各种折腾...
1 #include <iostream> 2 #define MAX(a,b) ((a)>(b)?(a):(b)) 3 #define SIZEOFARRY(a) sizeof(a)/sizeof(int) 4 #define ASSERT(a) if((a)==NULL)exit(0) 5 6 using namespace std; 7 8 typedef int Datatype; 9 10 typedef struct AVLTNode 11 { 12 struct AVLTNode* pLeft; 13 struct AVLTNode* pRight; 14 int height; 15 Datatype data; 16 }*pNode; 17 18 typedef struct AVLTNode* Tree; 19 20 21 class AVLTree 22 { 23 public: 24 AVLTree(){root=NULL;} 25 ~AVLTree(){} 26 void InsertNode(Datatype x){root=InsertNode(x,root);}; 27 void DeleteNode(Datatype x){root = DeleteNode(x, root);}; 28 void PrintTreeByMin(){_PrintTreeByMin(root);} 29 private: 30 int BalanceFactor(AVLTNode* node); 31 AVLTNode* Rotate(AVLTNode* node); 32 void _PrintTreeByMin(AVLTNode* node); 33 AVLTNode* InsertNode(Datatype x, AVLTNode* node); 34 AVLTNode* DeleteNode(Datatype x, AVLTNode* node); 35 int Height(AVLTNode* node); 36 AVLTNode* RightRotate(AVLTNode* root); 37 AVLTNode* LeftRotate(AVLTNode* root); 38 AVLTNode* RightLeftRotate(AVLTNode* root); 39 AVLTNode* LeftRightRotate(AVLTNode* root); 40 public: 41 AVLTNode* root; 42 }; 43 44 int AVLTree::Height(AVLTNode* node) 45 { 46 if (!node) 47 { 48 return 0; 49 } 50 return node->height; 51 } 52 AVLTNode* AVLTree::RightRotate(AVLTNode* root) 53 { 54 AVLTNode *temp; 55 temp = root->pLeft; 56 root->pLeft = temp->pRight; 57 temp->pRight = root; 58 59 root->height = MAX(Height(root->pLeft), Height(root->pRight)) + 1; 60 temp->height = MAX(Height(temp->pLeft), Height(temp->pRight)) + 1; 61 62 return temp; 63 } 64 AVLTNode* AVLTree::LeftRotate(AVLTNode* root) 65 { 66 AVLTNode *temp; 67 temp = root->pRight; 68 root->pRight = temp->pLeft; 69 temp->pLeft = root; 70 71 root->height = MAX(Height(root->pLeft), Height(root->pRight)) + 1; 72 temp->height = MAX(Height(temp->pLeft), Height(temp->pRight)) + 1; 73 74 return temp; 75 } 76 AVLTNode* AVLTree::RightLeftRotate(AVLTNode* root) 77 { 78 root->pRight = RightRotate(root->pRight); 79 80 return LeftRotate(root); 81 } 82 AVLTNode* AVLTree::LeftRightRotate(AVLTNode* root) 83 { 84 root->pLeft = LeftRotate(root->pLeft); 85 return RightRotate(root); 86 } 87 88 AVLTNode* AVLTree::InsertNode(Datatype x,AVLTNode* node) 89 { 90 if (node==NULL) 91 { 92 node = new AVLTNode; 93 ASSERT(node); 94 node->data = x; 95 node->pLeft = NULL; 96 node->pRight = NULL; 97 node->height = 1; 98 return node; 99 } 100 else if (x < node->data) 101 { 102 node->pLeft = InsertNode(x, node->pLeft); 103 if (Height(node->pLeft)-Height(node->pRight) == 2) 104 { 105 if (x < node->pLeft->data) 106 { 107 node = RightRotate(node); 108 } 109 else 110 { 111 node = LeftRightRotate(node); 112 } 113 } 114 } 115 else 116 { 117 node->pRight = InsertNode(x, node->pRight); 118 if (Height(node->pRight)-Height(node->pLeft) == 