标签：des style blog class code c
性质2. 根是黑色。
性质3. 所有叶子都是黑色（叶子是NIL节点）。
性质4. 每个红色节点的两个子节点都是黑色。(从每个叶子到根的所有路径上不能有两个连续的红色节点)
1 插入新节点总是红色节点
2 如果插入节点的父节点是黑色, 能维持性质
3 如果插入节点的父节点是红色, 破坏了性质. 故需要通过重新着色或旋转, 来维持性质
插入关键部分
解决相邻的两个节点为红色的结点，同时维持任意路径黑高度（黑色结点个数）相同
删除需要需要注意的点
1 如果删除的是红色节点, 不破坏性质
2 如果删除的是黑色节点, 那么这个路径上就会少一个黑色节点, 破坏了性质. 故需要通过重新着色或旋转, 来维持性质
删除关键部分
如果删除的是左子树黑色结点，维持的最终目的是左右黑高度相同，即维持右子树黑高度的同时，增加左子树的黑高度
代码主要根据上图实现
1 #include <iostream> 2 #include <crtdbg.h> 3 #include <string> 4 using namespace std; 5 /*红黑树*/ 6 /*实现中假设关键元素互不相同*/ 7 typedef int DataType; 8 9 class BST 10 { 11 private: 12 enum {BLACK = 0, RED = 1}; 13 /*结点的数据结构*/ 14 struct node 15 { 16 DataType data; 17 bool color; 18 node *left; 19 node *right; 20 node *parent; 21 22 node() 23 { 24 color = RED; 25 left = NULL; 26 right = NULL; 27 parent = NULL; 28 data = 0; 29 } 30 node *Grandfather() 31 { 32 if (parent == NULL) 33 { 34 return NULL; 35 } 36 return parent->parent; 37 } 38 node *Uncle() 39 { 40 if(Grandfather() == NULL) 41 return NULL; 42 if (parent == Grandfather()->left) 43 { 44 return Grandfather()->right; 45 } 46 else 47 { 48 return Grandfather()->left; 49 } 50 } 51 node *Sibling() 52 { 53 if (parent->left == this) 54 { 55 return parent->right; 56 } 57 else 58 { 59 return parent->left; 60 } 61 } 62 }; 63 void Left_rotate(node *p ) 64 { 65 //把y的左子树连接到p的右子树下面，并更新父节点 66 node *y = p->right; 67 p->right = y->left; 68 if (y->left != NIL) 69 { 70 y->left->parent = p; 71 } 72 //更新y的父节点 73 y->parent = p->parent; 74 if (p->parent == NIL) //判断根结点 75 { 76 root = y; 77 } 78 //更新原x父节点的子节点 79 else if (p == p->parent->left) 80 { 81 p->parent->left = y; 82 } 83 else 84 { 85 p->parent->right = y; 86 } 87 //更新x 与 y 的关系 88 y->left = p; 89 p->parent = y; 90 } 91 void Right_rotate(node *p) 92 { 93 node *y = p->left; 94 p->left = y->right; 95 if (y->right != NIL) 96 { 97 y->right->parent = p; 98 } 99 y->parent = p->parent; 100 if (p->parent == NIL) //判断根结点 101 { 102 root = y; 103 } 104 else if (p == p->parent->left) 105 { 106 p->parent->left = y; 107 } 108 else 109 { 110 p->parent->right = y; 111 } 112 y->right = p; 113 p->parent = y; 114 } 115 string OutputColor(bool color) 116 { 117 return color ? "RED":"BLACK"; 118 } 119 /*纠正因插入而破坏的性质*/ 120 void Insert_Fixup(node *p) 121 { 122 /*由于p结点为红色（新插入默认赋值为红色）， 123 判断p的父节点是否为红色，如果为红色则破坏了红黑树的性质，需要维护*/ 124 while(p->parent->color == RED) 125 { 126 if (p->parent == p->Grandfather()->left) 127 { 128 node *y = p->Grandfather()->right; 129 if (y->color == RED) /*case 3*/ 130 { 131 p->parent->color = BLACK; 132 y->color = BLACK; 133 p->Grandfather()->color = RED; 134 p = p->Grandfather();/*p结点向上移*/ 135 } 136 else if (p == p->parent->right) /*case 2*/ 137 { 138 p = p->parent;/*p结点向上移*/ 139 Left_rotate(p); 140 } 141 else 142 { 143 p->parent->color = BLACK; /*case 3*/ 