详解以后再补充。。。
代码
这是Qt Creator创建的工程
其余代码从此处获取：https://github.com/Duacai/Data-Structure-and-Algorithms/tree/master/BSTree
AVLTree.h
1 #ifndef AVLTREE_H 2 #define AVLTREE_H 3 4 #include <iostream> 5 #include <queue> 6 #include <iomanip> 7 8 #include "Exception.h" 9 10 using namespace std; 11 12 namespace LinWeiJie_lib 13 { 14 15 template <typename T> 16 class AVLTreeNode 17 { 18 public: 19 T key; 20 uint16_t height; 21 AVLTreeNode* left; 22 AVLTreeNode* right; 23 24 AVLTreeNode(T v, AVLTreeNode* l, AVLTreeNode* r) : 25 key(v), height(0), left(l), right(r) {} 26 }; 27 28 template <typename T> 29 class AVLTree 30 { 31 private: 32 AVLTreeNode<T>* mRoot; 33 uint64_t mCount; 34 35 void preOrder(AVLTreeNode<T>* tree) const; 36 void inOrder(AVLTreeNode<T>* tree) const; 37 void postOrder(AVLTreeNode<T>* tree) const; 38 39 void levelOrder(AVLTreeNode<T>* tree) const; 40 41 AVLTreeNode<T>* search(AVLTreeNode<T>* tree, T key) const; 42 AVLTreeNode<T>* iterativeSearch(AVLTreeNode<T>* tree, T key) const; 43 44 AVLTreeNode<T>* minimum(AVLTreeNode<T>* tree) const; 45 AVLTreeNode<T>* maximum(AVLTreeNode<T>* tree) const; 46 47 AVLTreeNode<T>* llRotation(AVLTreeNode<T>* tree) const; 48 AVLTreeNode<T>* rrRotation(AVLTreeNode<T>* tree) const; 49 AVLTreeNode<T>* lrRotation(AVLTreeNode<T>* tree) const; 50 AVLTreeNode<T>* rlRotation(AVLTreeNode<T>* tree) const; 51 52 AVLTreeNode<T>* insert(AVLTreeNode<T>* &tree, T key); 53 AVLTreeNode<T>* remove(AVLTreeNode<T>* &tree, AVLTreeNode<T>* del); 54 55 void printGraph(const void* mRoot, uint16_t m_keyStrLen) const; 56 void printTree(AVLTreeNode<T> const* const tree, bool firstNode) const; 57 58 void destroy(AVLTreeNode<T>* &tree) const; 59 uint16_t height(AVLTreeNode<T>* tree) const; 60 61 public: 62 AVLTree(); 63 virtual ~AVLTree(); 64 65 void preOrder() const; 66 void inOrder() const; 67 void postOrder() const; 68 69 void levelOrder() const; 70 71 AVLTreeNode<T>* search(T key) const; // 递归版 72 AVLTreeNode<T>* iterativeSearch(T key) const; // 非递归版 73 74 T minimum() const; 75 T maximum() const; 76 77 void insert(T key); 78 bool remove(T key); 79 80 void print() const; // 打印结点关系，谁是谁的结点 81 void printGraph(uint16_t keyStrLen) const; // 以图形树方式打印关系 82 void printTree() const; 83 84 void destroy(); 85 uint16_t height() const; 86 87 uint64_t getCount() const; 88 bool rootIsNullptr() const; 89 90 T getRootKey() const; 91 }; 92 93 template <typename T> 94 AVLTree<T>::AVLTree() : mRoot(nullptr), mCount(0) 95 { 96 } 97 98 template <typename T> 99 void AVLTree<T>::preOrder(AVLTreeNode<T>* tree) const // 前序遍历 100 { 101 if ( tree != nullptr ) 102 { 103 cout << tree->key << " " << flush; 104 preOrder(tree->left); 105 preOrder(tree->right); 106 } 107 } 108 109 template <typename T> 110 void AVLTree<T>::preOrder() const 111 { 112 preOrder(mRoot); 113 cout << endl; 114 } 115 116 template <typename T> 117 void AVLTree<T>::inOrder(AVLTreeNode<T>* tree) const // 