最近几月一直在自学C语言和数据结构,先是写了排序二叉树,觉得平衡二叉树作为一个经典数据结构,有必要实现一下。
网上看了些资料,在AVL和红黑树之间考虑,最后个人还是倾向于AVL。
不同于标准AVL的是,笔者没有使用平衡因子,直接根据左右孩子的高度差值判断是否平衡。整个平衡二叉树是在普通二叉查找树的基础上修改得到的,对于学习数据结构的同学来说,这样逐步提高难度,写起来挑战性没那么大。
代码经测试是可以运行,并实现插入、删除、修改节点时都可以保持平衡。相对于普通二叉查找树,AVL在查找时效率高耗时短,但为了保持高度平衡,必须牺牲插入和删除操作的复杂度。本文将分步讲解如何编写平衡二叉树,全文最后附有完整代码。
当左右子树的高度差超过1时(即≥2,在实际处理时,等于2即为不平衡,进行调整操作,所以不会出现大于2的情况),整棵树失去平衡。写代码之前先了解AVL是如何使二叉树保持平衡,这里涉及到对节点的旋转操作,分四种情况,左左,右右,左右,右左。下面分别解释:
一、左左单旋转
在节点x的左孩子插入节点b
①x无右孩子,旋转节点a即可达到平衡
②x有右孩子c,旋转节点a后,根据a>c>x,需将节点c移动到a的左子树
函数代码如下:
1 static BTNode *singleRotateLL(BTree *BT, BTNode *phead) 2 {//不平衡情况为左左的单旋转操作 3 BTNode *temp; 4 5 if(phead == NULL) 6 return 0; 7 8 temp = phead->lchild; 9 10 if(temp->rchild != NULL){ 11 phead->lchild = temp->rchild; 12 phead->lchild->height = tree_node_height(BT, phead->lchild); 13 } 14 else 15 phead->lchild = NULL; 16 17 temp->rchild = phead; 18 if(temp->rchild->data == BT->phead->data){ 19 BT->phead = temp; 20 } 21 phead = temp; 22 temp->rchild->height = tree_node_height(BT, temp->rchild); 23 temp->height = tree_node_height(BT, temp); 24 phead->height = tree_node_height(BT, phead); 25 26 return phead; 27 }
二、右右单旋转
在节点x的右孩子插入节点b
①x无左孩子,旋转节点a即可达到平衡
②x有左孩子c,旋转节点a后,根据x>c>a,需将节点c移动到a的右子树
函数代码如下:
1 static BTNode *singleRotateRR(BTree *BT, BTNode *phead) 2 {//不平衡情况为右右的单旋转操作 3 BTNode *temp; 4 5 if(phead == NULL) 6 return 0; 7 8 temp = phead->rchild; 9 10 if(temp->lchild != NULL){ 11 phead->rchild = temp->lchild; 12 phead->rchild->height = tree_node_height(BT, phead->rchild); 13 } 14 else 15 phead->rchild = NULL; 16 17 temp->lchild = phead; 18 if(temp->lchild->data == BT->phead->data){ 19 BT->phead = temp; 20 } 21 phead = temp; 22 temp->lchild->height = tree_node_height(BT, temp->lchild); 23 temp->height = tree_node_height(BT, temp); 24 phead->height = tree_node_height(BT, phead); 25 26 return phead; 27 }
注:需要注意的是节点旋转后,节点赋值和高度的更新,初学者很容易忽略或是弄错赋值顺序
三、左右双旋转
在节点x的右孩子插入节点b
①x无左孩子,②x有左孩子c,这两种情况的处理相同,首先对x节点进行右右单旋转操作,然后对a节点进行左左单旋转操作
函数代码如下:
1 static BTNode *doubleRotateLR(BTree *BT, BTNode *phead) 2 {//不平衡情况为左右的双旋转操作 3 BTNode *temp; 4 5 if(phead == NULL) 6 return 0; 7 8 temp = phead->lchild; 9 phead->lchild = singleRotateRR(BT, temp); 10 temp = phead; 11 phead = singleRotateLL(BT, temp); 12 13 return phead; 14 }
四、右左双旋转
在节点x的右孩子插入节点b
①x无右孩子,②x有右孩子c,这两种情况的处理相同,首先对x节点进行左左单旋转操作,然后对a节点进行右右单旋转操作
函数代码如下:
1 static BTNode *doubleRotateRL(BTree *BT, BTNode *phead) 2 {//不平衡情况为右左的双旋转操作 3 BTNode *temp; 4 5 if(phead == NULL) 6 return 0; 7 8 temp = phead->rchild; 9 phead->rchild = singleRotateLL(BT, temp); 10 temp = phead; 11 phead = singleRotateRR(BT, temp); 12 13 return phead; 14 }
弄清楚了怎样通过旋转达到平衡状态,接下来一步一步构造平衡二叉树。
第一步,我们要在二叉树的节点中加一个属性:高度,在后面的插入和删除函数中将会用到。
结构体代码如下:
