平衡有序二叉树(AVL Tree)的C++实现
平衡二叉树是一个重要的数据结构，它有很均衡的插入、删除以及查询性能（时间复杂度都是O(logn)）。Linux2.4以前的内核中，虚拟内存管理中用的容器就是AVL Tree，之后的版本都改成了RBTree即红黑树。AVL Tree对平衡的要求是比较严格的，它要求左右子数之间的长度差不能大于1，也正由于它的严格导致了AVL Tree的统计性能没有RBTree好。AVL Tree在插入或者删除节点时候出现不平衡情况，根据具体情况进行一次或者多次单旋或者双旋就可以使整棵树达到平衡。具体的旋转规则看这里，删除节点的算法看这里。下面是我根据AVL树的规则用C++实现的代码：
1 #ifndef __AVLTREE_H__ 2 #define __AVLTREE_H__ 3 4 #include <stdlib.h> 5 #include <iostream> 6 7 struct AVLNode 8 { 9 int nData; 10 AVLNode* pLeft; 11 AVLNode* pRight; 12 AVLNode* pParent; 13 int nHeight; 14 }; 15 16 class AVLTree 17 { 18 public: 19 AVLTree() : pRoot(NULL), nNodeCount(0){} 20 ~AVLTree(){ DeleteTree(&pRoot); } 21 public: 22 int Insert(int nData); 23 int Delete(int nData); 24 int Find(int nData) const; 25 int GetNodeCount() const; 26 void Display() const; 27 28 private: 29 int Max(int a, int b) const; 30 int Height(const AVLNode* pNode) const; 31 AVLNode* CreateNode(int nData); 32 AVLNode* DeleteNode(int nData, AVLNode* pNode); 33 AVLNode* BalanceAdjust(AVLNode* pNode); 34 AVLNode* RotateLeft(AVLNode* pNode); 35 AVLNode* RotateRight(AVLNode* pNode); 36 AVLNode* RotateLeftRight(AVLNode* pNode); 37 AVLNode* RotateRightLeft(AVLNode* pNode); 38 void DeleteTree(AVLNode** ppRoot); 39 void PrintTree(AVLNode* pNode) const; 40 41 AVLTree(const AVLTree&) {} 42 AVLTree& operator=(const AVLTree&) {} 43 44 private: 45 AVLNode* pRoot; 46 int nNodeCount; 47 }; 48 49 int AVLTree::Max(int a, int b) const 50 { 51 return (a > b ? a : b); 52 } 53 54 int AVLTree::Height(const AVLNode* pNode) const 55 { 56 if (NULL == pNode) 57 return -1; 58 59 return pNode->nHeight; 60 } 61 62 int AVLTree::Insert(int nData) 63 { 64 if(pRoot == NULL) 65 { 66 pRoot = CreateNode(nData); 67 68 return nNodeCount; 69 } 70 71 AVLNode* pInsertNode = pRoot; 72 73 while(pInsertNode != NULL) 74 { 75 if(nData < pInsertNode->nData) 76 { 77 if(pInsertNode->pLeft == NULL) 78 { 79 pInsertNode->pLeft = CreateNode(nData); 80 pInsertNode->pLeft->pParent = pInsertNode; 81 82 pRoot = BalanceAdjust(pInsertNode->pLeft); 83 break; 84 } 85 86 pInsertNode = pInsertNode->pLeft; 87 } 88 else if(nData > pInsertNode->nData) 89 { 90 if(pInsertNode->pRight == NULL) 91 { 92 pInsertNode->pRight = CreateNode(nData); 93 pInsertNode->pRight->pParent = pInsertNode; 94 95 pRoot = BalanceAdjust(pInsertNode->pRight); 96 break; 97 } 98 99 pInsertNode = pInsertNode->pRight; 100 } 101 else 102 { 103 return nNodeCount; 104 } 105 } 106 107 return nNodeCount; 108 } 109 110 int AVLTree::Delete(int nData) 111 { 112 //std::cout << "Delete nData = " << nData << std::endl; 113 //std::cout << "pNode->nData = " << pNode->nData << std::endl; 114 //std::cout << "pPNode->nData = " << pPNode->nData << std::endl; 115 116 AVLNode* pCurNode = pRoot; 117 118 while(pCurNode != NULL) 119 { 120 if(nData > pCurNode->nData) 121 { 122 pCurNode = pCurNode->pRight; 123 } 124 else if(nData < pCurNode->nData) 125 { 126 pCurNode = pCurNode->pLeft; 127 } 128 else 129 { 130 pRoot = DeleteNode(nData, pCurNode); 131 break; 132 } 133 } 134 135 136 if(pCurNode == NULL) 137 std::cout << "没有找到元素 nData = " << nData << std::endl; 138 //int x; 139 //std::cin >> x; 140 141 return nNodeCount;//没有找到要删除的元素 142 } 143 144 AVLNode* AVLTree::DeleteNode(int nData, AVLNode* pNode) 145 { 146 nNodeCount--; 147 148 if(pNode->pLeft && pNode->pRight)//删除节点有左右子树 149 { 150 AVLNode* pLMaxNode = pNode->pLeft;//删除节点左子树中最大的节点 151 AVLNode* pLMaxPNode = pNode;//删除节点左子树中最大节点的父节点 152 153 //将删除节点左孩子的最大节点替换删除节点,然后删除该节点 154 if(pLMaxNode->pRight == NULL) 155 { 156 pNode->nData = pLMaxNode->nData; 157 pNode->pLeft = pLMaxNode->pLeft; 158 159 if(pLMaxNode->pLeft != NULL) 160 pLMaxNode->pLeft->pParent = pNode; 161 } 162 else 163 { 164 while(pLMaxNode->pRight) 165 { 166 pLMaxPNode = pLMaxNode; 167 pLMaxNode = pLMaxNode->pRight; 168 } 169 pNode->nData = pLMaxNode->nData; 170 171 if(pLMaxNode == pLMaxPNode->pRight)//将替换后的删除节点删除 172 pLMaxPNode->pRight = pLMaxNode->pLeft; 173 else if(pLMaxNode == pLMaxPNode->pLeft) 174 pLMaxPNode->pLeft = NULL; 175 } 176 177 delete pLMaxNode; 178 179 return BalanceAdjust(pLMaxPNode); 180 } 181 else if(pNode->pLeft)//删除节点只有左子树 182 { 183 AVLNode* pLeft = pNode->pLeft; 184 185 pNode->nData = pLeft->nData; 186 187 pNode->pLeft = pLeft->pLeft; 188 if (pLeft->pLeft != NULL) 189 pLeft->pLeft->pParent = pNode; 190 191 pNode->pRight = pLeft->pRight; 192 if (pLeft->pRight != NULL) 193 pLeft->pRight->pParent = pNode; 194 195 delete pLeft; 196 197 return BalanceAdjust(pNode); 198 } 199 else if(pNode->pRight)//删除节点只有右子树 200 { 201 AVLNode* pRight = pNode->pRight; 202 203 pNode->nData = pRight->nData; 204 205 pNode->pLeft = pRight->pLeft; 206 if (pRight->pLeft != NULL) 207 pRight->pLeft->pParent = pNode; 208 209 pNode->pRight = pRight->pRight; 210 if (pRight->pRight != NULL) 211 pRight->pRight->pParent = pNode; 212 213 delete pRight; 214 215 return BalanceAdjust(pNode); 216 } 217 else//删除节点没有子树 218 { 219 AVLNode* pPNode = pNode->pParent; 220 221 if(pPNode->pLeft == pNode) 222 pPNode->pLeft = NULL; 223 else if(pPNode->pRight == pNode) 224 pPNode->pRight = NULL; 225 226 delete pNode; 227 228 return BalanceAdjust(pPNode); 229 } 230 } 231 232 AVLNode* AVLTree::BalanceAdjust(AVLNode* pNode) 233 { 234 AVLNode* pRoot; 235 AVLNode* pPNode; 236 237 while(pNode != NULL)//删除节点的子节点进行平衡 