1 // 前綴: STree
 2 
 3 /* 二叉搜索樹 */
 4 // 1. 簡化：使用int作為數據，各個數據互異。
 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 // 創建樹。返回NULL
15 SearchTree STree_Create();
16 // 清空樹並釋放其空間，返回NULL
 

17 SearchTree STree_Disponse( SearchTree Tree );
18 // 將X插入到Tree中，返回新樹
19 SearchTree STree_Insert( SearchTree Tree, STree_T X );
20 void STree_Insert2(SearchTree *pTree, STree_T X);   // 與STree_Insert等價
21 // 將X從Tree中刪除，返回新樹
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位置處的值
28 STree_T STree_Retrieve( STreePosition Pos );
29 // 中序遍歷
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 /* 將結構體定義放在.c文件中，可以更好的封裝模塊 */
  6 typedef struct STreeNode {
  7     STree_T Elem;
  8     SearchTree Left;    // 左子樹
  9     SearchTree Right;   // 右子樹
 10 }STreeNode;
 11 // 樹的遞歸定義
 12 
 13 // 創建樹。返回NULL
 14 SearchTree STree_Create()
 15 {
 16     return NULL;
 17 }
 18 
 19 // 清空樹並釋放其空間，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 // 將X插入到Tree中，返回新樹
 31 SearchTree STree_Insert(SearchTree Tree, STree_T X)
 32 {
 33     if(Tree == NULL) {  // 創建節點
 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) {     // 在左子樹中插入
 42         Tree->Left = STree_Insert(Tree->Left, X);
 43     } else if(X > Tree->Elem) {     // 在右子樹中插入
 44         Tree->Right = STree_Insert(Tree->Right, X);
 45     }
 46     // else X == Tree->Elem，不做任何事
 47     return Tree;
 48 }
 49 // 與Insert等價
 50 void STree_Insert2(SearchTree *pTree, STree_T X)
 51 {
 52     if(pTree == NULL) return ;  // 不是樹，直接返回
 53 
 54     if(*pTree == NULL) {  // 在此處插入
 55         *pTree = (SearchTree)malloc(sizeof(STreeNode));
 56         if(*pTree == NULL) {    // 申請內存失敗，返回
 57             return ;
 58         }else {
 59             (*pTree)->Elem = X;
 60             (*pTree)->Left = (*pTree)->Right = NULL;
 61         }
 62     }else if(X < (*pTree)->Elem) {  // 在左子樹插入
 63         STree_Insert2(&(*pTree)->Left, X);
 64     }else if(X > (*pTree)->Elem) {  // 在右子樹插入
 65         STree_Insert2(&(*pTree)->Right, X);
 66     }
 67     // else X == (*pTree)->Elem, do nothing.
 68 }
 69 
 70 // 將X從Tree中刪除，返回新樹
 71 SearchTree STree_Delete(SearchTree Tree, STree_T X)
 72 {
 73     if(Tree == NULL) {  // 該樹中沒有元素X
 74         return NULL;
 75     }else if (X < Tree->Elem) { // 在左子樹中刪除
 76         Tree->Left = STree_Delete(Tree->Left, X);
 77     }else if (X > Tree->Elem) { // 在右子樹中刪除
 78         Tree->Right = STree_Delete(Tree->Right, X);
 79     }else { // X == Tree->Elem 刪除該節點
 80         if(Tree->Left && Tree->Right) { // 2個非空子樹
 81             // 用右子樹最小值替換Tree的值，並刪除右子樹最小值的節點
 82             STree_T rightMin = STree_FindMin(Tree->Right)->Elem;    // 右子樹不為空，肯定有最小值
 83             Tree->Elem = rightMin;
 84             Tree->Right = STree_Delete(Tree->Right, rightMin);
 85         } else { // 0或1個非空子樹
 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) {  // 在左子樹中找
103         return STree_Find(Tree->Left, X);
104     }else {     // 在右子樹中找
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) {     // 一直向左子樹找，直到該節點無左孩子
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位置處的值
129 STree_T STree_Retrieve(STreePosition Pos)
130 {
131     if(Pos != NULL) {
132         return Pos->Elem;
133     }
134 }
135 // 中序遍歷
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 }

數據結構之查找樹