         if(y->color==0)
444         {
445             RBTreeFixup(x);
446         }
447         return 1;
448     }
449     void RBTreeFixup(BRTreeNode* x)
450     {
451         BRTreeNode*w;
452         while(x!=root&&x->color==0)
453         {
454             if(x==x->parent->left)
455             {
456                 w=x->parent->right;
457                 if(w->color==1)
458                 {
459                     w->color=0;
460                     x->parent->color=1;
461                     LeftRotate(x->parent);
462                     w=x->parent->right;
463                 }
464                 if(w->left->color==0&&w->right->color==0)
465                 {
466                     w->color=1;
467                     x=x->parent;
468                 }
469                 else
470                 {
471                     if(w->right->color==0)
472                     {
473                         w->color=1;
474                         RightRotate(w);
475                         w=x->parent->right;
476                     }
477                     w->color=x->parent->color;
478                     x->parent->color=0;
479                     w->right->color=0;
480                     LeftRotate(x->parent);
481                     x=root;
482                 }
483             }
484             else
485             {
486                 w=x->parent->left;
487                 if(w->color==1)
488                 {
489                     w->color=0;
490                     x->parent->color=1;
491                     RightRotate(x->parent);
492                     w=x->parent->left;
493                 }
494                 if(w->right->color==0&&w->left->color==0)
495                 {
496                     w->color=1;
497                     x=x->parent;
498                 }
499                 else
500                 {
501                     if(w->left->color==0)
502                     {
503                         w->color=1;
504                         LeftRotate(w);
505                         w=x->parent->left;
506                     }
507                     w->color=x->parent->color;
508                     x->parent->color=0;
509                     w->left->color=0;
510                     RightRotate(x->parent);
511                     x=root;
512                 }
513             }
514         }
515         x->color=0;
516     }
517 };
518 
519 #endif // BRTREE_H_INCLUDED

 

 

 

 


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