238 { 239 pPNode = pNode->pParent; 240 241 bool bIsLeft = false; 242 if(pPNode != NULL && pNode == pPNode->pLeft) 243 bIsLeft = true; 244 245 pNode->nHeight = Max(Height(pNode->pLeft), Height(pNode->pRight)) + 1; 246 247 if (Height(pNode->pLeft) - Height(pNode->pRight) == 2) // AVL树不平衡 执行LL型或者LR型旋转 248 { 249 if (Height(pNode->pLeft->pLeft) - Height(pNode->pLeft->pRight) == -1) 250 pNode = RotateLeftRight(pNode); 251 else 252 pNode = RotateLeft(pNode); 253 254 if(pPNode != NULL && bIsLeft) 255 pPNode->pLeft = pNode; 256 else if(pPNode != NULL) 257 pPNode->pRight = pNode; 258 } 259 else if(Height(pNode->pLeft) - Height(pNode->pRight) == -2) // AVL树不平衡 执行RR型或者RL型旋转 260 { 261 if (Height(pNode->pRight->pLeft) - Height(pNode->pRight->pRight) == 1) 262 pNode = RotateRightLeft(pNode); 263 else 264 pNode = RotateRight(pNode); 265 266 if (pPNode != NULL && bIsLeft) 267 pPNode->pLeft = pNode; 268 else if(pPNode != NULL) 269 pPNode->pRight = pNode; 270 } 271 272 pRoot = pNode; 273 pNode = pPNode; 274 } 275 276 return pRoot; 277 } 278 279 AVLNode* AVLTree::CreateNode(int nData) 280 { 281 nNodeCount++; 282 283 AVLNode* pNewNode = new AVLNode(); 284 pNewNode->nData = nData; 285 pNewNode->nHeight = 0; 286 pNewNode->pLeft = pNewNode->pRight = NULL; 287 288 return pNewNode; 289 } 290 291 int AVLTree::Find(int nData) const 292 { 293 AVLNode* pFindNode = pRoot; 294 while(pFindNode) 295 { 296 if(nData < pFindNode->nData) 297 pFindNode = pFindNode->pLeft; 298 else if(nData > pFindNode->nData) 299 pFindNode = pFindNode->pRight; 300 else 301 return pFindNode->nData; 302 } 303 304 return -1; 305 } 306 307 AVLNode* AVLTree::RotateLeft(AVLNode* pNode)//左单 308 { 309 AVLNode* pLeftChild; 310 311 pLeftChild = pNode->pLeft; 312 pNode->pLeft = pLeftChild->pRight; 313 pLeftChild->pRight = pNode; 314 315 pLeftChild->pParent = pNode->pParent; 316 pNode->pParent = pLeftChild; 317 318 if(pNode->pLeft) 319 pNode->pLeft->pParent = pNode; 320 321 // 结点的位置改变,节点高度要重新计算 322 pNode->nHeight = Max(Height(pNode->pLeft), Height(pNode->pRight)) + 1; 323 pLeftChild->nHeight = Max(Height(pLeftChild->pLeft), pNode->nHeight) + 1; 324 325 return pLeftChild; 326 } 327 328 AVLNode* AVLTree::RotateRight(AVLNode* pNode)//右单 329 { 330 AVLNode* pRightChild; 331 332 pRightChild = pNode->pRight; 333 pNode->pRight = pRightChild->pLeft; 334 pRightChild->pLeft = pNode; 335 336 pRightChild->pParent = pNode->pParent; 337 pNode->pParent = pRightChild; 338 339 if(pNode->pRight) 340 pNode->pRight->pParent = pNode; 341 342 // 结点的位置改变,节点高度要重新计算 343 pNode->nHeight = Max(Height(pNode->pLeft), Height(pNode->pRight)) + 1; 344 pRightChild->nHeight = Max(Height(pRightChild->pRight), pNode->nHeight) + 1; 345 346 return pRightChild; 347 } 348 349 AVLNode* AVLTree::RotateLeftRight(AVLNode* pNode)//左双 350 { 351 pNode->pLeft = RotateRight(pNode->pLeft); 352 353 return RotateLeft(pNode); 354 } 355 356 AVLNode* AVLTree::RotateRightLeft(AVLNode* pNode)//右双 357 { 358 pNode->pRight = RotateLeft(pNode->pRight); 359 360 return RotateRight(pNode); 361 } 362 363 // 后序遍历树以删除树 364 void AVLTree::DeleteTree(AVLNode** ppRoot) 365 { 366 if (NULL == ppRoot || NULL == *ppRoot) 367 return; 368 369 DeleteTree(&((*ppRoot)->pLeft)); 370 DeleteTree(&((*ppRoot)->pRight)); 371 delete *ppRoot; 372 *ppRoot = NULL; 373 } 374 375 int AVLTree::GetNodeCount() const 376 { 377 return nNodeCount; 378 } 379 380 void AVLTree::Display() const 381 { 382 PrintTree(this->pRoot); 383 } 384 385 void AVLTree::PrintTree(AVLNode* pNode) const 386 { 387 if (NULL == pRoot) 388 return; 389 390 if (NULL == pNode) 391 { 392 return; 393 } 394 395 static int n = 0; 396 397 if(pNode == pRoot) 398 { 399 std::cout << "[" << ++n << "]nData = " << pNode->nData << ",nParentData= 0 ,"; 400 401 if(pNode->pLeft) 402 std::cout << "nLeftData= " << pNode->pLeft->nData << " ,"; 403 if(pNode->pRight) 404 std::cout << "nRightData= " << pNode->pRight->nData << " ,"; 405 406 std::cout << "nHeight = " << pNode->nHeight << std::endl; 407 } 408 else 409 { 410 std::cout << "[" << ++n << "]nData = " << pNode->nData << ",nParentData= " << pNode->pParent->nData << " ,"; 411 412 if(pNode->pLeft) 413 std::cout << "nLeftData= " << pNode->pLeft->nData << " ,"; 414 if(pNode->pRight) 415 std::cout << "nRightData= " << pNode->pRight->nData << " ,"; 416 417 std::cout << "nHeight = " << pNode->nHeight << std::endl; 418 } 419 PrintTree(pNode->pLeft); 420 PrintTree(pNode->pRight); 421 } 422 #endif //__AVLTREE_H__
将上面的文件复制保存成文件AVLTree.h。然后将下面的复制到Test.cpp文件中。Test.cpp文件是简单的测试案例。
1 #include "AVLTree.h" 2 #include <iostream> 3 #include <exception> 4 5 int main() 6 { 7 try 8 { 9 AVLTree avl; 10 for(int i = 1; i < 10; i++) 11 { 12 avl.Insert(i); 13 } 14 15 avl.Delete(4); 16 avl.Display(); 17 } 18 catch (std::exception& e) 19 { 20 std::cout << e.what() << std::endl; 21 } 22 }
输入g++ -o Test Test.cpp然后回车就可以编译运行了。运行结果如下：
1 [kiven@localhost Test]$ g++ -o Test Test.cpp 2 [kiven@localhost Test]$ ./Test 3 [1]nData = 3,nParentData= 0 ,nLeftData= 2 ,nRightData= 6 ,nHeight = 3 4 [2]nData = 2,nParentData= 3 ,nLeftData= 1 ,nHeight = 1 5 [3]nData = 1,nParentData= 2 ,nHeight = 0 6 [4]nData = 6,nParentData= 3 ,nLeftData= 5 ,nRightData= 8 ,nHeight = 2 7 [5]nData = 5,nParentData= 6 ,nHeight = 0 8 [6]nData = 8,nParentData= 6 ,nLeftData= 7 ,nRightData= 9 ,nHeight = 1 9 [7]nData = 7,nParentData= 8 ,nHeight = 0 10 [8]nData = 9,nParentData= 8 ,nHeight = 0 11 [kiven@localhost Test]$