144 p->Grandfather()->color = RED; 145 Right_rotate(p->Grandfather());/*注意是祖父结点*/ 146 } 147 } 148 else 149 { 150 node *y = p->Grandfather()->left; 151 if (y->color == RED) /*case 3*/ 152 { 153 p->parent->color = BLACK; 154 y->color = BLACK; 155 p->Grandfather()->color = RED; 156 p = p->Grandfather(); 157 } 158 else if (p == p->parent->left) /*case 2*/ 159 { 160 p = p->parent; 161 Right_rotate(p); 162 } 163 else 164 { 165 p->parent->color = BLACK; /*case 3*/ 166 p->Grandfather()->color = RED; 167 Left_rotate(p->Grandfather()); 168 } 169 } 170 } 171 root->color = BLACK;/*确保插入根结点时，满足红黑树的性质*/ 172 } 173 /*纠正因删除而破坏的性质*/ 174 void Delete_Fixup(node *p) 175 { 176 /*判断p结点是否为黑色 177 如果是红色不破坏红黑树性质 178 原因1.删除红色树黑高度不变2.不存在两个相邻红色结点 179 3. 如果y是红色的，就不可能是根，即根仍然是黑色的 180 为保证性质任何路径上黑结点个数相同，假设p结点为多重颜色（双黑或红黑）*/ 181 while (p != root && p->color == BLACK) 182 { 183 if(p == p->parent->left) 184 { 185 node *pSibling = p->parent->right; 186 if (pSibling->color == RED)/*case1*/ 187 { 188 pSibling->color = BLACK; 189 Left_rotate(p->parent); 190 pSibling = p->parent->right; 191 } 192 else if (pSibling->left->color == BLACK && pSibling->right->color == BLACK)/*case2*/ 193 { 194 pSibling->color = RED; 195 p = p->parent; 196 } 197 else 198 { 199 if (pSibling->right->color == BLACK)/*case3*/ 200 { 201 pSibling->left->color = BLACK; 202 pSibling->color = RED; 203 Right_rotate(pSibling); 204 pSibling = p->parent->right; 205 } 206 pSibling->color = p->parent->color;/*case4*/ 207 p->parent->color = BLACK; 208 pSibling->right->color = BLACK; 209 Left_rotate(p->parent); 210 p = root; 211 } 212 } 213 else 214 { 215 node *pSibling = p->parent->left; 216 if (pSibling->color == RED)/*case1*/ 217 { 218 pSibling->color = BLACK; 219 Left_rotate(p->parent); 220 pSibling = p->parent->left; 221 } 222 else if (pSibling->left->color == BLACK && pSibling->right->color == BLACK)/*case2*/ 223 { 224 pSibling->color = RED; 225 p = p->parent; 226 } 227 else 228 { 229 if (pSibling->left->color == BLACK)/*case3*/ 230 { 231 pSibling->right->color = BLACK; 232 pSibling->color = RED; 233 Left_rotate(pSibling); 234 pSibling = p->parent->left; 235 } 236 pSibling->color = p->parent->color;/*case4*/ 237 p->parent->color = BLACK; 238 pSibling->right->color = BLACK; 239 Right_rotate(p->parent); 240 p = root; 241 } 242 } 243 } 244 p->color = BLACK; 245 } 246 /*中序遍历*/ 247 void InOrderTree(node *p) 248 { 249 if (p == NULL || p == NIL) 250 { 251 return; 252 } 253 InOrderTree(p->left); 254 cout << p->data << "\t" << OutputColor(p->color) << endl; 255 InOrderTree(p->right); 256 } 257 /*获取结点的后继*/ 258 node *TreeAfter(node *p) 259 { 260 if (p->right != NIL) 261 { 262 node *pTemp = p->right; 263 while(pTemp != NIL) 264 { 265 p = pTemp; 266 pTemp = p->left; 267 } 268 } 269 return p; 270 } 271 private: 272 