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二叉搜索树的搜索和插入与删除算法优化

代码是根据之前的二叉树模板修改来的，删去了非递归遍历，加入二叉搜索树的搜索、插入和删除，实现方法在73~153行
  1 #include<iostream>
  2 #include<stack>
  3 #include<queue>
  4 using namespace std;
  5 template <class T> class BinaryTree;
  6 template <class T>
  7 class BinaryTreeNode
  8 {
  9     friend class BinaryTree<T>;
 10 private:
 11     T data; //二叉树数据域
 12     BinaryTreeNode *leftchild; //左孩子指针
 13     BinaryTreeNode *rightchild; //右孩子指针
 14 public:
 15     BinaryTreeNode(){leftchild=rightchild=NULL;}
 16     BinaryTreeNode(const T elem)
 17     {
 18         data=elem;
 19         leftchild=rightchild=NULL;
 20     }
 21     BinaryTreeNode(const T elem,BinaryTreeNode<T> *l,BinaryTreeNode<T> *r)
 22     {
 23         data=elem;
 24         leftchild=l;
 25         rightchild=r;
 26     }
 27     BinaryTreeNode<T> * left() const{return leftchild;}
 28     BinaryTreeNode<T> * right() const{return rightchild;}
 29     void setLeft(BinaryTreeNode *l){leftchild=l;}
 30     void setRight(BinaryTreeNode *r){rightchild=r;}
 31     void setValue(const T value){data=value;}
 32     T Value(){return data;}
 33     bool isLeaf()
 34     {
 35         if(leftchild==NULL&&rightchild==NULL)
 36             return true;
 37         else
 38             return false;
 39     }
 40     BinaryTreeNode<T>& operator = (const BinaryTreeNode<T> &Node)
 41     {
 42         cout << "=" ;
 43         data=Node.data;
 44         leftchild=Node.leftchild;
 45         rightchild=Node.leftchild;
 46         return *this;
 47     }
 48 };
 49 template <class T>
 50 class BinaryTree
 51 {
 52 private:
 53     BinaryTreeNode<T> *root;
 54     void setRoot(BinaryTreeNode<T> *r){root=r;}
 55 public:
 56     BinaryTree(){root=NULL;}
 57     bool isEmpty() const
 58     {
 59         if(root==NULL)
 60             return true;
 61         return false;
 62     };
 63     BinaryTreeNode<T> * Root(){return root;}
 64     BinaryTreeNode<T> * Parent(BinaryTreeNode<T> *current);
 65     BinaryTreeNode<T> * LeftSibling(BinaryTreeNode<T> *current);
 66     BinaryTreeNode<T> * RightSibling(BinaryTreeNode<T> *current);
 67     void CreatTree(const T &info,BinaryTree<T> &left,BinaryTree<T> &right);
 68     void PreOrder(BinaryTreeNode<T> *root);
 69     void InOrder(BinaryTreeNode<T> *root);
 70     void PostOrder(BinaryTreeNode<T> *root);
 71     void LevelOrder(BinaryTreeNode<T> *root);
 72     void deleteBinaryTree(BinaryTreeNode<T> *root);
 73     void InsertNode(BinaryTreeNode<T> *root,BinaryTreeNode<T> *newpointer)
 74     {
 75         BinaryTreeNode<T> *pointer=NULL;
 76         if(root==NULL)//根节点为空,直接插入
 77         {
 78             setRoot(newpointer);
 79             return;
 80         }
 81         else pointer=root;
 82         while(pointer!=NULL)
 83         {
 84             if(newpointer->Value()==pointer->Value())
 85                 return;
 86             else if((newpointer->Value())<(pointer->Value()))
 87             {
 88                 if(pointer->left()==NULL)
 89                 {
 90                     pointer->setLeft(newpointer);
 91                     return;
 92                 }
 93                 else
 94                     pointer=pointer->left();
 95             }
 96             else
 97             {
 98                 if(pointer->right()==NULL)
 99                 {
100                     pointer->setRight(newpointer);
101                     return;
102                 }
103                 else pointer=pointer->right();
104             }
105         }
106     }
107     void DeleteNodeEx(BinaryTreeNode<T> *pointer)
108     {
109         //优化的搜索二叉树删除算法
110         //若待删结点有左子树，则寻找左子树中最大的结点，将此结点的左子树挂接到其父节点的右子树上
111         //将待删结点替换成左子树中最大的结点，删除待删结点
112         if(pointer==NULL)return;
