1 // 前缀: STree
2
3 /* 二叉搜索树 */
4 // 1. 简化：使用int作为数据，各个数据互异。
5
6 #ifndef _TREE_H
7 #define _TREE_H
8
9 typedef int STree_T;
10 struct STreeNode;
11 typedef struct STreeNode *STreePosition;
12 typedef struct STreeNode *SearchTree;
13
14 // 创建树。返回NULL
15 SearchTree STree_Create();
16 // 清空树并释放其空间，返回NULL
17 SearchTree STree_Disponse( SearchTree Tree );
18 // 将X插入到Tree中，返回新树
19 SearchTree STree_Insert( SearchTree Tree, STree_T X );
20 void STree_Insert2(SearchTree *pTree, STree_T X); // 与STree_Insert等价
21 // 将X从Tree中删除，返回新树
22 SearchTree STree_Delete( SearchTree Tree, STree_T X );
23 // 查找X在Tree中的位置
24 STreePosition STree_Find( SearchTree Tree, STree_T X);
25 STreePosition STree_FindMin( SearchTree Tree ); // 最小元素
26 STreePosition STree_FindMax( SearchTree Tree ); // 最大元素
27 // 取Pos位置处的值
28 STree_T STree_Retrieve( STreePosition Pos );
29 // 中序遍历
30 void STree_InOrderTraverse(SearchTree Tree);
31
32 #endif /* _TREE_H */
1 #include <stdlib.h>
2 #include <stdio.h>
3 #include "searchTree.h"
4
5 /* 将结构体定义放在.c文件中，可以更好的封装模块 */
6 typedef struct STreeNode {
7 STree_T Elem;
8 SearchTree Left; // 左子树
9 SearchTree Right; // 右子树
10 }STreeNode;
11 // 树的递归定义
12
13 // 创建树。返回NULL
14 SearchTree STree_Create()
15 {
16 return NULL;
17 }
18
19 // 清空树并释放其空间，返回NULL
20 SearchTree STree_Disponse(SearchTree Tree)
21 {
22 if(Tree != NULL) {
23 STree_Disponse(Tree->Left);
24 STree_Disponse(Tree->Right);
25 free(Tree);
26 }
27 return NULL;
28 }
29
30 // 将X插入到Tree中，返回新树
31 SearchTree STree_Insert(SearchTree Tree, STree_T X)
32 {
33 if(Tree == NULL) { // 创建节点
34 Tree = (SearchTree)malloc(sizeof(STreeNode));
35 if(Tree == NULL) {
36 return NULL;
37 }else {
38 Tree->Elem = X;
39 Tree->Left = Tree->Right = NULL;
40 }
41 } else if(X < Tree->Elem) { // 在左子树中插入
42 Tree->Left = STree_Insert(Tree->Left, X);
43 } else if(X > Tree->Elem) { // 在右子树中插入
44 Tree->Right = STree_Insert(Tree->Right, X);
45 }
46 // else X == Tree->Elem，不做任何事
47 return Tree;
48 }
49 // 与Insert等价
50 void STree_Insert2(SearchTree *pTree, STree_T X)
51 {
52 if(pTree == NULL) return ; // 不是树，直接返回
53
54 if(*pTree == NULL) { // 在此处插入
55 *pTree = (SearchTree)malloc(sizeof(STreeNode));
56 if(*pTree == NULL) { // 申请内存失败，返回
57 return ;
58 }else {
59 (*pTree)->Elem = X;
60 (*pTree)->Left = (*pTree)->Right = NULL;
61 }
62 }else if(X < (*pTree)->Elem) { // 在左子树插入
63 STree_Insert2(&(*pTree)->Left, X);
64 }else if(X > (*pTree)->Elem) { // 在右子树插入
65 STree_Insert2(&(*pTree)->Right, X);
66 }
67 // else X == (*pTree)->Elem, do nothing.
68 }
69
70 // 将X从Tree中删除，返回新树
71 SearchTree STree_Delete(SearchTree Tree, STree_T X)
72 {
73 if(Tree == NULL) { // 该树中没有元素X
74 return NULL;
75 }else if (X < Tree->Elem) { // 在左子树中删除
76 Tree->Left = STree_Delete(Tree->Left, X);
77 }else if (X > Tree->Elem) { // 在右子树中删除
78 Tree->Right = STree_Delete(Tree->Right, X);
79 }else { // X == Tree->Elem 删除该节点
80 if(Tree->Left && Tree->Right) { // 2个非空子树
81 // 用右子树最小值替换Tree的值，并删除右子树最小值的节点
82 STree_T rightMin = STree_FindMin(Tree->Right)->Elem; // 右子树不为空，肯定有最小值
83 Tree->Elem = rightMin;
84 Tree->Right = STree_Delete(Tree->Right, rightMin);
85 } else { // 0或1个非空子树
86 STreeNode *temp = Tree;
87 Tree = Tree->Left == NULL ? Tree->Right : Tree->Left;
88 free(temp);
89 }
90 }
91
92 return Tree;
93 }
94
95 // 查找X在Tree中的位置
96 STreePosition STree_Find(SearchTree Tree, STree_T X)
97 {
98 if(Tree == NULL) { // 未找到
99 return NULL;
100 }else if(Tree->Elem == X) { // 找到
101 return Tree;
102 }else if(X < Tree->Elem) { // 在左子树中找
103 return STree_Find(Tree->Left, X);
104 }else { // 在右子树中找
105 return STree_Find(Tree->Right, X);
106 }
107 }
108
109 STreePosition STree_FindMin(SearchTree Tree)
110 {
111 if(Tree != NULL) {
112 while(Tree->Left != NULL) { // 一直向左子树找，直到该节点无左孩子
113 Tree = Tree->Left;
114 }
115 }
116 return Tree;
117 }
118
119 STreePosition STree_FindMax(SearchTree Tree)
120 {
121 if(Tree != NULL) {
122 while(Tree->Right != NULL) {
123 Tree = Tree->Right;
124 }
125 }
126 return Tree;
127 }
128 // 取Pos位置处的值
129 STree_T STree_Retrieve(STreePosition Pos)
130 {
131 if(Pos != NULL) {
132 return Pos->Elem;
133 }
134 }
135 // 中序遍历
136 void STree_InOrderTraverse(SearchTree Tree)
137 {
138 if(Tree != NULL) {
139 STree_InOrderTraverse(Tree->Left);
140 printf("%d ", Tree->Elem);
141 STree_InOrderTraverse(Tree->Right);
142 }
143 }
searchTree.c