我上面实现的版本也只是为了研究AVL树的属性而做的实验版本，节点中的数据也直接使用了整形，而在实际使用时需要实现模板的版本，或者用万能的指针。但是指针的方式显然没有模板好。我自己也实现了一个模板的版本，也是比较粗糙的，代码如下：
1 #ifndef __AVLTREE_H__ 2 #define __AVLTREE_H__ 3 4 #include <iostream> 5 6 template <typename T> 7 class AVLNode 8 { 9 public: 10 T data; 11 AVLNode<T>* pLeft; 12 AVLNode<T>* pRight; 13 AVLNode<T>* pParent; 14 int nHeight; 15 }; 16 17 template <typename T> 18 class AVLTree 19 { 20 public: 21 AVLTree() : pRoot(NULL), nNodeCount(0){} 22 virtual ~AVLTree(){ DeleteTree(&pRoot); } 23 public: 24 virtual AVLTree<T>& Insert(T data); 25 virtual AVLTree<T>& Delete(T data); 26 virtual int Find(T data) const; 27 virtual int GetNodeCount() const; 28 virtual void Display() const; 29 30 private: 31 int Max(int a, int b) const; 32 int Height(const AVLNode<T>* pNode) const; 33 AVLNode<T>* CreateNode(T data); 34 AVLNode<T>* DeleteNode(T data, AVLNode<T>* pNode); 35 AVLNode<T>* BalanceAdjust(AVLNode<T>* pNode); 36 AVLNode<T>* RotateLeft(AVLNode<T>* pNode); 37 AVLNode<T>* RotateRight(AVLNode<T>* pNode); 38 AVLNode<T>* RotateLeftRight(AVLNode<T>* pNode); 39 AVLNode<T>* RotateRightLeft(AVLNode<T>* pNode); 40 void DeleteTree(AVLNode<T>** ppRoot); 41 void PrintTree(AVLNode<T>* pNode) const; 42 43 AVLTree(const AVLTree<T>&) {} 44 AVLTree<T>& operator=(const AVLTree<T>&) {} 45 46 private: 47 AVLNode<T>* pRoot; 48 int nNodeCount; 49 }; 50 51 template <typename T> 52 int AVLTree<T>::Max(int a, int b) const 53 { 54 return (a > b ? a : b); 55 } 56 57 template <typename T> 58 int AVLTree<T>::Height(const AVLNode<T>* pNode) const 59 { 60 if (NULL == pNode) 61 return -1; 62 63 return pNode->nHeight; 64 } 65 66 template <typename T> 67 AVLTree<T>& AVLTree<T>::Insert(T data) 68 { 69 if(pRoot == NULL) 70 { 71 pRoot = CreateNode(data); 72 73 return *this; 74 } 75 76 AVLNode<T>* pInsertNode = pRoot; 77 78 while(pInsertNode != NULL) 79 { 80 if(data < pInsertNode->data) 81 { 82 if(pInsertNode->pLeft == NULL) 83 { 84 pInsertNode->pLeft = CreateNode(data); 85 pInsertNode->pLeft->pParent = pInsertNode; 86 87 pRoot = BalanceAdjust(pInsertNode->pLeft); 88 break; 89 } 90 91 pInsertNode = pInsertNode->pLeft; 92 } 93 else if(data > pInsertNode->data) 94 { 95 if(pInsertNode->pRight == NULL) 96 { 97 pInsertNode->pRight = CreateNode(data); 98 pInsertNode->pRight->pParent = pInsertNode; 99 100 pRoot = BalanceAdjust(pInsertNode->pRight); 101 break; 102 } 103 104 pInsertNode = pInsertNode->pRight; 105 } 106 else 107 { 108 return *this; 109 } 110 } 111 112 return *this; 113 } 114 115 template <typename T> 116 AVLTree<T>& AVLTree<T>::Delete(T data) 117 { 118 //std::cout << "Delete nData = " << nData << std::endl; 119 //std::cout << "pNode->nData = " << pNode->nData << std::endl; 120 //std::cout << "pPNode->nData = " << pPNode->nData << std::endl; 121 122 AVLNode<T>* pCurNode = pRoot; 123 124 while(pCurNode != NULL) 125 { 126 if(data > pCurNode->data) 127 { 128 pCurNode = pCurNode->pRight; 129 } 130 else if(data < pCurNode->data) 131 { 132 pCurNode = pCurNode->pLeft; 133 } 134 else 135 { 136 pRoot = DeleteNode(data, pCurNode); 137 break; 138 } 139 } 140 141 142 if(pCurNode == NULL) 143 std::cout << "没有找到元素 nData = " << data << std::endl; 144 //int x; 145 //std::cin >> x; 146 147 return *this;//没有找到要删除的元素 148 } 149 150 template <typename T> 151 AVLNode<T>* AVLTree<T>::DeleteNode(T data, AVLNode<T>* pNode) 152 { 153 nNodeCount--; 154 155 if(pNode->pLeft && pNode->pRight)//删除节点有左右子树 156 { 157 AVLNode<T>* pLMaxNode = pNode->pLeft;//删除节点左子树中最大的节点 158 AVLNode<T>* pLMaxPNode = pNode;//删除节点左子树中最大节点的父节点 159 160 //将删除节点左孩子的最大节点替换删除节点,然后删除该节点 161 if(pLMaxNode->pRight == NULL) 162 { 163 pNode->data = pLMaxNode->data; 164 pNode->pLeft = pLMaxNode->pLeft; 165 166 if(pLMaxNode->pLeft != NULL) 167 pLMaxNode->pLeft->pParent = pNode; 168 } 169 else 170 { 171 while(pLMaxNode->pRight) 172 { 173 pLMaxPNode = pLMaxNode; 174 pLMaxNode = pLMaxNode->pRight; 175 } 176 pNode->data = pLMaxNode->data; 177 178 if(pLMaxNode == pLMaxPNode->pRight)//将替换后的删除节点删除 179 pLMaxPNode->pRight = pLMaxNode->pLeft; 180 else if(pLMaxNode == pLMaxPNode->pLeft) 181 pLMaxPNode->pLeft = NULL; 182 } 183 184 delete pLMaxNode; 185 186 return BalanceAdjust(pLMaxPNode); 187 } 188 else if(pNode->pLeft)//删除节点只有左子树 189 { 190 AVLNode<T>* pLeft = pNode->pLeft; 191 192 pNode->data = pLeft->data; 193 194 pNode->pLeft = pLeft->pLeft; 195 if (pLeft->pLeft != NULL) 196 pLeft->pLeft->pParent = pNode; 197 198 pNode->pRight = pLeft->pRight; 199 if (pLeft->pRight != NULL) 200 pLeft->pRight->pParent = pNode; 201 202 delete pLeft; 203 204 return BalanceAdjust(pNode); 205 } 206 else if(pNode->pRight)//删除节点只有右子树 207 { 208 AVLNode<T>* pRight = pNode->pRight; 209 210 pNode->data = pRight->data; 211 212 pNode->pLeft = pRight->pLeft; 213 if (pRight->pLeft != NULL) 214 pRight->pLeft->pParent = pNode; 215 216 pNode->pRight = pRight->pRight; 217 if (pRight->pRight != NULL) 218 pRight->pRight->pParent = pNode; 219 220 delete pRight; 221 222 return BalanceAdjust(pNode); 223 } 224 else//删除节点没有子树 225 { 226 AVLNode<T>* pPNode = pNode->pParent; 227 228 if(pPNode->pLeft == pNode) 229 pPNode->pLeft = NULL; 230 else