[数据结构与算法] : 二叉查找树

Posted 2020-10-06 moon1992

头文件

 1 typedef int ElementType;
 2 #ifndef _TREE_H_
 3 #define _TREE_H_
 4 
 5 struct TreeNode;
 6 typedef struct TreeNode *Position;
 7 typedef struct TreeNode *SearchTree;
 8 
 9 SearchTree MakeEmpty(SearchTree T);
10 Position Find(ElementType X, SearchTree T);
11 Position FindMin(SearchTree T);
12 Position FindMin2(SearchTree T);
13 Position FindMax2(SearchTree T);
14 SearchTree Insert(ElementType X, SearchTree T);
15 SearchTree Delete(ElementType X, SearchTree T);
16 ElementType Retrieve(Position P);
17 
18 #endif

 

源文件

  1 #include "tree.h"
  2 #include "fatal.h"
  3 #include <malloc.h>
  4 
  5 struct TreeNode
  6 {
  7     ElementType Element;
  8     SearchTree  Left;
  9     SearchTree  Right;
 10 };
 11 
 12 // 先清空左子树, 再清空又子树, 再释放自身节点
 13 SearchTree MakeEmpty(SearchTree T)
 14 {
 15     if(T != NULL)
 16     {
 17         MakeEmpty(T->Left);
 18         MakeEmpty(T->Right);
 19         free(T);
 20     }
 21     return NULL; // 递归终止条件
 22 }
 23 
 24 // 查找, 类似二分查找
 25 Position Find(ElementType X, SearchTree T)
 26 {
 27     if(T == NULL) // 递归终止条件
 28         return NULL;
 29     if(X < T->Element)
 30         return Find(X, T->Left);
 31     else if(X > T->Element)
 32         return Find(X, T->Right);
 33     else
 34         return T;
 35 }
 36 
 37 Position FindMin(SearchTree T) // 递归实现
 38 {
 39     if(T == NULL) // 防止非法输入
 40         return NULL;
 41     if(T->Left == NULL) // 递归终止
 42         return T;
 43     else
 44         return FindMin(T->Left);
 45 }
 46 
 47 Position FindMin2(SearchTree T) // 非递归实现
 48 {
 49     if(T == NULL)
 50         return NULL;
 51     while(T->Left != NULL)
 52         T = T->Left;
 53     return T;
 54 }
 55 
 56 Position FindMax(SearchTree T)
 57 {
 58     if(T == NULL)
 59         return NULL;
 60     if(T->Right == NULL)
 61         return T;
 62     else
 63         return FindMax(T->Right);
 64 }
 65 
 66 Position FindMax2(SearchTree T)
 67 {
 68     if(T == NULL)
 69         return NULL;
 70     while(T->Right != NULL)
 71         T = T->Right;
 72     return T;
 73 }
 74 
 75 // 插入
 76 SearchTree Insert(ElementType X, SearchTree T)
 77 {
 78     if(T == NULL) // 如果T为NULL, 创建节点, 递归终止条件
 79     {
 80         T = (SearchTree)malloc(sizeof(struct TreeNode));
 81         if(T == NULL)
 82             FatalError("Out of space!");
 83         else
 84         {
 85             T->Element = X;
 86             T->Left = T->Right = NULL;
 87         }
 88     }
 89     else if(X < T->Element)
 90         T->Left = Insert(X, T->Left);
 91     else if(X > T->Element)
 92         T->Right = Insert(X, T->Right);
 93     // 如果X已经在数中, 则什么也不做
 94     return T; // Do not forget this line!!
 95 }
 96 
 97 // 删除
 98 SearchTree Delete(ElementType X, SearchTree T)
 99 {
100     Position TempCell;
101     if(T == NULL) // 递归终止
102         Error("Element not found!");
103     else if(X < T->Element)
104         T->Left = Delete(X, T->Left);
105     else if(X > T->Element)
106         T->Right = Delete(X, T->Right);
107     else if(T->Left && T->Right)  // Two children
108     {
109         TempCell = FindMin(T->Right);// 找一个替身, 右子树的最小值
110         T->Element = TempCell->Element;
111         T->Right = Delete(T->Element, T->Right);// 替身已经放到T->Element, 再从右子树删除该值即可
112     }
113     else                          // One or zero childern
114     {
115         TempCell = T;
116         if(T->Left == NULL)
117             T = T->Right;
118         else if(T->Right = NULL)
119             T = T->Left;
120         free(TempCell);
121     }
122     return T; // Do not forget this line!!
123 }
124 
125 ElementType Retrieve(Position P)
126 {
127     return P->Element;
128 }

 

测试文件

 1 #include "tree.h"
 2 #include <stdio.h>
 3 
 4 int main()
 5 {
 6     SearchTree T;
 7     Position P;
 8     int i = 0, j = 0;
 9 
10     T = MakeEmpty(NULL);
11     for( i = 0; i < 50; i++, j = ( j + 7 ) % 50 )
12         T = Insert( j, T );
13     for( i = 0; i < 50; i++ )
14         if( ( P = Find( i, T ) ) == NULL || Retrieve( P ) != i )
15             printf( "Error at %d\n", i );
16 
17     for( i = 0; i < 50; i += 2 )
18         T = Delete( i, T );
19 
20     for( i = 1; i < 50; i += 2 )
21         if( ( P = Find( i, T ) ) == NULL || Retrieve( P ) != i )
22             printf( "Error at %d\n", i );
23     for( i = 0; i < 50; i += 2 )
24         if( ( P = Find( i, T ) ) != NULL )
25             printf( "Error at %d\n", i );
26 
27     printf( "Min is %d, Max is %d\n", Retrieve( FindMin2( T ) ),
28                Retrieve( FindMax2( T ) ) );
29 
30     return 0;
31 }