AVLTree

  1 #include <iostream>
  2 using namespace std;
  3 
  4 struct TreeNode
  5 {
  6     char data;
  7     int heigth;
  8     TreeNode* rchild;
  9     TreeNode* lchild;
 10 };
 11 
 12 class AVLTree
 13 {
 14 public:
 15     AVLTree(){top = NULL;}
 16     TreeNode* MakeEmpty();
 17     void Delete(char elem,TreeNode* &position,bool& isdel);
 18     TreeNode* Insert(char elem,TreeNode* &position);
 19     TreeNode* IsExist(char elem);
 20     void Create();
 21 
 22     //处理之后position指向原position的左根
 23     TreeNode* SingleRotateWithLeft(TreeNode* &position);
 24     //处理之后position指向原position的右根
 25     TreeNode* SingleRotateWithRight(TreeNode* &position);
 26     TreeNode* DoubleRotateWithLeft(TreeNode* &position);
 27     TreeNode* DoubleRotateWithRight(TreeNode* &position);
 28     int Max(int n1,int n2);
 29     int Heigth(TreeNode* position);
 30 
 31 
 32 private:
 33     TreeNode* top;
 34 
 35 };
 36 
 37 //判断节点高度
 38 int AVLTree::Heigth(TreeNode* position)
 39 {
 40     if (position == NULL)
 41     {
 42         return -1;
 43     }
 44     else
 45     {
 46         int n = position->heigth;
 47         return n;
 48     }
 49 }
 50 
 51 //判断大小、
 52 int AVLTree::Max(int n1,int n2)
 53 {
 54     return (n1>n2)?n1:n2;
 55 }
 56 
 57 //左旋,左孩子作为新的根节点,新根的右孩子成为原根的左孩子，原根成为新根的右孩子
 58 TreeNode* AVLTree::SingleRotateWithLeft(TreeNode* &position)
 59 {
 60     TreeNode* pos = (position)->lchild;
 61     (position)->lchild = pos->rchild;
 62     pos->rchild = position;
 63 
 64     (position)->heigth = Max(Heigth((position)->lchild),Heigth((position)->rchild)) + 1;
 65     (pos)->heigth = Max(Heigth((pos)->lchild),Heigth((pos)->rchild)) + 1;
 66     return pos;
 67 }
 68 
 69 //右旋,右孩子作为新的根节点,新根的左孩子成为原根的右孩子，原根成为新根的左孩子
 70 TreeNode* AVLTree::SingleRotateWithRight(TreeNode* &position)
 71 {
 72     TreeNode* pos = (position)->rchild;
 73     (position)->rchild = pos->lchild;
 74     pos->lchild = position;
 75 
 76     (position)->heigth = Max(Heigth((position)->lchild),Heigth((position)->rchild)) + 1;
 77     (pos)->heigth = Max(Heigth((pos)->lchild),Heigth((pos)->rchild)) + 1;
 78     return pos;
 79 }
 80 
 81 //左侧双旋
 82 TreeNode* AVLTree::DoubleRotateWithLeft(TreeNode* &position)
 83 {
 84     position->lchild = SingleRotateWithRight(position->lchild);
 85     return SingleRotateWithLeft(position);
 86 }
 87 
 88 //右侧双旋
 89 TreeNode* AVLTree::DoubleRotateWithRight(TreeNode* &position)
 90 {
 91     position->rchild = SingleRotateWithLeft(position->rchild);
 92     return SingleRotateWithRight(position);
 93 }
 94 
 95 TreeNode* AVLTree::Insert(char elem,TreeNode* &position)
 96 {
 97     if (position == NULL)
 98     {
 99         position = new TreeNode;
100         position->data = elem;
101         position->lchild = position->rchild = NULL;
102         position->heigth = 0;
103     }
104     else if (elem < position->data)
105     {
106         position->lchild = Insert(elem,position->lchild);
107         if (Heigth(position->lchild) - Heigth(position->rchild) == 2)
108         {
109             if (elem < position->lchild->data)
110             {
111                 position = SingleRotateWithLeft(position);
112             } 
113             else
114             {
115                 position = DoubleRotateWithLeft(position);
116             }
117         }
118     } 
119     else if(elem > position->data)
120     {
121         position->rchild = Insert(elem,position->rchild);
122         if (Heigth(position->rchild) - Heigth(position->lchild) == 2)
123         {
124             if (elem < position->rchild->data)
125             {
126                 position = DoubleRotateWithRight(position);
127             } 
128             else
129             {
130                 position = SingleRotateWithRight(position);
131             }
132         }
133     }
134     else
135     {
136         //数据已存在
137     }
138 
139     position->heigth = Max(Heigth(position->lchild) , Heigth(position->rchild)) + 1;
140     return position;
141 }
142 
143 void AVLTree::Delete(char elem,TreeNode* &position,bool& isdel)
144 {
145     bool is_left = false;
146     //寻找值并删除
147     if (position == NULL)
148     {
149         cout<<"This elem is not existed!"<<endl;
150         isdel = false;
151     }
152     else if (position->data == elem)
153     {
154         if (position->lchild == NULL)//包括右孩子为空和右孩子不为空
155         {
156             TreeNode* temp = position;
157             position = position->rchild;
158             delete temp;
159             temp = NULL;
160         }
161         else if (position->rchild == NULL)//右孩子为空做孩子不为空
162         {
163             TreeNode* temp = position;
164             position = position->lchild;
165             delete temp;
166             temp = NULL;
167         }
168         else//做右孩子都不为空
169         {
170             TreeNode* temp = position;
171             temp = temp->lchild;
172             while (temp->rchild)
173             {
174                 temp = temp->rchild;
175             }
176             position->data = temp->data;
177             Delete(temp->data,position->lchild,isdel);
178             is_left = true;
179         }
180         isdel = true;
181     }
182     else if (position->data > elem)
183     {
184         Delete(elem,position->lchild,isdel);
185         is_left = true;
186     } 
187     else if(position->data < elem)
188     {
189         Delete(elem,position->rchild,isdel);
190         is_left = false;
191     }
192 
193     //平衡并重新制定高度
194     if (isdel && position)
195     {
196         if (is_left)//删除的为左子树部分
197         {
198             if (Heigth(position->rchild) - Heigth(position->lchild) == 2)
199             {
200                 if (elem < position->rchild->data)
201                 {
202                     position = DoubleRotateWithRight(position);
203                 } 
204                 else
205                 {
206                     position = SingleRotateWithRight(position);
207                 }
208             }
209         } 
210         else//删除为右子树部分
211         {
212             if (Heigth(position->lchild) - Heigth(position->rchild) == 2)
213             {
214                 if (elem < position->lchild->data)
215                 {
216                     position = SingleRotateWithLeft(position);
217                 } 
218                 else
219                 {
220                     position = DoubleRotateWithLeft(position);
221                 }
222             }
223         }
224         //重新制定高度，position ！= NULL
225         position->heigth = Max(Heigth(position->lchild) , Heigth(position->rchild)) + 1;
226     }
227 }
228 
229 void AVLTree::Create()
230 {
231     char a[10] = {‘a‘,‘b‘,‘c‘,‘d‘,‘e‘,‘f‘,‘g‘,‘p‘,‘o‘,‘n‘};
232     for (int i = 0;i < 10; i++)
233     {
234         Insert(a[i],top);
235     }
236 
237     //test
238     bool bl;
239     //     Delete(‘e‘,top,bl);
240     //     Delete(‘f‘,top,bl);
241     Delete(‘d‘,top,bl);
242 }