if(pPNode->pRight == pNode) 231 pPNode->pRight = NULL; 232 233 delete pNode; 234 235 return BalanceAdjust(pPNode); 236 } 237 } 238 239 template <typename T> 240 AVLNode<T>* AVLTree<T>::BalanceAdjust(AVLNode<T>* pNode) 241 { 242 AVLNode<T>* pRoot; 243 AVLNode<T>* pPNode; 244 245 while(pNode != NULL)//删除节点的子节点进行平衡 246 { 247 pPNode = pNode->pParent; 248 249 bool bIsLeft = false; 250 if(pPNode != NULL && pNode == pPNode->pLeft) 251 bIsLeft = true; 252 253 pNode->nHeight = Max(Height(pNode->pLeft), Height(pNode->pRight)) + 1; 254 255 if (Height(pNode->pLeft) - Height(pNode->pRight) == 2) // AVL树不平衡 执行LL型或者LR型旋转 256 { 257 if (Height(pNode->pLeft->pLeft) - Height(pNode->pLeft->pRight) == -1) 258 pNode = RotateLeftRight(pNode); 259 else 260 pNode = RotateLeft(pNode); 261 262 if(pPNode != NULL && bIsLeft) 263 pPNode->pLeft = pNode; 264 else if(pPNode != NULL) 265 pPNode->pRight = pNode; 266 } 267 else if(Height(pNode->pLeft) - Height(pNode->pRight) == -2) // AVL树不平衡 执行RR型或者RL型旋转 268 { 269 if (Height(pNode->pRight->pLeft) - Height(pNode->pRight->pRight) == 1) 270 pNode = RotateRightLeft(pNode); 271 else 272 pNode = RotateRight(pNode); 273 274 if (pPNode != NULL && bIsLeft) 275 pPNode->pLeft = pNode; 276 else if(pPNode != NULL) 277 pPNode->pRight = pNode; 278 } 279 280 pRoot = pNode; 281 pNode = pPNode; 282 } 283 284 return pRoot; 285 } 286 287 template <typename T> 288 AVLNode<T>* AVLTree<T>::CreateNode(T data) 289 { 290 nNodeCount++; 291 292 AVLNode<T>* pNewNode = new AVLNode<T>(); 293 pNewNode->data = data; 294 pNewNode->nHeight = 0; 295 pNewNode->pLeft = pNewNode->pRight = NULL; 296 297 return pNewNode; 298 } 299 300 template <typename T> 301 int AVLTree<T>::Find(T data) const 302 { 303 AVLNode<T>* pFindNode = pRoot; 304 while(pFindNode) 305 { 306 if(data < pFindNode->data) 307 pFindNode = pFindNode->pLeft; 308 else if(data > pFindNode->data) 309 pFindNode = pFindNode->pRight; 310 else 311 return 1;//pFindNode->data; 312 } 313 314 return 0; 315 } 316 317 template <typename T> 318 AVLNode<T>* AVLTree<T>::RotateLeft(AVLNode<T>* pNode)//左单 319 { 320 AVLNode<T>* pLeftChild; 321 322 pLeftChild = pNode->pLeft; 323 pNode->pLeft = pLeftChild->pRight; 324 pLeftChild->pRight = pNode; 325 326 pLeftChild->pParent = pNode->pParent; 327 pNode->pParent = pLeftChild; 328 329 if(pNode->pLeft) 330 pNode->pLeft->pParent = pNode; 331 332 // 结点的位置改变,节点高度要重新计算 333 pNode->nHeight = Max(Height(pNode->pLeft), Height(pNode->pRight)) + 1; 334 pLeftChild->nHeight = Max(Height(pLeftChild->pLeft), pNode->nHeight) + 1; 335 336 return pLeftChild; 337 } 338 339 template <typename T> 340 AVLNode<T>* AVLTree<T>::RotateRight(AVLNode<T>* pNode)//右单 