1 typedef struct _BTNode{ 2 TYPE data; 3 int height; 4 struct _BTNode *lchild; 5 struct _BTNode *rchild; 6 }BTNode;
第二步,需要添加三个辅助函数,一是求节点的高度,而是遍历求树中每个节点的高度(在删除函数中会用到),三是求两个高度的最大值。
1 static int tree_node_height(BTree *BT, BTNode *phead) 2 {//求节点的高度,写成函数解决指针为空的情况,默认空节点的高度为-1,只有一个根节点的节点的高度为0,每多一层高度加1 3 if(phead != NULL){ 4 if(phead->lchild == NULL && phead->rchild == NULL){ 5 return 0; 6 } 7 else{ 8 return phead->height = max_height(tree_node_height(BT, phead->lchild), tree_node_height(BT, phead->rchild)) + 1; 9 } 10 } 11 else{ 12 return -1; 13 } 14 } 15 16 static void tree_height(BTree *BT, BTNode *phead) 17 {//遍历求树中每个节点的高度 18 if(phead == NULL) 19 return; 20 21 tree_node_height(BT, phead); 22 if(phead->lchild != NULL) 23 tree_node_height(BT, phead->lchild); 24 if(phead->rchild != NULL) 25 tree_node_height(BT, phead->rchild); 26 } 27 28 static int max_height(int height1, int height2) 29 {//求两个高度的最大值 30 if(height1 > height2) 31 return height1; 32 else 33 return height2; 34 }
第三步,插入
插入操作与二叉查找树的操作基本相同,只是在插入后需判断是否平衡,如果不平衡,进行旋转调整。因为BTNode没有使用父节点属性,所以需要用变量存储插入位置,以便调整后可以接回到二叉树上。树顶的根节点需特殊处理
1 static BOOL tree_add(BTree *BT, BTNode *phead, TYPE value) 2 {//按序插入结点 3 if(phead == NULL) 4 return 0; 5 6 if(phead->data == value) 7 return 0; 8 9 else{ 10 if(phead->data > value){ 11 if(phead->lchild == NULL){ 12 BTNode *newnode = (BTNode*)calloc(1, sizeof(BTNode)); 13 newnode->data = value; 14 newnode->lchild = newnode->rchild = NULL; 15 phead->lchild = newnode; 16 } 17 else{ 18 tree_add(BT, phead->lchild, value); 19 20 //判断插入节点后是否平衡,并调整 21 BTNode *root; 22 if(phead = BT->phead) 23 root = phead; 24 else 25 root = phead->lchild; 26 27 if(tree_node_height(BT, root->lchild) - tree_node_height(BT, root->rchild) == 2){ 28 if(root->lchild->data > value){ 29 root = singleRotateLL(BT, root); 30 } 31 else{ 32 root = doubleRotateLR(BT, root); 33 } 34 } 35 phead = root; 36 } 37 } 38 else{ 39 if(phead->rchild == NULL){ 40 BTNode *newnode = (BTNode*)calloc(1, sizeof(BTNode)); 41 newnode->data = value; 42 newnode->lchild = newnode->rchild = NULL; 43 phead->rchild = newnode; 44 } 45 else{ 46 tree_add(BT, phead->rchild, value); 47 48 //判断插入节点后是否平衡,并调整 49 BTNode *root; 50 if(phead = BT->phead) 51 root = phead; 52 else 53 root = phead->rchild; 54 55 if(tree_node_height(BT, root->rchild) - tree_node_height(BT, root->lchild) == 2){ 56 if(root->rchild->data < value){ 57 root = singleRotateRR(BT, root); 58 } 59 else{ 60 root = doubleRotateRL(BT, root); 61 } 62 } 63 phead = root; 64 } 65 } 66 phead->height = tree_node_height(BT, phead); 67 return 1; 68 } 69 70 return 0; 71 }
第四步,删除
平衡二叉树的删除操作比插入更复杂,因为删除后会引起一系列节点高度的改变,删除后将剩余子树接回二叉树时,要分三种情况处理,被删除节点是:顶部根节点、底部叶子(无子树)、普通节点。
