1 #include "stdafx.h"
2
3 /*
4 * @author Wu Jingan
5 * @created June 6, 2018
6 */
7
8 #include <iostream>
9 #include <string>
10 #include <algorithm>
11 #include <ctime>
12 #include <Windows.h>
13 #include <vector>
14 using namespace std;
15
16 class Node
17 {
18 public:
19 Node() {}
20 Node(int value, Node *parent, Node *left, Node *right)
21 {
22 this->value = value;
23 this->parent = parent;
24 this->left = left;
25 this->right = right;
26 }
27
28 Node operator=(const Node &_Right)
29 {
30 this->value = _Right.value;
31 this->parent = _Right.parent;
32 this->right = _Right.right;
33 this->left = _Right.left;
34 return *this;
35 }
36
37 bool isLeaf()
38 {
39 return this->left == nullptr && this->right == nullptr;
40 }
41
42 int value;
43 Node *parent;
44 Node *left;
45 Node *right;
46 };
47
48 class AbstractBinarySearchTree
49 {
50 public:
51 int getMinimumNodeValue()
52 {
53 return getMinimumNode(root)->value;
54 }
55
56 int getMaximumNodeValue()
57 {
58 return getMaximumNode(root)->value;
59 }
60
61 int getSize()
62 {
63 return this->size;
64 }
65
66 //若元素不存在, 返回1
67 bool isContains(int element)
68 {
69 return search(element) == nullptr;
70 }
71
72 //先序遍历二叉搜索树
73 void printtAbstractBinarySearchTreePreOrder(Node *root)
74 {
75 if (root == nullptr)
76 return;
77 cout << root->value << " ";
78 printtAbstractBinarySearchTreePreOrder(root->left);
79 printtAbstractBinarySearchTreePreOrder(root->right);
80 }
81
82 //中序遍历二叉搜索树
83 void printtAbstractBinarySearchTreeInOrder(Node *root)
84 {
85 if (root == nullptr)
86 return;
87 printtAbstractBinarySearchTreeInOrder(root->left);
88 cout << root->value << " ";
89 printtAbstractBinarySearchTreeInOrder(root->right);
90 }
91
92 //后序遍历二叉搜索树
93 void printtAbstractBinarySearchTreePostOrder(Node *root)
94 {
95 if (root == nullptr)
96 return;
97 printtAbstractBinarySearchTreePostOrder(root->left);
98 printtAbstractBinarySearchTreePostOrder(root->right);
99 cout << root->value << " ";
100 }
101
102 void printTree()
103 {
104 printSubtree(root);
105 }
106
107 protected:
108 Node * createNode(int value, Node *parent, Node *left, Node *right)
109 {
110 Node *node = new Node(value, parent, left, right);
111 return node;
112 }
113
114 Node * deleteNode(int element)
115 {
116 Node *node = search(element);
117 if (node != nullptr)
118 return deleteNode(node);
119 else
120 return nullptr;
121 }
122
123 Node *search(int element)
124 {
125 Node *node = root;
126 while (node != nullptr && node->value != element)
127 {
128 if (node->value < element)
129 node = node->right;
130 else
131 node = node->left;
132 }
133 return node;
134 }
135
136 Node *insertNode(int element)
137 {
138 if (root == nullptr)
139 {
140 root = createNode(element, nullptr, nullptr, nullptr);
141 size++;
142 return root;
143 }
144 Node *insertParentNode = root;
145 Node *searchTempNode = root;
146 while (searchTempNode != nullptr)
147 {
148 insertParentNode = searchTempNode;
149 if (element < searchTempNode->value)
150 searchTempNode = searchTempNode->left;
151 else if (element > searchTempNode->value)
152 searchTempNode = searchTempNode->right;
153 else
154 return searchTempNode;
155 }
156 Node *NewNode = createNode(element, insertParentNode, nullptr, nullptr);
157 if (insertParentNode->value > element)
158 insertParentNode->left = NewNode;
159 else
160 insertParentNode->right = NewNode;
161 size++;
162 return NewNode;
163 }
164
165 Node * deleteNode(Node *deleteNode)
166 {
167 Node *nodeToReturn = nullptr;
168 if (deleteNode != nullptr)
169 {
170 if (deleteNode->left == nullptr)
171 nodeToReturn = transplantNode(deleteNode, deleteNode->right);
172 else if (deleteNode->right == nullptr)
173 nodeToReturn = transplantNode(deleteNode, deleteNode->left);
174 else
175 {
176 Node *successorNode = getMinimumNode(deleteNode->right);
177 if (successorNode->parent != deleteNode)
178 {
179 transplantNode(successorNode, successorNode->right);
180 successorNode->right = deleteNode->right;
181 successorNode->right->parent = successorNode;
182 }
183 transplantNode(deleteNode, successorNode);