中序遍历 118 { 119 if ( tree != nullptr ) 120 { 121 inOrder(tree->left); 122 cout << tree->key << " " << flush; 123 inOrder(tree->right); 124 } 125 } 126 127 template <typename T> 128 void AVLTree<T>::inOrder() const 129 { 130 inOrder(mRoot); 131 cout << endl; 132 } 133 134 template <typename T> 135 void AVLTree<T>::postOrder(AVLTreeNode<T>* tree) const // 后续遍历 136 { 137 if ( tree != nullptr ) 138 { 139 postOrder(tree->left); 140 postOrder(tree->right); 141 cout << tree->key << " " << flush; 142 } 143 } 144 145 template <typename T> 146 void AVLTree<T>::postOrder() const 147 { 148 postOrder(mRoot); 149 cout << endl; 150 } 151 152 template <typename T> 153 void AVLTree<T>::levelOrder(AVLTreeNode<T>* tree) const // 广度优先 154 { 155 if ( tree != nullptr ) 156 { 157 queue<AVLTreeNode<T>*> tmp; 158 tmp.push(tree); 159 160 while( tmp.size() > 0 ) 161 { 162 AVLTreeNode<T>* t = tmp.front(); 163 164 if ( t->left != nullptr ) 165 tmp.push(t->left); 166 167 if ( t->right != nullptr ) 168 tmp.push(t->right); 169 170 tmp.pop(); 171 172 cout << t->key << " " << flush; 173 } 174 } 175 } 176 177 template <typename T> 178 void AVLTree<T>::levelOrder() const 179 { 180 levelOrder(mRoot); 181 cout << endl; 182 } 183 184 template <typename T> 185 AVLTreeNode<T>* AVLTree<T>::search(AVLTreeNode<T>* tree, T key) const // 递归版搜索 186 { 187 if ( (tree == nullptr) || (tree->key == key) ) 188 return tree; 189 190 if ( key < tree->key ) 191 return search(tree->left, key); 192 else 193 return search(tree->right, key); 194 } 195 196 template <typename T> 197 AVLTreeNode<T>* AVLTree<T>::search(T key) const 198 { 199 return search(mRoot, key); 200 } 201 202 template <typename T> 203 AVLTreeNode<T>* AVLTree<T>::iterativeSearch(AVLTreeNode<T>* tree, T key) const // 非递归版搜索 204 { 205 while ( (tree != nullptr) && (tree->key != key) ) 206 { 207 if ( key < tree->key ) 208 tree = tree->left; 209 else 210 tree = tree->right; 211 } 212 213 return tree; 214 } 215 216 template <typename T> 217 AVLTreeNode<T>* AVLTree<T>::iterativeSearch(T key) const 218 { 219 return iterativeSearch(mRoot, key); 220 } 221 222 template <typename T> 223 AVLTreeNode<T>* AVLTree<T>::minimum(AVLTreeNode<T>* tree) const 224 { 225 if ( tree == nullptr ) 226 return nullptr; 227 228 while ( tree->left != nullptr ) 229 tree = tree->left; 230 231 return tree; 232 } 233 234 template <typename T> 235 T AVLTree<T>::minimum() const 236 { 237 AVLTreeNode<T> *ret = minimum(mRoot); 238 if ( ret == nullptr ) 239 THROW_EXCEPTION(EmptyTreeException, "The tree is empty ..."); 240 241 return ret->key; 242 } 243 244 template <typename T> 245 AVLTreeNode<T>* AVLTree<T>::maximum(AVLTreeNode<T>* tree) const 246 { 247 if ( tree == nullptr ) 248 return nullptr; 249 250 while ( tree->right != nullptr ) 251 tree = tree->right; 252 253 return tree; 254 } 255 256 template <typename T> 257 T AVLTree<T>::maximum() const 258 { 259 AVLTreeNode<T> *ret = maximum(mRoot); 260 if ( ret == nullptr ) 261 THROW_EXCEPTION(EmptyTreeException, "The tree is empty ..."); 262 263 return ret->key; 264 } 265 266 template <typename T> 267 AVLTreeNode<T>* AVLTree<T>::llRotation(AVLTreeNode<T>* tree) const // 左单旋，旋转前左孩子有孩子右孩子没有 268 { 269 AVLTreeNode<T>* ret; 270 271 ret = tree->left; 272 tree->left = tree->left->right; 273 ret->right = tree; 274 275 tree->height = max( height(tree->left), height(tree->right) ) + 1; 276 ret->height = max( height(ret->left), height(ret->right) ) + 1; 277 278 return ret; 279 } 280 281 template <typename T> 282 AVLTreeNode<T>* AVLTree<T>::rrRotation(AVLTreeNode<T>* tree) const // 右单旋，旋转前右孩子有孩子左孩子没有 283 { 284 AVLTreeNode<T>* ret; 285 286 ret = tree->right; 287 tree->right = tree->right->left; 288 ret->left = tree; 289 290 tree->height = max( height(tree->left), height(tree->right) ) + 1; 291 ret->height = max ( height(ret->left), height(ret->right) ) + 1; 292 293 return ret; 294 } 295 296 template <typename T> 297 AVLTreeNode<T>* AVLTree<T>::lrRotation(AVLTreeNode<T>* tree) const // 左右双旋，先右旋，后左旋；tree左孩子的右孩子有后代，tree右孩子没有后代 298 { 299 tree->left = rrRotation(tree->left); // 确保多出的后代在左子树的左子树上 300 301 return llRotation(tree); 302 } 303 304 template <typename T> 305 AVLTreeNode<T>* AVLTree<T>::rlRotation(AVLTreeNode<T>* tree) const // 右左双旋，先左旋，后右旋；tree右孩子的左孩子有后代，tree左孩子没有后代 306 { 307 tree->right = llRotation(tree->right); // 确保多出的后代在右子树的右子树上 308 309 return rrRotation(tree); 310 } 311 312 template <typename T> 313 AVLTreeNode<T>* AVLTree<T>::insert(AVLTreeNode<T>* &tree, T key) 314 { 315 if ( tree == nullptr ) // 创建新结点，下面的两个else if会最终递归进入此if创建新结点 316 { 317 tree = new AVLTreeNode<T>(key, nullptr, nullptr); 318 ++mCount; 319 } 320 else if ( key < tree->key ) // 将新结点交给左子树负责插入 321 { 322 tree->left = insert(tree->left, key); // 注意更新左结点，因为它可能旋转或是新创建的结点 323 324 if ( height(tree->left) - height(tree->right) == 2) // 如果插入的左子树超重 325 { 326 if ( key < tree->left->key ) 327 tree = llRotation(tree); // 如果插入的位置是左孩子的左孩子，左单旋 328 else 329 tree = lrRotation(tree); // 否则插入的位置是左孩子的右孩子，右单旋；最外层的else保证不会有重复值 330 } 331 } 332 else if ( key > tree->key ) // 将新结点交给右子树负责插入 333 { 334 tree->right = insert(tree->right, key); 335 336 if ( height(tree->right) - height(tree->left) == 2 ) 337 { 338 if ( key > tree->right->key ) 339 tree = rrRotation(tree); 340 else 341 tree = rlRotation(tree); 342 } 343 } 344 else // 结点重复 345 THROW_EXCEPTION(DuplicateDataException, "Can't create duplicate nodes ..."); 346 347 tree->height = max(height(tree->left), height(tree->right)) + 1; 348 349 return tree; 350 } 351 352 template <typename T> 353 void AVLTree<T>::insert(T key) 354 { 355 insert(mRoot, key); 356 } 357 358 template <typename T> 359 AVLTreeNode<T>* AVLTree<T>::remove(AVLTreeNode<T>* &tree, AVLTreeNode<T>* del) 360 { 361 if ( (tree == nullptr) || (del == nullptr) ) 362 return nullptr; 363 364 if ( del->key < tree->key ) // 交给左子树删除，最终进入最外层else 