113         BinaryTreeNode<T> *temppointer;
114         BinaryTreeNode<T> *tempparent=NULL;
115         BinaryTreeNode<T> *parent=Parent(pointer);
116         if(pointer->left()==NULL)
117             temppointer=pointer->right();
118         else{
119             temppointer=pointer->left();
120             while(temppointer->right()!=NULL)
121             {
122                 tempparent=temppointer;
123                 temppointer=temppointer->right();
124             }
125             if(tempparent==NULL)
126                 pointer->setLeft(temppointer->left());
127             else tempparent->setRight(temppointer->left());
128             temppointer->setLeft(pointer->left());
129             temppointer->setRight(pointer->right());
130         }
131         if(parent==NULL)root=temppointer;
132         else if((parent->left())==pointer)parent->setLeft(temppointer);
133         else parent->setRight(temppointer);
134         delete pointer;
135         pointer=NULL;
136         return;
137     }
138     BinaryTreeNode<T> * Find(const T value)
139     {
140         if(root==NULL)return NULL;
141         BinaryTreeNode<T> *p;
142         p=root;
143         while(p!=NULL&&(p->Value())!=value)
144         {
145             if((p->Value())>value)
146                 p=p->left();
147             else p=p->right();
148         }
149         if((p->Value())==value)return p;
150         cout << "non-exist" <<endl;
151         return NULL;
152     }
153 };
154 template <class T>
155 class StackElem{
156 public:
157     BinaryTreeNode<T> *pointer;
158     int tag;
159 };
160 template <class T>
161 BinaryTreeNode<T> * BinaryTree<T>::Parent(BinaryTreeNode<T> *current) //返回当前结点的父结点
162 {
163     using std::stack;
164     stack<BinaryTreeNode<T> *> aStack; //使用栈存放未访问右子树的结点
165     BinaryTreeNode<T> *pointer=root;
166     if(root!=NULL&&current!=NULL)
167     {
168         while(!aStack.empty()||pointer!=NULL)
169         {
170             if(pointer!=NULL)
171             {
172                 if(current==pointer->left()||current==pointer->right())
173                     return pointer;
174                 aStack.push(pointer);
175                 pointer=pointer->left();
176             }
177             else
178             {
179                 pointer=aStack.top();
180                 aStack.pop();
181                 pointer=pointer->right();
182             }
183         }
184         return NULL;
185     }
186     else
187         return NULL;
188 }
189 template <class T>
190 BinaryTreeNode<T> * BinaryTree<T>::LeftSibling(BinaryTreeNode<T> *current) //返回当前节点左兄弟
191 {
192     using std::stack;
193     stack<BinaryTreeNode<T> *>aStack;
194     BinaryTreeNode<T> *pointer=root;
195     if(root!=NULL&&current!=NULL)
196     {
197         while(!aStack.empty()||pointer!=NULL)
198         {
199             if(pointer!=NULL)
200             {
201                 if(current==pointer->right()&&(pointer->left())!=NULL)
202                     return pointer->left();
203                 aStack.push(pointer);
204                 aStack.pop();
205                 pointer=pointer->left();
206             }
207             else
208             {
209                 pointer=aStack.top();
210                 aStack.pop();
211                 pointer=pointer->right();
212             }
213         }
214         return NULL;
215     }
216     else
217         return NULL;
218 }
219 template <class T>
220 BinaryTreeNode<T> * BinaryTree<T>::RightSibling(BinaryTreeNode<T> *current) //返回当前节点右兄弟
221 {
222     using std::stack;
223     stack<BinaryTreeNode<T> *>aStack;
224     BinaryTreeNode<T> *pointer=root;
225     if(root!=NULL&&current!=NULL)
226     {
227         while(!aStack.empty()||pointer!=NULL)
228         {