184 successorNode->left = deleteNode->left;
185 successorNode->left->parent = successorNode;
186 nodeToReturn = successorNode;
187 }
188 size--;
189 return nodeToReturn;
190 }
191 else
192 return nullptr;
193 }
194
195 Node *transplantNode(Node *nodeToReplace, Node *newNode)
196 {
197 if (nodeToReplace->parent == nullptr)
198 this->root = newNode;
199 else if (nodeToReplace == nodeToReplace->parent->left)
200 nodeToReplace->parent->left = newNode;
201 else
202 nodeToReplace->parent->right = newNode;
203 if (newNode != nullptr)
204 newNode->parent = nodeToReplace->parent;
205 return newNode;
206 }
207
208 void printNodeValue(Node *node)
209 {
210 if (node == nullptr)
211 cout << "<null>";
212 else
213 cout << node->value;
214 cout << endl;
215 }
216
217 void printSubtree(Node *node)
218 {
219 if (node->right != nullptr) {
220 printTree(node->right, true, "");
221 }
222 printNodeValue(node);
223 if (node->left != nullptr) {
224 printTree(node->left, false, "");
225 }
226 }
227
228 void printTree(Node *node, bool isRight, string indent)
229 {
230 if (node->right != nullptr)
231 printTree(node->right, true, indent + (isRight ? " " : " | "));
232 cout << indent;
233 if (isRight)
234 cout << " /";
235 else
236 cout << " \\";
237 cout << "----- ";
238 printNodeValue(node);
239 if (node->left != nullptr)
240 printTree(node->left, false, indent + (isRight ? " | " : " "));
241 }
242
243 Node *getMinimumNode(Node *node)
244 {
245 while (node->left != nullptr)
246 node = node->left;
247 return node;
248 }
249
250 Node *getMaximumNode(Node *node)
251 {
252 while (node->right != nullptr)
253 node = node->right;
254 return node;
255 }
256
257 Node *root = nullptr;
258 int size;
259 };
260
261 class AbstractSelfBalancingBinarySearchTree :public AbstractBinarySearchTree
262 {
263 protected:
264 Node * rotateLeft(Node *node)
265 {
266 Node *tempNode = node->right;
267 tempNode->parent = node->parent;
268 node->right = tempNode->left;
269 if (node->right != nullptr)
270 node->right->parent = node;
271 tempNode->left = node;
272 node->parent = tempNode;
273 if (tempNode->parent != nullptr)
274 {
275 if (node == tempNode->parent->left)
276 tempNode->parent->left = tempNode;
277 else
278 tempNode->parent->right = tempNode;
279 }
280 else
281 root = tempNode;
282 return tempNode;
283 }
284
285 Node *rotateRight(Node *node)
286 {
287 Node * tempNode = node->left;
288 tempNode->parent = node->parent;
289 node->left = tempNode->right;
290 if (node->left != nullptr)
291 node->left->parent = node;
292
293 tempNode->right = node;
294 node->parent = tempNode;
295 if (tempNode->parent != nullptr)
296 {
297 if (node == tempNode->parent->left)
298 tempNode->parent->left = tempNode;
299 else
300 tempNode->parent->right = tempNode;
301 }
302 else
303 root = tempNode;
304 return tempNode;
305 }
306 };
307
308 class AVLNode :public Node
309 {
310 public:
311 AVLNode(int value, Node *parent, Node *left, Node *right)
312 {
313 Node(value, parent, left, right);
314 }
315
316 int height;
317 };
318
319 class AVLTree :public AbstractSelfBalancingBinarySearchTree
320 {
321 public:
322 Node * insert(int element)
323 {
324 Node *newNode = this->insertNode(element);
325 rebalance((AVLNode *)newNode);
326 return newNode;
327 }
328
329 Node *deleteAVLNode(int element)
330 {
331 Node *delete_Node = AbstractSelfBalancingBinarySearchTree::search(element);
332 if (delete_Node != nullptr)
333 {
334 Node *successorNode = AbstractSelfBalancingBinarySearchTree::deleteNode(delete_Node);
335 if (successorNode != nullptr)
336 {
337 AVLNode *minimum = successorNode->right != nullptr ? (AVLNode *)getMinimumNode(successorNode->right) : (AVLNode *)successorNode;
338 recomputeHeight(minimum);
339 rebalance((AVLNode *)minimum);
340 }
341 else
342 {
343 recomputeHeight((AVLNode *)delete_Node->parent);
344 rebalance((AVLNode *)delete_Node->parent);
345 }
346 return successorNode;
347 }
348 return nullptr;
349 }
350
351 protected:
352 Node * createNode(int value, Node *parent, Node *left, Node *right)
353 {