365 { 366 tree->left = remove(tree->left, del); // 更新可能旋转的结点 367 368 if ( height(tree->right) - height(tree->left) == 2 ) // 删除左子树结点后如果右子树超重 369 { 370 if ( height(tree->right->left) > height(tree->right->right) ) 371 tree = rlRotation(tree); // 右左重 372 else 373 tree = rrRotation(tree); // 右右重 374 } 375 } 376 else if ( del->key > tree->key ) // 交给右子树删除，最终进入最外层else 377 { 378 tree->right = remove(tree->right, del); 379 380 if ( height(tree->left) - height(tree->right) == 2 ) 381 { 382 if ( height(tree->left->right) - height(tree->left->left) == 2 ) 383 tree = lrRotation(tree); 384 else 385 tree = llRotation(tree); 386 } 387 } 388 else // 找到删除节点 389 { 390 if ( (tree->left != nullptr) && (tree->right != nullptr) ) // 删除点有两个孩子，在较重的分支找替换者 391 { 392 if ( height(tree->left) > height(tree->right) ) // 左孩子重 393 { 394 AVLTreeNode<T>* lmax = maximum(tree->left); // 查找左边最大者用于替换；如果用右边的最小者，当右边没有孩子就会删除自身导致不平衡 395 tree->key = lmax->key; // 采用值拷贝的方式删除，否则你还要处理子结点 396 tree->left = remove(tree->left, lmax); // 更新可能旋转的结点 397 } 398 else // 右孩子重 399 { 400 AVLTreeNode<T>* rmin = minimum(tree->right); 401 tree->key = rmin->key; 402 tree->right = remove(tree->right, rmin); 403 } 404 } 405 else // 删除点孩子不足两个，直接删除并用孩子替换 406 { 407 AVLTreeNode<T>* tmp = tree; 408 tree = (tree->left != nullptr) ? tree->left : tree->right; // 替换删除结点 409 delete tmp; 410 --mCount; 411 } 412 } 413 414 if ( tree != nullptr ) 415 tree->height = max(height(tree->left), height(tree->right)) + 1; 416 417 return tree; 418 } 419 420 template <typename T> 421 bool AVLTree<T>::remove(T key) 422 { 423 bool ret = false; 424 AVLTreeNode<T>* tmp; 425 426 if ( (tmp = search(mRoot, key)) != nullptr ) // 查找并删除节点 427 { 428 mRoot = remove(mRoot, tmp); // remove()的返回值用于不能修改参数的编程语言，函数左边的参数是左值mRoot的引用 429 ret = true; 430 } 431 432 return ret; 433 } 434 435 template <typename T> 436 void AVLTree<T>::printGraph(const void* Root, uint16_t m_keyStrLen) const 437 { 438 AVLTreeNode<T>const* node = static_cast<AVLTreeNode<T>const*>(Root); 439 if ( node == nullptr ) 440 return; 441 442 uint16_t height = node->height; // 要打印的树总高度 443 uint16_t layer = 1; // 当前层，root为第一层 444 uint64_t i, index; 445 uint64_t keyStrLen = m_keyStrLen; // i: 循环变量；index: 当前层最大结点数；keyStrLen: 结点输出占用字符宽度 446 queue<AVLTreeNode<T>const *> q; // 记录每层的所有节点，包括nullptr 447 q.push(node); 448 cout << "输出树形关系图！！！" << endl; 449 while ( true ) 450 { 451 cout << layer << "\t" << flush; // 输出当前层号和当前层满节点数 452 AVLTreeNode<T> const* tmp = nullptr; // 取出结点变量 453 index = 1ull<<(layer-1); 454 while ( index-- ) 455 { 456 tmp = q.front(); // 取出结点 457 q.pop(); 458 for ( i=0; i<((1ull<<(height-layer))-1ull)*keyStrLen; ++i ) // 结点前的填充 459 cout << " "; 460 cout << flush; 461 462 if ( tmp != nullptr ) // 打印有效结点 463 { 464 cout << right << setw(keyStrLen) << setfill('0') << tmp->key << flush; 465 466 if ( tmp->left != nullptr ) // 加入左结点 467 q.push(tmp->left); 468 else 469 q.push(nullptr); 470 471 