二叉平衡查找树AvlTree(C实现)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 | 二叉平衡查找树即是一棵树中所有节点的左右子树高度差不超过1的查找树 头文件—————————————————————————————— #ifndef _AVLTREE_H_ #define _AVLTREE_H_ #include <stdlib.h> #include <iomanip> #include <iostream> typedef struct AvlNode *Position; typedef Position AvlTree; #define Element int struct AvlNode { Element data; int height; //叶子节点高度定义为0,其父节点为1以此类推 AvlTree left; AvlTree right; }; static int Height(AvlTree avl); void SwapAvlNode(Position *p1, Position *p2); Position GetNotBalancedNode(AvlTree avl); void MakeEmpty(AvlTree* pavl); Position Find(Element x, AvlTree avl); Position FindMin(AvlTree avl); Position FindMax(AvlTree avl); void Insert(Element x, AvlTree* pavl); void Delete(Element x, AvlTree* pavl); Element Retrieve(Position p); void SingleRotateWithLeftLeft(Position *pK2); void SingleRotateWithRightRight(Position *pK2); void DoubleRotateWithLeftRight(Position *pK3); void DoubleRotateWithRightLeft(Position *pK3); void PrintTree(AvlTree avl, int Depth, int ctrl); #endif 源文件———————————————————————————————— #include "./AvlTree.h" int Max( int a, int b) { if (a <= b) return b; return a; } void SwapAvlNode(Position *p1, Position *p2) { Position tmp = *p1; *p1 = *p2; *p2 = tmp; } int Abs( int a) { if (a < 0) return -a; return a; } static int Height(AvlTree avl) { if (NULL == avl) return -1; else return avl->height; } Position GetNotBalancedNode(AvlTree avl) { if (NULL == avl) return NULL; else { if (Height(avl->left) - Height(avl->right) == Abs(2)) //not balanced return avl; else { Position res = GetNotBalancedNode(avl->left); if (NULL != res) //avl->left is not balanced return res; else return GetNotBalancedNode(avl->right); } } } void MakeEmpty(AvlTree* pavl) { if (NULL != (*pavl)) { MakeEmpty(&((*pavl)->left)); MakeEmpty(&((*pavl)->right)); free (*pavl); *pavl = NULL; } } Position Find(Element x, AvlTree avl) { Position pos = avl; while (NULL != pos) { if (x < Retrieve(pos)) pos = pos->left; else if (x > Retrieve(pos)) pos = pos->right; else break ; } return pos; } Position FindMin(AvlTree avl) { while (NULL != avl && NULL != avl->left) avl = avl->left; return avl; } Position FindMax(AvlTree avl) { while (NULL != avl && NULL != avl->right) avl = avl->right; return avl; } void Insert(Element x, AvlTree* pavl) { if (NULL == (*pavl)) { Position tmp = (Position) malloc ( sizeof ( struct AvlNode)); if (NULL == tmp) return ; tmp->data = x; tmp->height = 0; tmp->left = tmp->right = NULL; *pavl = tmp; } else { if (x < Retrieve(*pavl)) //在*pavl的左儿子上插入 { Insert(x, &((*pavl)->left)); if (Height((*pavl)->left) - Height((*pavl)->right) == 2) //不平衡 { if (x < Retrieve((*pavl)->left)) //左儿子的左子树 SingleRotateWithLeftLeft(pavl); else //左儿子的右子树 DoubleRotateWithLeftRight(pavl); } } else if (x > Retrieve(*pavl)) //在*pavl的右儿子上插入 { Insert(x, &((*pavl)->right)); if (Height((*pavl)->right) - Height((*pavl)->left) == 2) //不平衡 { if (x > Retrieve((*pavl)->right)) //右儿子的右子树 SingleRotateWithRightRight(pavl); else //右儿子的左子树 DoubleRotateWithRightLeft(pavl); } } } (*pavl)->height = Max(Height((*pavl)->left), Height((*pavl)->right)) + 1; } void Delete(Element x, AvlTree* pavl) { if (NULL == *pavl) return ; if (x < Retrieve((*pavl))) //go left Delete(x, &((*pavl)->left)); else if (x > Retrieve((*pavl))) //go right Delete(x, &((*pavl)->right)); else if (NULL != (*pavl)->left && NULL != (*pavl)->right) //*pavl has two children { //利用右子树的最小值tmp->data来替代被删除的节点上的值x,然后在右子树上递归的删除值tmp->data Position tmp = FindMin((*pavl)->right); (*pavl)->data = tmp->data; Delete(tmp->data, &((*pavl)->right)); } else //*pavl has none or one child { Position tmp = *pavl; if (NULL == (*pavl)->left) //*pavl has right child *pavl = (*pavl)->right; else if (NULL == (*pavl)->right) //*pavl has left child *pavl = (*pavl)->left; free (tmp); } if (NULL != *pavl) //最后更新*pavl节点上的高度 { (*pavl)->height = Max(Height((*pavl)->left), Height((*pavl)->right)) + 1; if (2 == Height((*pavl)->left) - Height((*pavl)->right)) //not balanced { if (NULL == (*pavl)->left->right) SingleRotateWithLeftLeft(pavl); else DoubleRotateWithLeftRight(pavl); } else if (2 == Height((*pavl)->right) - Height((*pavl)->left)) //not balance { if (NULL == (*pavl)->right->left) SingleRotateWithRightRight(pavl); else DoubleRotateWithRightLeft(pavl); } } } Element Retrieve(Position p) { return p->data; } void SingleRotateWithLeftLeft(Position *pK2) { Position k2 = *pK2; Position k1 = k2->left; k2->left = k1->right; k1->right = k2; k1->height = Max(Height(k1->left), Height(k2)) + 1; k2->height = Max(Height(k2->left), Height(k2->right)) + 1; *pK2 = k1; } void SingleRotateWithRightRight(Position *pK2) { Position k2 = *pK2; Position k1 = k2->right; k2->right = k1->left; k1->left = k2; k1->height = Max(Height(k2), Height(k1->right)) + 1; k2->height = Max(Height(k2->left), Height(k2->right)) + 1; *pK2 = k1; } void DoubleRotateWithLeftRight(Position *pK3) { SingleRotateWithRightRight(&((*pK3)->left)); SingleRotateWithLeftLeft(pK3); } void DoubleRotateWithRightLeft(Position *pK3) { SingleRotateWithLeftLeft(&((*pK3)->right)); SingleRotateWithRightRight(pK3); } void PrintTree(AvlTree avl, int Depth, int ctrl) //ctrl:0=root 1=left 2=right { if (NULL != avl) { std::cout<<std::setw(Depth); if (0 == ctrl) std::cout<< "rt:" ; else if (1 == ctrl) std::cout<< "l" ; else if (2 == ctrl) std::cout<< "r" ; std::cout<<avl->data<<std::endl; PrintTree(avl->left, Depth+3, 1); PrintTree(avl->right, Depth+3, 2); } } |
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数据结构与算法
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