341 { 342 AVLNode<T>* pRightChild; 343 344 pRightChild = pNode->pRight; 345 pNode->pRight = pRightChild->pLeft; 346 pRightChild->pLeft = pNode; 347 348 pRightChild->pParent = pNode->pParent; 349 pNode->pParent = pRightChild; 350 351 if(pNode->pRight) 352 pNode->pRight->pParent = pNode; 353 354 // 结点的位置改变,节点高度要重新计算 355 pNode->nHeight = Max(Height(pNode->pLeft), Height(pNode->pRight)) + 1; 356 pRightChild->nHeight = Max(Height(pRightChild->pRight), pNode->nHeight) + 1; 357 358 return pRightChild; 359 } 360 361 template <typename T> 362 AVLNode<T>* AVLTree<T>::RotateLeftRight(AVLNode<T>* pNode)//左双 363 { 364 pNode->pLeft = RotateRight(pNode->pLeft); 365 366 return RotateLeft(pNode); 367 } 368 369 template <typename T> 370 AVLNode<T>* AVLTree<T>::RotateRightLeft(AVLNode<T>* pNode)//右双 371 { 372 pNode->pRight = RotateLeft(pNode->pRight); 373 374 return RotateRight(pNode); 375 } 376 377 // 后序遍历树以删除树 378 template <typename T> 379 void AVLTree<T>::DeleteTree(AVLNode<T>** ppRoot) 380 { 381 if (NULL == ppRoot || NULL == *ppRoot) 382 return; 383 384 DeleteTree(&((*ppRoot)->pLeft)); 385 DeleteTree(&((*ppRoot)->pRight)); 386 delete ppRoot; 387 *ppRoot = NULL; 388 389 //std::cout << "AVLTree delete completed !" << std::endl; 390 } 391 392 template <typename T> 393 int AVLTree<T>::GetNodeCount() const 394 { 395 return nNodeCount; 396 } 397 398 template <typename T> 399 void AVLTree<T>::Display() const 400 { 401 PrintTree(this->pRoot); 402 } 403 404 template <typename T> 405 void AVLTree<T>::PrintTree(AVLNode<T>* pNode) const 406 { 407 if (NULL == pRoot) 408 return; 409 410 if (NULL == pNode) 411 { 412 return; 413 } 414 415 static int n = 0; 416 417 if(pNode == pRoot) 418 { 419 std::cout << "[" << ++n << "]nData = " << pNode->data << ",nParentData= 0 ,"; 420 421 if(pNode->pLeft) 422 std::cout << "nLeftData= " << pNode->pLeft->data << " ,"; 423 if(pNode->pRight) 424 std::cout << "nRightData= " << pNode->pRight->data << " ,"; 425 426 std::cout << "nHeight = " << pNode->nHeight << std::endl; 427 } 428 else 429 { 430 std::cout << "[" << ++n << "]nData = " << pNode->data << ",nParentData= " << pNode->pParent->data << " ,"; 431 432 if(pNode->pLeft) 433 std::cout << "nLeftData= " << pNode->pLeft->data << " ,"; 434 if(pNode->pRight) 435 std::cout << "nRightData= " << pNode->pRight->data << " ,"; 436 437 std::cout << "nHeight = " << pNode->nHeight << std::endl; 438 } 439 PrintTree(pNode->pLeft); 440 PrintTree(pNode->pRight); 441 } 442 #endif //__AVLTREE_H__
PS：编译和测试的方式与上面不是模板的版本一样。AVL Tree是我刚学C++不久的时候写的，存在问题在所难免。现在已经没有时间来进一步研究这个代码，放在这里做个备份，说不定什么时候就能用到呢。
完美之道，不在于无可增加，而在于无可减少。
