1 inline int max(int x, int y){ return x>y?x:y; } 2 3 template<typename Element> 4 class AVLTree 5 { 6 public: 7 AVLTree():root(NULL) {} 8 AVLTree(const AVLTree &avl):root(NULL) { operator=(avl); } 9 virtual ~AVLTree() { clear(root); } 10 11 void clear() { clear(root); } 12 bool isEmpty() const 13 { return root==NULL; } 14 void insert(const Element& e) 15 { insert(root, e); } 16 void remove(const Element& e) 17 { remove(root, e); } 18 bool contains(const Element& e) const 19 { return contains(root, e); } 20 const Element& findMin() const 21 { return findMin(root); } 22 const Element& findMax() const 23 { return findMax(root); } 24 25 const AVLTree& operator=(const AVLTree &avl) 26 { 27 if(this!=&avl) 28 { 29 clear(); 30 root = clone(avl.root); 31 } 32 return *this; 33 } 34 35 private: 36 struct AVLNode 37 { 38 Element element; 39 int height; 40 AVLNode *left; 41 AVLNode *right; 42 AVLNode(const Element &e, AVLNode *lt, AVLNode *rt, int h=0): 43 element(e), left(lt), right(rt), height(h) {} 44 }; 45 AVLNode *root; 46 47 AVLNode* clone(AVLNode *t) 48 { 49 if(t!=NULL) 50 { 51 return new AVLNode(t->element, clone(t->left), clone(t->right), t->height); 52 } 53 return NULL; 54 } 55 void clear(AVLNode * &t) 56 { 57 if(t!=NULL) 58 { 59 clear(t->left); 60 clear(t->right); 61 delete t; 62 } 63 t = NULL; 64 } 65 int height(AVLNode *t) const 66 { return t==NULL?-1:t->height; } 67 void insert(AVLNode* &t, const Element& e) 68 { 69 if(t==NULL) 70 { 71 t = new AVLNode(e, NULL, NULL); 72 } 73 else if(e<t->element) 74 { 75 insert(t->left, e); 76 if(height(t->left)-height(t->right)==2) 77 { 78 if(e<t->left->element) 79 { 80 rotateLchildLtree(t); 81 } 82 else 83 { 84 doubleRotateLchildRtree(t); 85 } 86 } 87 } 88 else if(e>t->element) 89 { 90 insert(t->right, e); 91 if(height(t->right)-height(t->left)==2) 92 { 93 if(e>t->right->element) 94 { 95 rotateRchildRtree(t); 96 } 97 else 98 { 99 doubleRotateRchildLtree(t); 100 } 101 } 102 } 103 else 104 { 105 } 106 t->height = max(height(t->left), height(t->right))+1; 107 } 108 void remove(AVLNode* &t, const Element& e) 109 { 110 if(t!=NULL) 111 { 112 if(e<t->element) 113 { 114 remove(t->left, e); 115 } 116 else if(e>t->element) 117 { 118 remove(t->right, e); 119 } 120 else if(t->left!=NULL&&t->right!=NULL) 121 { 122 t->element = findMin(t->right); 123 remove(t->right, t->element); 124 } 125 else 126 { 127 AVLNode *tmp = t; 128 t = t->left!=NULL?t->left:t->right; 129 delete tmp; 130 } 131 if(t!=NULL) 132 { 133 t->height = max(height(t->left), height(t->right))+1; 134 if(height(t->left)-height(t->right)==2) 135 { 136 if(height(t->left->left)>height(t->left->right)) 137 { 138 rotateLchildLtree(t); 139 } 140 else 141 { 142 doubleRotateLchildRtree(t); 143 } 144 } 145 else if(height(t->right)-height(t->left)==2) 146 { 147 if(height(t->right->right)>height(t->right->left)) 148 { 149 rotateRchildRtree(t); 150 } 151 else 152 { 153 doubleRotateRchildLtree(t); 154 } 155 } 156 else 157 { 158 } 159 } 160 } 161 } 162 void rotateLchildLtree(AVLNode * &k2) 163 { 164 AVLNode *k1 = k2->left; 165 k2->left = k1->right; 166 k1->right = k2; 167 k2 = k1; 168 } 169 void rotateRchildRtree(AVLNode * &k2) 170 { 171 AVLNode *k1 = k2->right; 172 k2->right = k1->left; 173 k1->left = k2; 174 k2 = k1; 175 } 176 void doubleRotateLchildRtree(AVLNode * &k3) 177 { 178 rotateRchildRtree(k3->left); 179 rotateLchildLtree(k3); 180 } 181 void doubleRotateRchildLtree(AVLNode * &k3) 182 { 183 rotateLchildLtree(k3->right); 184 rotateRchildRtree(k3); 185 } 186 bool contains(AVLNode *t, const Element& e) const 187 { 188 if(t!=NULL) 189 { 190 if(e<t->element) 191 { 192 return contains(t->left, e); 193 } 194 else if(e>t->element) 195 { 196 return contains(t->right, e); 197 } 198 else 199 { 200 return true; 201 } 202 } 203 else 204 { 205 return false; 206 } 207 } 208 const Element& findMin(AVLNode *t) const 209 { 210 return t->left!=NULL?findMin(t->left):t->element; 211 } 212 const Element& findMax(AVLNode *t) const 213 { 214 return t->right!=NULL?findMax(t->right):t->element; 215 } 216 };
注：不支持重复元素。