229             if(pointer!=NULL)
230             {
231                 if(current==pointer->left()&&(pointer->right())!=NULL)
232                     return pointer->right();
233                 aStack.push(pointer);
234                 aStack.pop();
235                 pointer=pointer->left();
236             }
237             else
238             {
239                 pointer=aStack.top();
240                 aStack.pop();
241                 pointer=pointer->right();
242             }
243         }
244         return NULL;
245     }
246     else
247         return NULL;
248 }
249 template <class T>
250 void BinaryTree<T>::CreatTree(const T &info,BinaryTree<T> &left,BinaryTree<T> &right) //创建树
251 {
252     root=new BinaryTreeNode<T>(info,left.root,right.root);
253     left.root=right.root=NULL;
254 }
255 template <class T>
256 void BinaryTree<T>::PreOrder(BinaryTreeNode<T> *root) //先序遍历
257 {
258     if(root!=NULL)
259         visit(root);
260     else
261         return;
262     PreOrder(root->left());
263     PreOrder(root->right());
264 }
265 template <class T>
266 void BinaryTree<T>::InOrder(BinaryTreeNode<T> *root) //中序遍历
267 {
268     if(root==NULL)
269         return;
270     InOrder(root->left());
271     visit(root);
272     InOrder(root->right());
273 }
274 template <class T>
275 void BinaryTree<T>::PostOrder(BinaryTreeNode<T> *root) //后序遍历
276 {
277     if(root==NULL)
278         return;
279     PostOrder(root->left());
280     PostOrder(root->right());
281     visit(root);
282 }
283 template <class T>
284 void BinaryTree<T>::LevelOrder(BinaryTreeNode<T> *root) //层次遍历
285 {
286     using std::queue;
287     queue<BinaryTreeNode<T> *> aQueue;
288     BinaryTreeNode<T> *p=root,*q;
289     aQueue.push(p);
290     while(!aQueue.empty())
291     {
292         p=aQueue.front();
293         aQueue.pop();
294         visit(p);
295         q=p;
296         if((p->left())!=NULL)
297         {
298             q=p->left();
299             aQueue.push(q);
300         }
301         if((p->right())!=NULL)
302         {
303             q=p->right();
304             aQueue.push(q);
305         }
306     }
307 }
308 template <class T>
309 void BinaryTree<T>::deleteBinaryTree(BinaryTreeNode<T> *root) //删除以root为根节点的树
310 {
311     if(root==NULL)return;
312     deleteBinaryTree(root->left());
313     deleteBinaryTree(root->right());
314     delete root;
315     root=NULL;
316 }
317 
318 void visit(BinaryTreeNode<int> *Root) //访问结点元素
319 {
320     if(Root!=NULL)
321         cout << Root->Value() <<" ";
322 }
323 int main()
324 {
325     BinaryTreeNode<int> *p;
326     BinaryTreeNode<int> e(10);
327     BinaryTree<int> a,b,c;
328     int n,s,l=1;
329     cout << "Enter the number of node" <<endl;
330     while(cin>>n)
331     {
332         for(int i=0;i<n;i++)
333         {
334             cin>>s;
335             p=new BinaryTreeNode<int>(s);
336             a.InsertNode(a.Root(),p);
337         }
338         a.InOrder(a.Root());
339         cout <<endl;
340         a.PreOrder(a.Root());
341         cout <<endl;
342         a.LevelOrder(a.Root());
343         cout <<endl;
344         cin>>l;
345         cout << "Enter the number of delete node" <<endl;
346         for(int i=0;i<l;i++)
347         {
348             cin>>s;
349             p=a.Find(s);
350             if(p!=NULL)
351             {
352                 a.DeleteNodeEx(p);
353                 a.InOrder(a.Root());
354                 cout << endl;
355                 a.PreOrder(a.Root());
356                 cout <<endl;
357                 a.LevelOrder(a.Root());
358                 cout <<endl;
359             }
360         }
361     }
362     return 0;
363 }
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原文地址：https://www.cnblogs.com/LowBee/p/9023981.html