1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
|
/*
* Author: Tanky Woo
* Blog: www.WuTianQi.com
* Description: 《算法导论》第13章 Red Black Tree
*/
#include <iostream>
//#define NULL 0
using namespace std;
const int RED = 0;
const int BLACK = 1;
// ①
typedef struct Node{
int color;
int key;
Node *lchild, *rchild, *parent;
}Node, *RBTree;
static Node NIL = {BLACK, 0, 0, 0, 0};
#define NULL (&NIL)
// ②
Node * RBTreeSearch(RBTree T, int k)
{
if(T == NULL || k == T->key)
return T;
if(k < T->key)
return RBTreeSearch(T->lchild, k);
else
return RBTreeSearch(T->rchild, k);
}
/*
BSNode * IterativeRBTreeSearch(RBTree T, int k)
{
while(T != NULL && k != T->key)
{
if(k < T->lchild->key);
x = T->lchild;
else
x = T->rchild;
}
return x;
}
*/
// ③
Node * RBTreeMinimum(RBTree T)
{
while(T->lchild != NULL)
T = T->lchild;
return T;
}
Node * RBTreeMaximum(RBTree T)
{
while(T->rchild != NULL)
T = T->rchild;
return T;
}
// ④
Node *RBTreeSuccessor(Node *x)
{
if(x->rchild != NULL)
return RBTreeMinimum(x->rchild);
Node *y = x->parent;
while(y != NULL && x == y->rchild)
{
x = y;
y = y->parent;
}
return y;
}
void LeftRotate(RBTree &T, Node *x)
{
Node *y = x->rchild;
x->rchild = y->lchild;
if(y->lchild != NULL)
y->lchild->parent = x;
y->parent = x->parent;
if(x->parent == NULL)
T = y;
else
{
if(x == x->parent->lchild)
x->parent->lchild = y;
else
x->parent->rchild = y;
}
y->lchild = x;
x->parent = y;
}
void RightRotate(RBTree &T, Node *x)
{
Node *y = x->rchild;
x->rchild = y->lchild;
if(y->lchild != NULL)
y->lchild->parent = x;
y->parent = x->parent;
if(x->parent == NULL)
T = y;
else
{
if(x == x->parent->lchild)
x->parent->lchild = y;
else
x->parent->rchild = y;
}
y->lchild = x;
x->parent = y;
}
// ⑤
void RBInsertFixup(RBTree &T, Node *z)
{
while(z->parent->color == RED)
{
if(z->parent == z->parent->parent->lchild)
{
Node *y = z->parent->parent->rchild;
//////////// Case1 //////////////
if(y->color == RED)
{
z->parent->color = BLACK;
y->color = BLACK;
z->parent->parent->color = RED;
z = z->parent->parent;
}
else
{
////////////// Case 2 //////////////
if(z == z->parent->rchild)
{
z = z->parent;
LeftRotate(T, z);
}
////////////// Case 3 //////////////
z->parent->color = BLACK;
z->parent->parent->color = RED;
RightRotate(T, z->parent->parent);
}
}
else
{
Node *y = z->parent->parent->lchild;
if(y->color == RED)
{
z->parent->color = BLACK;
y->color = BLACK;
z->parent->parent->color = RED;
z = z->parent->parent;
}
else
{
if(z == z->parent->lchild)
{
z = z->parent;
RightRotate(T, z);
}
z->parent->color = BLACK;
z->parent->parent->color = RED;
LeftRotate(T, z->parent->parent);
}
}
}
T->color = BLACK;
}
void RBTreeInsert(RBTree &T, int k)
{
//T->parent->color = BLACK;
Node *y = NULL;
Node *x = T;
Node *z = new Node;
z->key = k;
z->lchild = z->parent = z->rchild = NULL;
while(x != NULL)
{
y = x;
if(k < x->key)
x = x->lchild;
else
x = x->rchild;
}
z->parent = y;
if(y == NULL)
{
T = z;
T->parent = NULL;
T->parent->color = BLACK;
}
else