354 return new AVLNode(value, parent, left, right);
355 }
356
357 Node * doubleRotateRightLeft(Node *node)
358 {
359 node->right = avlRotateRight(node->right);
360 return avlRotateLeft(node);
361 }
362
363 Node * doubleRotateLeftRight(Node *node)
364 {
365 node->left = avlRotateLeft(node->left);
366 return avlRotateRight(node);
367 }
368
369 private:
370 void rebalance(AVLNode *node)
371 {
372 while (node != nullptr)
373 {
374 Node *parent = node->parent;
375
376 int leftHeight = (node->left == nullptr) ? -1 : ((AVLNode *)node->left)->height;
377 int rightHeight = (node->right == nullptr) ? -1 : ((AVLNode *)node->right)->height;
378 int nodeBalance = leftHeight - rightHeight;
379 if (nodeBalance == -2)
380 {
381 if (node->right->right != nullptr)
382 {
383 node = (AVLNode *)avlRotateLeft(node);
384 break;
385 }
386 else
387 {
388 node = (AVLNode *)doubleRotateRightLeft(node);
389 break;
390 }
391 }
392 else if (nodeBalance == 2)
393 {
394 if (node->left->left != nullptr)
395 {
396 node = (AVLNode *)avlRotateRight(node);
397 break;
398 }
399 else
400 {
401 node = (AVLNode *)doubleRotateLeftRight(node);
402 break;
403 }
404 }
405 else
406 updateHeight(node);
407 node = (AVLNode*)parent;
408 }
409
410 }
411
412 void recomputeHeight(AVLNode *node)
413 {
414 while (node != nullptr)
415 {
416 node->height = maxHeight((AVLNode *)node->left, (AVLNode *)node->right) + 1;
417 node = (AVLNode *)node->parent;
418 }
419 }
420
421 int maxHeight(AVLNode *_LeftNode, AVLNode *_RightNode)
422 {
423 if (_LeftNode != nullptr && _RightNode != nullptr)
424 return _LeftNode->height > _RightNode->height ? _LeftNode->height : _RightNode->height;
425 else if (_LeftNode == nullptr)
426 return _RightNode != nullptr ? _RightNode->height : -1;
427 else if (_RightNode == nullptr)
428 return _LeftNode != nullptr ? _LeftNode->height : -1;
429 return -1;
430 }
431
432 Node * avlRotateLeft(Node *node)
433 {
434 Node *temp = AbstractSelfBalancingBinarySearchTree::rotateLeft(node);
435 updateHeight((AVLNode *)temp->left);
436 updateHeight((AVLNode *)temp);
437 return temp;
438 }
439
440 Node * avlRotateRight(Node *node)
441 {
442 Node *temp = AbstractSelfBalancingBinarySearchTree::rotateRight(node);
443
444 updateHeight((AVLNode *)temp->right);
445 updateHeight((AVLNode *)temp);
446 return temp;
447 }
448
449 void updateHeight(AVLNode *node)
450 {
451 int leftHeight = (node->left == nullptr) ? -1 : ((AVLNode *)node->left)->height;
452 int rightHeight = (node->right == nullptr) ? -1 : ((AVLNode *)node->right)->height;
453 node->height = max(leftHeight, rightHeight) + 1;
454 }
455 };
456
457 //for test
458 class RandomArray
459 {
460 public:
461 RandomArray() { }
462 RandomArray(int maxValue, int maxSize)
463 {
464 this->maxValue = maxValue;
465 this->maxSize = maxSize;
466 this->randomVec = new vector<int>(rand() % maxSize + 5);
467 }
468
469 vector<int> *getRandomArray()
470 {
471 for (vector<int>::size_type i = 0; i < randomVec->size(); i++)
472 (*randomVec)[i] = rand() % maxValue + 1;
473 return randomVec;
474 }
475
476 int getSize()
477 {
478 return (int)randomVec->size();
479 }
480
481 private:
482 int maxValue;
483 int maxSize;
484 vector<int> *randomVec;
485 };
486
487 int main()
488 {
489 srand((unsigned)time(NULL));
490 RandomArray randomArray(100, 15);
491 vector<int> *randomVec = randomArray.getRandomArray();
492 AVLTree AVLtree;
493 AVLNode *root = (AVLNode *)AVLtree.insert((*randomVec)[0]);
494 cout << "the array for test is : " << (*randomVec)[0] << " ";
495 for (int i = 1; i < randomArray.getSize(); i++)
496 {
497 cout << (*randomVec)[i] << " ";
498 AVLtree.insert((*randomVec)[i]);
499 }
500 cout << endl;
501
502 AVLtree.printTree();
503
504 cout << "============================" << endl;
505
506 int randomIndex = rand() % randomArray.getSize();
507 cout << "the value of delete AVLnode is : " << (*randomVec)[randomIndex] << endl;
508 AVLtree.deleteAVLNode((*randomVec)[randomIndex]);
509 AVLtree.printTree();
510
511
512 return 0;
513 }
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