1 static BOOL tree_del(BTree *BT, BTNode **phead, TYPE value) 2 {//删除结点 3 BTNode *temp; 4 BTNode *root; 5 int flag; //flag标记被删除的节点,默认顶部节点flag为0,左边节点flag为-1,右边节点flag为1 6 7 if(*phead == NULL) 8 return 0; 9 10 if(*phead == BT->phead){ 11 flag = 0; 12 root = *phead; 13 } 14 15 else if((*phead)->lchild != NULL){ 16 flag = -1; 17 root = (*phead)->lchild; 18 } 19 20 else if((*phead)->rchild != NULL){ 21 flag = 1; 22 root = (*phead)->rchild; 23 } 24 else if((*phead)->lchild == NULL && (*phead)->rchild == NULL) 25 root = *phead; 26 27 if(root->data == value){ 28 if(root->lchild != NULL){ 29 temp = BT->search_max(BT, &root->lchild, 1); 30 temp->lchild = root->lchild; 31 temp->rchild = root->rchild; 32 free(root); 33 root = temp; 34 if(flag == 0) 35 BT->phead = root; 36 else 37 (*phead)->lchild = root; 38 } 39 else if(root->rchild != NULL){ 40 temp = BT->search_min(BT, &root->rchild, 1); 41 temp->lchild = root->lchild; 42 temp->rchild = root->rchild; 43 free(root); 44 root = temp; 45 if(flag == 0) 46 BT->phead = root; 47 else 48 (*phead)->rchild = root; 49 } 50 else{ 51 if(flag == 0) 52 free(*phead); 53 else if(flag = -1){ 54 free((*phead)->lchild); 55 (*phead)->lchild = NULL; 56 } 57 else if(flag = 1){ 58 free((*phead)->rchild); 59 (*phead)->rchild = NULL; 60 } 61 } 62 63 tree_height(BT, BT->phead); //删除节点后,求每个节点的新高度 64 65 if(flag == 0) 66 return 1; 67 if(flag == -1){ 68 if(tree_node_height(BT, (*phead)->rchild) - tree_node_height(BT, (*phead)->lchild) == 2){ 69 if((*phead)->rchild->rchild != NULL){ 70 root = singleRotateRR(BT, *phead); 71 } 72 else{ 73 root = doubleRotateRL(BT, *phead); 74 } 75 } 76 } 77 else{ 78 if(tree_node_height(BT, (*phead)->lchild) - tree_node_height(BT, (*phead)->rchild) == 2){ 79 if((*phead)->lchild->lchild != NULL){ 80 root = singleRotateLL(BT, *phead); 81 } 82 else{ 83 root = doubleRotateLR(BT, *phead); 84 } 85 } 86 } 87 88 return 1; 89 } 90 else if(root->data > value) 91 return BT->del(BT, &root->lchild, value); 92 else 93 return BT->del(BT, &root->rchild, value); 94 95 return 0; 96 }
除了插入和删除操作,其他操作均与普通二叉查找树一样。
如果读者发现错误或有更好的处理方法,请指出,以便修改完善。
头文件binary.h代码:
1 #ifndef BINARY_H 2 #define BINARY_H 3 4 typedef int TYPE; 5 typedef int BOOL; 6 7 typedef struct _BTNode{ 8 TYPE data; 9 int height; 10 struct _BTNode *lchild; 11 struct _BTNode *rchild; 12 }BTNode; 13 14 typedef struct _BTree{ 15 BTNode *phead; 16 17 void(*init)(struct _BTree *BT, TYPE head_value); 18 void(*exit)(struct _BTree *BT); 19 void(*print)(struct _BTree *BT, BTNode *phead); 20 21 BOOL(*add)(struct _BTree *BT, BTNode *phead, TYPE value); 22 BOOL(*del)(struct _BTree *BT, BTNode **phead, TYPE value); 23 BOOL(*del_tree)(struct _BTree *BT, BTNode **phead); 24 BOOL(*alter)(struct _BTree *BT, BTNode *phead, TYPE value, TYPE new_value); 25 BTNode *(*search)(struct _BTree *BT, BTNode *phead, TYPE value); 26 27 