if(k < y->key)
y->lchild = z;
else
y->rchild = z;
z->lchild = NULL;
z->rchild = NULL;
z->color = RED;
RBInsertFixup(T, z);
}
// ⑤
void RBDeleteFixup(RBTree &T, Node *x)
{
while(x != T && x->color == BLACK)
{
if(x == x->parent->lchild)
{
Node *w = x->parent->rchild;
///////////// Case 1 /////////////
if(w->color == RED)
{
w->color = BLACK;
x->parent->color = RED;
LeftRotate(T, x->parent);
w = x->parent->rchild;
}
///////////// Case 2 /////////////
if(w->lchild->color == BLACK && w->rchild->color == BLACK)
{
w->color = RED;
x = x->parent;
}
else
{
///////////// Case 3 /////////////
if(w->rchild->color == BLACK)
{
w->lchild->color = BLACK;
w->color = RED;
RightRotate(T, w);
w = x->parent->rchild;
}
///////////// Case 4 /////////////
w->color = x->parent->color;
x->parent->color = BLACK;
w->rchild->color = BLACK;
LeftRotate(T, x->parent);
x = T;
}
}
else
{
Node *w = x->parent->lchild;
if(w->color == RED)
{
w->color = BLACK;
x->parent->color = RED;
RightRotate(T, x->parent);
w = x->parent->lchild;
}
if(w->lchild->color == BLACK && w->rchild->color == BLACK)
{
w->color = RED;
x = x->parent;
}
else
{
if(w->lchild->color == BLACK)
{
w->rchild->color = BLACK;
w->color = RED;
LeftRotate(T, w);
w = x->parent->lchild;
}
w->color = x->parent->color;
x->parent->color = BLACK;
w->lchild->color = BLACK;
RightRotate(T, x->parent);
x = T;
}
}
}
x->color = BLACK;
}
Node* RBTreeDelete(RBTree T, Node *z)
{
Node *x, *y;
// z是要删除的节点,而y是要替换z的节点
if(z->lchild == NULL || z->rchild == NULL)
y = z; // 当要删除的z至多有一个子树，则y=z；
else
y = RBTreeSuccessor(z); // y是z的后继
if(y->lchild != NULL)
x = y->lchild;
else
x = y->rchild;
// 无条件执行p[x] = p[y]
x->parent = y->parent; //如果y至多只有一个子树，则使y的子树成为y的父亲节点的子树
if(y->parent == NULL) // 如果y没有父亲节点，则表示y是根节点，词典其子树x为根节点
T = x;
else if(y == y->parent->lchild)
// 如果y是其父亲节点的左子树，则y的子树x成为其父亲节点的左子树，
// 否则成为右子树
y->parent->lchild = x;
else
y->parent->rchild = x;
if(y != z)
z->key = y->key;
if(y->color == BLACK)
RBDeleteFixup(T, x);
return y;
}
void InRBTree(RBTree T)
{
if(T != NULL)
{
InRBTree(T->lchild);
cout << T->key << " ";
InRBTree(T->rchild);
}
}
void PrintRBTree(RBTree T)
{
if(T != NULL)
{
PrintRBTree(T->lchild);
cout << T->key << ": ";
// 自身的颜色
if(T->color == 0)
cout << " Color: RED ";
else
cout << " Color: BLACK ";
// 父亲结点的颜色
if(T == NULL)
cout << " Parent: BLACK ";
else
{
if(T->color == 0)
cout << " Parent: RED ";
else
cout << " Parent: BLACK ";
}
// 左儿子结点的颜色
if(T->lchild == NULL)
cout << " Lchild: BLACK ";
else
{
if(T->lchild->color == 0)
cout << " Lchild: RED ";
else
cout << " Lchild: BLACK ";
}
// 右儿子结点的颜色
if(T->rchild == NULL)
cout << " Rchild: BLACK ";
else
{
if(T->rchild->color == 0)
cout << " Rchild: RED ";
else
cout << " Rchild: BLACK ";
}
cout << endl;
PrintRBTree(T->rchild);
}
}
int main()
{
int m;
RBTree T = NULL;
for(int i=0; i<9; ++i)
{
cin >> m;
RBTreeInsert(T, m);
cout << "在红黑树中序查找：";
InRBTree(T);
cout << endl;
}
PrintRBTree(T);
cout << "删除根节点后：";
RBTreeDelete(T, T);
InRBTree(T);
}
|