2) 119 { 120 if (x > node->pRight->data) 121 { 122 node = LeftRotate(node); 123 } 124 else 125 { 126 node = RightLeftRotate(node); 127 } 128 } 129 } 130 node->height = MAX(Height(node->pLeft), Height(node->pRight)) + 1; 131 return node; 132 } 133 134 void AVLTree::_PrintTreeByMin(AVLTNode* node) 135 { 136 if (!node) 137 { 138 return; 139 } 140 _PrintTreeByMin(node->pLeft); 141 cout<<node->data<<"("<<node->height<<")"<<" "; 142 _PrintTreeByMin(node->pRight); 143 } 144 //对于二叉树的删除操作，先递归的搜索要删除的节点A，用该节点的右儿子 145 //的最左儿子B代替该节点，以A的右儿子和B当前的数值作为线索继续遍历， 146 //只到找到B，删除B。然后递归的对B的祖先节点进行平衡调整，具体调整操作 147 //和二叉树的插入操作的平衡调整相同。 148 AVLTNode* AVLTree::DeleteNode(Datatype x, AVLTNode* node) 149 { 150 AVLTNode *temp=NULL; 151 if (node == NULL) 152 { 153 return NULL; 154 } 155 if (node->data == x) 156 { 157 if (node->pRight==NULL) 158 { 159 //无有孩子 160 temp = node; 161 node = node->pLeft; 162 free(temp); 163 temp = NULL; 164 } 165 else 166 { 167 //有则用其右孩子的最左孩子替换该节点 168 temp = node->pRight; 169 while(temp->pLeft) 170 { 171 temp = temp->pLeft; 172 } 173 node->data = temp->data; 174 node->pRight = DeleteNode(node->data, node->pRight);//删除的值，和传入的根结点发生了变化 175 node->height = MAX(Height(node->pLeft), Height(node->pRight))+1; 176 } 177 return node; // 178 }else if (node->data < x) 179 { 180 node->pRight = DeleteNode(x, node->pRight); 181 if (node->pRight) 182 { 183 node->pRight = Rotate(node->pRight); 184 } 185 186 } 187 else 188 { 189 node->pLeft = DeleteNode(x, node->pLeft); 190 if (node->pLeft) 191 { 192 node->pLeft = Rotate(node->pLeft); 193 } 194 } 195 node->height = MAX(Height(node->pLeft), Height(node->pRight))+1; 196 node = Rotate(node); 197 return node; 198 } 199 200 int AVLTree::BalanceFactor(AVLTNode* node) 201 { 202 if (!node) 203 { 204 return 0; 205 } 206 return Height(node->pLeft)-Height(node->pRight); 207 } 208 209 AVLTNode* AVLTree::Rotate(AVLTNode* node) 210 { 211 if(Height(node->pLeft) - Height(node->pRight) == 2) 212 { 213 if(Height(node->pLeft->pLeft) >= Height(node->pLeft->pRight)) 214 { 215 node = RightRotate(node); 216 } 217 else{ 218 node = LeftRightRotate(node); 219 } 220 } 221 if(Height(node->pRight) - Height(node->pLeft) == 2) 222 { 223 if(Height(node->pRight->pRight) >= Height(node->pRight->pLeft)) 224 { 225 node = LeftRotate(node); 226 } 227 else{ 228 node = RightLeftRotate(node); 229 } 230 } 231 232 return node; 233 } 234 235 236 int main() 237 { 238 AVLTree avltree; 239 240 int num[] = {16,3,7,11,9,26,18,14,15}; 241 for (int i=0; i<SIZEOFARRY(num); i++) 242 { 243 avltree.InsertNode(num[i]); 244 } 245 246 avltree.PrintTreeByMin(); 247 cout<<endl; 248 avltree.DeleteNode(14); 249 avltree.PrintTreeByMin(); 250 cout<<endl; 251 avltree.DeleteNode(26); 252 avltree.PrintTreeByMin(); 253 254 cout<<endl; 255 return 0; 256 }