BTNode *(*search_min)(struct _BTree *BT, BTNode **phead, int flag); 28 BTNode *(*search_max)(struct _BTree *BT, BTNode **phead, int flag); 29 30 void(*pre_traverse)(struct _BTree *BT, BTNode *phead); 31 void(*mid_traverse)(struct _BTree *BT, BTNode *phead); 32 void(*last_traverse)(struct _BTree *BT, BTNode *phead); 33 34 //以下为实现AVL所需函数 35 int (*node_height)(_BTree *BT, BTNode *phead); 36 void (*height)(_BTree *BT, BTNode *phead); 37 int (*max_height)(int height1, int height2); 38 BTNode *(*singleRotateLL)(_BTree *BT, BTNode *phead); 39 BTNode *(*singleRotateRR)(_BTree *BT, BTNode *phead); 40 BTNode *(*doubleRotateLR)(_BTree *BT, BTNode *phead); 41 BTNode *(*doubleRotateRL)(_BTree *BT, BTNode *phead); 42 }BTree; 43 44 void tree_init(BTree *BT, TYPE value); 45 void tree_exit(BTree *BT); 46 47 #endif
源文件binary.cpp代码:
1 #include <stdio.h> 2 #include <string.h> 3 #include <stdlib.h> 4 5 #include "binary.h" 6 7 void tree_init(BTree *BT, TYPE head_value); 8 void tree_exit(BTree *BT); 9 void tree_print(BTree *BT, BTNode *phead); 10 static BOOL tree_add(BTree *BT, BTNode *phead, TYPE value); 11 static BOOL tree_del(BTree *BT, BTNode **phead, TYPE value); 12 static BOOL tree_del_tree(BTree *BT, BTNode **phead); 13 static BOOL tree_alter(BTree *BT, BTNode *phead, TYPE value, TYPE new_value); 14 static BTNode *tree_search(BTree *BT, BTNode *phead, TYPE value); 15 static BTNode *tree_search_min(BTree *BT, BTNode **phead, int flag); 16 static BTNode *tree_search_max(BTree *BT, BTNode **phead, int flag); 17 static void tree_pre_traverse(BTree *BT, BTNode *phead); 18 static void tree_mid_traverse(BTree *BT, BTNode *phead); 19 static void tree_last_traverse(BTree *BT, BTNode *phead); 20 21 //以下为实现AVL所需函数 22 static int tree_node_height(BTree *BT, BTNode *phead); 23 static void tree_height(BTree *BT, BTNode *phead); 24 static int max_height(int height1, int height2); 25 static BTNode *singleRotateLL(BTree *BT, BTNode *phead); 26 static BTNode *singleRotateRR(BTree *BT, BTNode *phead); 27 static BTNode *doubleRotateLR(BTree *BT, BTNode *phead); 28 static BTNode *doubleRotateRL(BTree *BT, BTNode *phead); 29 30 31 void tree_init(BTree *BT, TYPE head_value) 32 {//初始化 33 BT->phead = (BTNode*)calloc(1, sizeof(BTNode)); 34 BT->phead->data = head_value; 35 36 BT->phead->lchild = BT->phead->rchild = NULL; 37 38 BT->add = tree_add; 39 BT->del = tree_del; 40 BT->print = tree_print; 41 BT->del_tree = tree_del_tree; 42 BT->alter = tree_alter; 43 BT->search = tree_search; 44 BT->search_min = tree_search_min; 45 BT->search_max = tree_search_max; 46 BT->pre_traverse = tree_pre_traverse; 47 BT->mid_traverse = tree_mid_traverse; 48 BT->last_traverse = tree_last_traverse; 49 BT->exit = tree_exit; 50 51 BT->node_height = tree_node_height; 52 BT->height = tree_height; 53 BT->max_height = max_height; 54 BT->singleRotateLL = singleRotateLL; 55 BT->singleRotateRR = singleRotateRR; 56 BT->doubleRotateLR = doubleRotateLR; 57 BT->doubleRotateRL = doubleRotateRL; 58 } 59 60 void tree_exit(BTree *BT) 61 {//结束操作 62 if(BT != NULL) 63 BT->del_tree(BT, &BT->phead); 64 } 65 66 void tree_print(BTree *BT, BTNode *phead) 67 {//打印结点 68 if(phead != NULL) 69 printf("%d\n", phead->data); 70 } 71 72 static BOOL tree_add(BTree *BT, BTNode *phead, TYPE value) 73 {//按序插入结点 74 if(phead == NULL) 75 return 0; 76 77 if(phead->data == value) 78 return 0; 79 80 else{ 81 if(phead->data > value){ 82 if(phead->lchild == NULL){ 83 BTNode *newnode = (BTNode*)calloc(1, sizeof(BTNode)); 84 newnode->data = value; 85 newnode->lchild = newnode->rchild = NULL; 86 phead->lchild = newnode; 87 } 88 else{ 89 tree_add(BT, phead->lchild, value); 90 91 //判断插入节点后是否平衡,并调整 92 BTNode *root; 93 if(phead = BT->phead) 94 root = phead; 95 else 96 root = phead->lchild; 97 98 if(tree_node_height(BT, root->lchild) - tree_node_height(BT, root->rchild) == 2){ 99 if(root->lchild->data > value){ 100 root = singleRotateLL(BT, root); 101 } 102 else{ 103 root = doubleRotateLR(BT, root); 104 } 105 } 106 phead = root; 107 } 108 } 109 else{ 110 if(phead->rchild == NULL){ 111 BTNode *newnode = (BTNode*)calloc(1, sizeof(BTNode)); 112 newnode->data = value; 113 newnode->lchild = newnode->rchild = NULL; 114 phead->rchild = newnode; 115 } 116 else{ 117 tree_add(BT, phead->rchild, value); 118 119 //判断插入节点后是否平衡,并调整 120 BTNode *root; 121 if(phead = BT->phead) 122 root = phead; 123 else 124 root = phead->rchild; 125 126 if(tree_node_height(BT, root->rchild) - tree_node_height(BT, root->lchild) == 2){ 127 if(root->rchild->data < value){ 128 root = singleRotateRR(BT, root); 129 } 130 else{ 131 root = doubleRotateRL(BT, root); 132 } 133 } 134 phead = root; 135 } 136 } 137 phead->height = tree_node_height(BT, phead); 138 return 1; 139 } 140 141 return 0; 142 } 143 144 static BOOL tree_del(BTree *BT, BTNode **phead, TYPE value) 145 {//删除结点 146 BTNode *temp; 147 BTNode *root; 148 int flag; //flag标记被删除的节点,默认顶部节点flag为0,左边节点flag为-1,右边节点flag为1 149 150 if(*phead == NULL) 151 return 0; 152 153 if(*phead == BT->phead){ 154 flag = 0; 155 root = *phead; 156 } 157 158 else if((*phead)->lchild != NULL){ 159 flag = -1; 160 root = (*phead)->lchild; 161 } 162 163 else if((*phead)->rchild != NULL){ 164 flag = 1; 165 root = (*phead)->rchild; 166 } 167 else if((*phead)->lchild == NULL && (*phead)->rchild == NULL) 168 root = *phead; 169 170 if(root->data == value){ 171 if(root->lchild != NULL){ 172 temp = BT->search_max(BT, &root->lchild, 1); 173 temp->lchild = root->lchild; 174 temp->rchild = root->rchild; 