if ( tmp->right != nullptr ) // 加入右节点 472 q.push(tmp->right); 473 else 474 q.push(nullptr); 475 } 476 else // 打印无效结点 477 { 478 for ( i=0; i<keyStrLen; ++i ) 479 cout << "#"; 480 cout << flush; 481 482 q.push(nullptr); // 如果结点是空的则为其加入两个空子结点 483 q.push(nullptr); 484 } 485 486 for ( i=0; i<((1ull<<(height-layer))-1ull)*keyStrLen; ++i ) // 结点后的填充 487 cout << " "; 488 cout << flush; 489 490 if ( q.size() != (1ull<<(layer)) ) 491 for ( i=0; i<keyStrLen; ++i ) // 两节点间填充，因为父节点位于两节点的中间上面，而不是其中一个的上面 492 cout << " "; 493 else 494 cout << "\t"; 495 cout << flush; 496 } 497 cout << layer << endl; // 输出一层换行 498 499 if ( ++layer > height ) // while循环出口，当前层大于总高度时退出 500 break; 501 } 502 } 503 504 template <typename T> 505 void AVLTree<T>::printGraph(uint16_t keyStrLen) const 506 { 507 if ( mRoot == nullptr ) 508 return; 509 510 printGraph(mRoot, keyStrLen); 511 } 512 513 template <typename T> 514 void AVLTree<T>::printTree(AVLTreeNode<T> const* const tree, bool firstNode) const 515 { 516 if ( tree==nullptr ) 517 return; 518 519 bool static outTag[64] = {false}; // size = max layer limit; 520 uint8_t static layer = 0; 521 uint8_t i; 522 ++layer; 523 524 if ( layer >= 2 ) 525 { 526 for (i=2; i<layer; ++i ) 527 if ( outTag[i] ) 528 cout << "| "; 529 else 530 cout << " "; 531 cout << "+-------" << flush; 532 } 533 cout << tree->key << endl; 534 535 for ( i=2-1; i>0; --i) // 从右往左输出结点，即先打印最右边结点，其次次右边的结点；此循环不输出最左边的结点 536 { 537 if ( (tree->left+i) != nullptr ) // 注意树的子结点指针必须是从左往右依次排列，中间不能有其它变量（left_1,left_2,left_3...left_n） 538 { // 如果你的子结点数量不定，一定要把后面的首个指针设为nullptr 539 outTag[layer] = !firstNode; 540 printTree(tree->right, false); 541 } 542 } 543 if ( tree->left != nullptr ) // 输出最左边的结点 544 { 545 printTree(tree->left, true); 546 outTag[layer] = firstNode; 547 } 548 549 --layer; 550 } 551 552 template <typename T> 553 void AVLTree<T>::printTree() const 554 { 555 printTree(mRoot, true); // 右边参数此时无意义 556 } 557 558 template <typename T> 559 void AVLTree<T>::destroy(AVLTreeNode<T>* &tree) const 560 { 561 if ( tree == nullptr ) 562 return; 563 564 if ( tree->left != nullptr ) 565 destroy(tree->left); 566 else 567 destroy(tree->right); 568 569 delete tree; 570 } 571 572 template <typename T> 573 void AVLTree<T>::destroy() 574 { 575 destroy(mRoot); 576 mRoot = nullptr; 577 mCount = 0; 578 } 579 580 template <typename T> 581 uint16_t AVLTree<T>::height(AVLTreeNode<T>* tree) const 582 { 583 if ( tree != nullptr ) 584 return tree->height; 585 586 return 0; 587 } 588 589 template <typename T> 590 uint16_t AVLTree<T>::height() const 591 { 592 return height(mRoot); 593 } 594 595 template <typename T> 596 uint64_t AVLTree<T>::getCount() const 597 { 598 return mCount; 599 } 600 601 template <typename T> 602 bool AVLTree<T>::rootIsNullptr() const 603 { 604 return mRoot == nullptr; 605 } 606 607 template <typename T> 608 T AVLTree<T>::getRootKey() const 609 { 610 if ( mRoot == nullptr ) 611 THROW_EXCEPTION(EmptyTreeException, "The tree is empty ..."); 612 613 return mRoot->key; 614 } 615 616 template <typename T> 617 AVLTree<T>::~AVLTree() 618 { 619 destroy(); 620 } 621 622 } 623 624 #endif // AVLTREE_H