node *root; 273 node *NIL; 274 public: 275 BST() 276 { 277 NIL = new node(); 278 NIL->color = BLACK; 279 root = NULL; 280 } 281 ~BST() 282 { 283 if (root != NULL) 284 { 285 Destory(root); 286 root = NULL; 287 } 288 delete NIL; 289 NIL = NULL; 290 } 291 void Destory(node *p) 292 { 293 if (p == NULL || p == NIL) 294 return; 295 Destory(p->left); 296 Destory(p->right); 297 delete p; 298 } 299 void Insert(DataType data) 300 { 301 node *p = root; 302 node *pTemp = NIL; 303 while( p != NIL && p != NULL) 304 { 305 pTemp = p; 306 if (data < p->data) 307 { 308 p = p->left; 309 } 310 else 311 { 312 p = p->right; 313 } 314 } 315 node *pNew = new node(); 316 pNew->parent = pTemp; 317 pNew->data = data; 318 if (pTemp == NIL) 319 { 320 root = pNew; 321 } 322 else 323 { 324 if (pNew->data < pTemp->data) 325 { 326 pTemp->left = pNew; 327 } 328 else 329 { 330 pTemp->right = pNew; 331 } 332 } 333 pNew->left = NIL; 334 pNew->right = NIL; 335 Insert_Fixup(pNew); 336 } 337 /*非递归版本*/ 338 node* Find(DataType key) 339 { 340 node *p = root; 341 while(p != NULL && p->data != key) 342 { 343 if (key < p->data) 344 { 345 p = p->left; 346 } 347 else 348 { 349 p = p->right; 350 } 351 } 352 return p; 353 } 354 void Delete(DataType data) 355 { 356 /*获取data的指针*/ 357 node *p = Find(data); 358 node *pDelete= NIL; 359 node *pNode = NIL;/*要删除节点的子节点*/ 360 if (p->left == NIL || p->right == NIL) 361 { 362 pDelete = p; 363 } 364 else 365 { 366 pDelete = TreeAfter(p); 367 } 368 /*获取子结点*/ 369 if(pDelete->left != NIL) 370 { 371 pNode = pDelete->left; 372 } 373 else 374 { 375 pNode = pDelete->right; 376 } 377 /*更新父结点*/ 378 pNode->parent = pDelete->parent; 379 /*更新子结点*/ 380 if (pDelete->parent == NIL) 381 { 382 root = pNode; 383 } 384 else if(pDelete->parent->left == pDelete) 385 { 386 pDelete->parent->left = pNode; 387 } 388 else 389 { 390 pDelete->parent->right = pNode; 391 } 392 if (pDelete != p) 393 { 394 p->data = pDelete->data; 395 } 396 /*如果要删除的结点pDelete是红色的， 397 不影响黑高度，即不会破坏红黑树的性质*/ 398 if (pDelete->color == BLACK) 399 { 400 Delete_Fixup(pNode); 401 } 402 delete pDelete; 403 pDelete = NULL; 404 } 405 void InOrder() 406 { 407 if (root == NULL) 408 { 409 return; 410 } 411 InOrderTree(root); 412 cout << endl; 413 } 414 }; 415 416 void main() 417 { 418 _CrtSetDbgFlag(_CRTDBG_ALLOC_MEM_DF | _CRTDBG_LEAK_CHECK_DF); 419 420 BST bst; 421 422 bst.Insert(11); 423 bst.Insert(2); 424 bst.Insert(14); 425 bst.Insert(15); 426 bst.Insert(1); 427 bst.Insert(7); 428 bst.Insert(5); 429 bst.Insert(8); 430 bst.Insert(4); 431 432 bst.InOrder(); 433 434 //bst.Delete(4); 435 //bst.Delete(14); 436 bst.Delete(7); 437 bst.InOrder(); 438 439 system("pause"); 440 }
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标签：des style blog class code c
原文地址：http://www.cnblogs.com/sevenPP/p/3733450.html