175 free(root); 176 root = temp; 177 if(flag == 0) 178 BT->phead = root; 179 else 180 (*phead)->lchild = root; 181 } 182 else if(root->rchild != NULL){ 183 temp = BT->search_min(BT, &root->rchild, 1); 184 temp->lchild = root->lchild; 185 temp->rchild = root->rchild; 186 free(root); 187 root = temp; 188 if(flag == 0) 189 BT->phead = root; 190 else 191 (*phead)->rchild = root; 192 } 193 else{ 194 if(flag == 0) 195 free(*phead); 196 else if(flag = -1){ 197 free((*phead)->lchild); 198 (*phead)->lchild = NULL; 199 } 200 else if(flag = 1){ 201 free((*phead)->rchild); 202 (*phead)->rchild = NULL; 203 } 204 } 205 206 tree_height(BT, BT->phead); //删除节点后,求每个节点的新高度 207 208 if(flag == 0) 209 return 1; 210 if(flag == -1){ 211 if(tree_node_height(BT, (*phead)->rchild) - tree_node_height(BT, (*phead)->lchild) == 2){ 212 if((*phead)->rchild->rchild != NULL){ 213 root = singleRotateRR(BT, *phead); 214 } 215 else{ 216 root = doubleRotateRL(BT, *phead); 217 } 218 } 219 } 220 else{ 221 if(tree_node_height(BT, (*phead)->lchild) - tree_node_height(BT, (*phead)->rchild) == 2){ 222 if((*phead)->lchild->lchild != NULL){ 223 root = singleRotateLL(BT, *phead); 224 } 225 else{ 226 root = doubleRotateLR(BT, *phead); 227 } 228 } 229 } 230 231 return 1; 232 } 233 else if(root->data > value) 234 return BT->del(BT, &root->lchild, value); 235 else 236 return BT->del(BT, &root->rchild, value); 237 238 return 0; 239 } 240 241 static BOOL tree_del_tree(BTree *BT, BTNode **phead) 242 {//删除二叉树 243 if(*phead == NULL) 244 return 0; 245 246 if((*phead)->lchild != NULL) 247 BT->del_tree(BT, &(*phead)->lchild); 248 if((*phead)->rchild != NULL) 249 BT->del_tree(BT, &(*phead)->rchild); 250 251 free(*phead); 252 *phead = NULL; 253 254 return 1; 255 } 256 257 static BOOL tree_alter(BTree *BT, BTNode *phead, TYPE value, TYPE new_value) 258 {//更改结点的值(先删除,后插入) 259 if(phead == NULL) 260 return 0; 261 262 if(value == new_value) 263 return 1; 264 265 if(BT->del(BT, &phead, value) != 0){ 266 if(BT->add(BT, phead, new_value) != 0) 267 return 1; 268 else 269 return 0; 270 } 271 else 272 return 0; 273 } 274 275 static BTNode *tree_search(BTree *BT, BTNode *phead, TYPE value) 276 {//查找结点 277 BTNode *temp; 278 279 if(phead == NULL) 280 return NULL; 281 282 if(phead->data == value) 283 return phead; 284 if(phead->lchild != NULL){ 285 temp = BT->search(BT, phead->lchild, value); 286 if(temp != NULL) 287 return temp; 288 } 289 if(phead->rchild != NULL){ 290 temp = BT->search(BT, phead->rchild, value); 291 if(temp != NULL) 292 return temp; 293 } 294 295 return NULL; 296 } 297 298 static BTNode *tree_search_min(BTree *BT, BTNode **phead, int flag) 299 {//查找最小结点 300 BTNode *temp; 301 302 if(*phead == NULL) 303 return NULL; 304 305 if((*phead)->lchild == NULL){ 306 temp = *phead; 307 if(flag == 1) 308 *phead = (*phead)->rchild; 309 return temp; 310 } 311 else 312 return BT->search_min(BT, &(*phead)->lchild, flag); 313 } 314 315 static BTNode *tree_search_max(BTree *BT, BTNode **phead, int flag) 316 {//查找最大结点 317 BTNode *temp; 318 319 if(*phead == NULL) 320 return NULL; 321 322 if((*phead)->rchild == NULL){ 323 temp = *phead; 324 if(flag == 1) 325 *phead = (*phead)->lchild; 326 return temp; 327 } 328 else 329 return BT->search_max(BT, &(*phead)->rchild, flag); 330 } 331 332 static void tree_pre_traverse(BTree *BT, BTNode *phead) 333 {//先序遍历二叉树 334 if(phead == NULL) 335 return; 336 337 BT->print(BT, phead); 338 if(phead->lchild != NULL) 339 BT->pre_traverse(BT, phead->lchild); 340 if(phead->rchild != NULL) 341 BT->pre_traverse(BT, phead->rchild); 342 } 343 344 static void tree_mid_traverse(BTree *BT, BTNode *phead) 345 {//中序遍历二叉树 346 if(phead == NULL) 347 return; 348 349 if(phead->lchild != NULL) 350 BT->mid_traverse(BT, phead->lchild); 351 BT->print(BT, phead); 352 if(phead->rchild != NULL) 353 BT->mid_traverse(BT, phead->rchild); 354 } 355 356 static void tree_last_traverse(BTree *BT, BTNode *phead) 357 {//后序遍历二叉树 358 if(phead == NULL) 359 return; 360 361 if(phead->lchild != NULL) 362 BT->last_traverse(BT, phead->lchild); 363 if(phead->rchild != NULL) 364 BT->last_traverse(BT, phead->rchild); 365 BT->print(BT, phead); 366 } 367 368 static int tree_node_height(BTree *BT, BTNode *phead) 369 {//求节点的高度,写成函数解决指针为空的情况,默认空节点的高度为-1,只有一个根节点的节点的高度为0,每多一层高度加1 370 if(phead != NULL){ 371 if(phead->lchild == NULL && phead->rchild == NULL){ 372 return 0; 373 } 374 else{ 375 return phead->height = max_height(tree_node_height(BT, phead->lchild), tree_node_height(BT, phead->rchild)) + 1; 376 } 377 } 378 else{ 379 return -1; 380 } 381 } 382 383 static void tree_height(BTree *BT, BTNode *phead) 384 {//遍历求树中每个节点的高度 385 if(phead == NULL) 386 return; 387 388 tree_node_height(BT, phead); 389 if(phead->lchild != NULL) 390 tree_node_height(BT, phead->lchild); 391 if(phead->rchild != NULL) 392 tree_node_height(BT, phead->rchild); 393 } 394 395 static int max_height(int height1, int height2) 396 {//求两个高度的最大值 397 if(height1 > height2) 398 return height1; 399 else 400 return height2; 401 } 402 403 static BTNode *singleRotateLL(BTree *BT, BTNode *phead) 404 {//不平衡情况为左左的单旋转操作 405 BTNode *temp; 406 407 if(phead == NULL) 408 return 0; 409 410 temp = phead->lchild; 411 412 if(temp->rchild != NULL){ 413 phead->lchild = temp->rchild; 414 phead->lchild->height = tree_node_height(BT, phead->lchild); 415 } 416 else 417 phead->lchild = NULL; 418 419 temp->rchild = phead; 420 if(temp->rchild->data == BT->phead->data){ 421 BT->phead = temp; 422 } 423 phead = temp; 424 