main.cpp
1 #include <iostream> 2 #include <cmath> 3 #include <thread> 4 5 #include "AVLTree.h" 6 #include "Times.h" 7 8 using namespace std; 9 using namespace LinWeiJie_lib; 10 11 typedef uint64_t templateType; 12 typedef uint64_t sizeType; 13 14 int main(int argc, char* argv[]) 15 { 16 sizeType i, len = 28; 17 uint16_t keyStrLen = 3; // 打印结点占用的字符宽度，printGraph(node, keyStrLen) 18 19 if ( argc == 2 ) 20 len = static_cast<sizeType>(atoi(argv[1])); 21 else { 22 cout << "请输入结点层数，输入值取模33限定上限，注意内存大小" << endl; 23 cin >> len; 24 } 25 26 len %= 33+1; 27 28 timingStart(); 29 30 templateType tmp = 0; 31 AVLTree<templateType>* tree = new AVLTree<templateType>(); 32 33 cout << "添加元素：\nkey\tcount\tlayer" << endl; 34 srand(static_cast<uint32_t>(time(nullptr))); 35 i = 0; 36 while ( tree->getCount() < (1ull<<len)-1 ) 37 { 38 do 39 { 40 tmp = static_cast<templateType>( 41 static_cast<sizeType>(rand()) 42 * static_cast<sizeType>(rand()) 43 * static_cast<sizeType>(rand()) 44 ); 45 } while(tree->iterativeSearch(tmp)); 46 tree->insert(tmp); 47 cout << tmp << "\t" << ++i << "\t" << tree->height() << endl; 48 if ( tree->height() >= static_cast<int>(len) ) // 限制树的高度 49 break; 50 } 51 cout << endl; 52 53 cout << "先序遍历：" << endl; 54 tree->preOrder(); 55 cout << endl; 56 cout << "中序遍历：" << endl; 57 tree->inOrder(); 58 cout << endl; 59 cout << "后序遍历：" << endl; 60 tree->postOrder(); 61 cout << endl; 62 cout << "广度优先：" << endl; 63 tree->levelOrder(); 64 cout << endl; 65 66 // 输出树形描述的关系图 67 tree->printGraph(keyStrLen); 68 cout << endl; 69 70 tree->printTree(); 71 cout << endl; 72 73 cout << "最小结点：" << tree->minimum() << endl; 74 cout << "最大结点：" << tree->maximum() << endl; 75 cout << "树的高度：" << tree->height() << endl; 76 cout << "树的结点数：" << tree->getCount() << endl; 77 78 cout << "\n开始删除！！！\nkey\tlayer" << endl; 79 while ( !tree->rootIsNullptr() ) // 随机数删除 80 { 81 // tmp = static_cast<templateType>( 82 // static_cast<sizeType>(rand()) 83 // * static_cast<sizeType>(rand()) 84 // * static_cast<sizeType>(rand()) 85 // % ( (1ull<<len)-1) ); 86 if ( tree->remove(tree->getRootKey()) ) 87 cout << tmp << "\t" << tree->height() << "\t" << endl; 88 } 89 cout << endl; 90 91 cout << "删除后输出===" << endl; 92 cout << "树的高度：" << tree->height() << endl; 93 cout << "树的结点数：" << tree->getCount() << endl; 94 cout << "中序遍历：" << endl; 95 tree->inOrder(); 96 97 cout << "\n销毁AVL树。" << endl; 98 tree->destroy(); 99 cout << "\n树的高度：" << tree->height() << endl; 100 cout << "树的结点数：" << tree->getCount() << endl; 101 delete tree; 102 tree = nullptr; 103 104 cout << endl; 105 timingEnd(); 106 cout << endl; 107 108 return 0; 109 }
其余代码请到这查找：https://github.com/Duacai/Data-Structure-and-Algorithms/tree/master/BSTree