temp->rchild->height = tree_node_height(BT, temp->rchild); 425 temp->height = tree_node_height(BT, temp); 426 phead->height = tree_node_height(BT, phead); 427 428 return phead; 429 } 430 431 static BTNode *singleRotateRR(BTree *BT, BTNode *phead) 432 {//不平衡情况为右右的单旋转操作 433 BTNode *temp; 434 435 if(phead == NULL) 436 return 0; 437 438 temp = phead->rchild; 439 440 if(temp->lchild != NULL){ 441 phead->rchild = temp->lchild; 442 phead->rchild->height = tree_node_height(BT, phead->rchild); 443 } 444 else 445 phead->rchild = NULL; 446 447 temp->lchild = phead; 448 if(temp->lchild->data == BT->phead->data){ 449 BT->phead = temp; 450 } 451 phead = temp; 452 temp->lchild->height = tree_node_height(BT, temp->lchild); 453 temp->height = tree_node_height(BT, temp); 454 phead->height = tree_node_height(BT, phead); 455 456 return phead; 457 } 458 static BTNode *doubleRotateLR(BTree *BT, BTNode *phead) 459 {//不平衡情况为左右的双旋转操作 460 BTNode *temp; 461 462 if(phead == NULL) 463 return 0; 464 465 temp = phead->lchild; 466 phead->lchild = singleRotateRR(BT, temp); 467 temp = phead; 468 phead = singleRotateLL(BT, temp); 469 470 return phead; 471 } 472 473 static BTNode *doubleRotateRL(BTree *BT, BTNode *phead) 474 {//不平衡情况为右左的双旋转操作 475 BTNode *temp; 476 477 if(phead == NULL) 478 return 0; 479 480 temp = phead->rchild; 481 phead->rchild = singleRotateLL(BT, temp); 482 temp = phead; 483 phead = singleRotateRR(BT, temp); 484 485 return phead; 486 } 487 488 int main(int argc, char* argv[]) 489 {//测试 490 BTree testtree; 491 testtree.init = tree_init; 492 testtree.init(&testtree, 9); 493 494 testtree.add(&testtree, testtree.phead, 4); 495 testtree.add(&testtree, testtree.phead, 5); 496 testtree.add(&testtree, testtree.phead, 6); 497 testtree.add(&testtree, testtree.phead, 1); 498 testtree.add(&testtree, testtree.phead, 7); 499 testtree.add(&testtree, testtree.phead, 8); 500 testtree.add(&testtree, testtree.phead, 11); 501 testtree.add(&testtree, testtree.phead, 10); 502 503 testtree.pre_traverse(&testtree, testtree.phead); 504 printf("\n"); 505 testtree.mid_traverse(&testtree, testtree.phead); 506 printf("\n"); 507 testtree.last_traverse(&testtree, testtree.phead); 508 printf("\n"); 509 510 printf("%d\n", (testtree.search(&testtree, testtree.phead, 8))->data); 511 printf("\n"); 512 513 testtree.del(&testtree, &testtree.phead, 4); 514 testtree.del(&testtree, &testtree.phead, 1); 515 testtree.del(&testtree, &testtree.phead, 6); 516 testtree.alter(&testtree, testtree.phead, 9, 2); 517 518 testtree.pre_traverse(&testtree, testtree.phead); 519 printf("\n"); 520 testtree.mid_traverse(&testtree, testtree.phead); 521 printf("\n"); 522 testtree.last_traverse(&testtree, testtree.phead); 523 printf("\n"); 524 525 return 0; 526 }