数据结构----二叉搜索树

Posted 2022-12-06 hywhyme

 

 

二叉查找树（Binary Search Tree），（又：二叉搜索树，二叉排序树）它或者是一棵空树，或者是具有下列性质的二叉树： 若它的左子树不空，则左子树上所有结点的值均小于它的根结点的值； 若它的右子树不空，则右子树上所有结点的值均大于它的根结点的值； 它的左、右子树也分别为二叉排序树。 百度百科

 

• 函数Insert将X插入二叉搜索树BST并返回结果树的根结点指针；
• 函数Delete将X从二叉搜索树BST中删除，并返回结果树的根结点指针；如果X不在树中，则打印一行Not Found并返回原树的根结点指针；
• 函数Find在二叉搜索树BST中找到X，返回该结点的指针；如果找不到则返回空指针；
• 函数FindMin返回二叉搜索树BST中最小元结点的指针；

函数FindMax返回二叉搜索树BST中最大元结点的指针。

  1 #include <stdio.h>
  2 #include <stdlib.h>
  3 
  4 
  5 
  6 
  7 
  8 typedef int ElementType;
  9 
 10 typedef struct TNode * Position;
 11 
 12 typedef Position BinTree;
 13 
 14 struct TNode
 15     
 16     ElementType Data;
 17     BinTree Left;
 18     BinTree Right;
 19 ;
 20 
 21 void PreorderTraversal( BinTree BT )     
 22     if(BT)
 23         printf(" %d ",BT->Data);
 24         PreorderTraversal(BT->Left);
 25         PreorderTraversal(BT->Right);
 26     
 27 
 28 void InorderTraversal( BinTree BT )    
 29     if(BT)
 30         InorderTraversal(BT->Left);
 31         printf(" %d ",BT->Data);
 32         InorderTraversal(BT->Right);
 33     
 34 
 35   /* 中序遍历，由裁判实现，细节不表 */
 36 
 37 BinTree Insert( BinTree BST, ElementType X )
 38     //printf("插入%d\\n",X);
 39     BinTree new_node = NULL;
 40     if(BST==NULL)
 41         //printf("建立根\\n");
 42         BST = (Position)malloc(sizeof(struct TNode));
 43         BST->Data = X;
 44         BST->Left = NULL;
 45         BST->Right = NULL;
 46     else
 47         //printf("有根了\\n");
 48         if(X < BST->Data)
 49             //printf("在根的左边\\n");
 50             if(BST->Left)
 51                 Insert(BST->Left,X);
 52             else
 53                 BinTree new_node = (Position)malloc(sizeof(struct TNode));
 54                 new_node->Data = X;
 55                 new_node->Left = NULL;
 56                 new_node->Right = NULL;
 57                 BST->Left = new_node;
 58             
 59         else if(X > BST->Data)
 60             //printf("在根的右边%d  --- %d  \\n",X,BST->Data);
 61                 if(BST->Right)
 62                     Insert(BST->Right,X);
 63                 else
 64                     BinTree new_node = (Position)malloc(sizeof(struct TNode));
 65                     new_node->Data = X;
 66                     new_node->Left = NULL;
 67                     new_node->Right = NULL;
 68                     BST->Right = new_node;
 69             
 70         
 71     
 72     return BST;
 73 
 74 
 75 
 76 Position Find( BinTree BST, ElementType X )
 77     if(BST==NULL)
 78         return NULL;
 79     
 80     if(BST->Data==X)
 81         return BST;
 82     else if(X < BST->Data)
 83         return Find(BST->Left,X);
 84     else if(X > BST->Data)
 85         return Find(BST->Right,X);
 86     
 87 
 88 Position FindMin( BinTree BST )
 89     if(BST==NULL)
 90         return NULL;
 91     
 92     else if(BST->Left==NULL)
 93         return BST;
 94     
 95     else
 96         return (FindMin(BST->Left));
 97     
 98 
 99 Position FindMax( BinTree BST )
100     if(BST==NULL)
101         return NULL;
102     
103     else if(BST->Right==NULL)
104         return BST;
105     
106     else
107         return (FindMax(BST->Right));
108     
109 
110 
111 //删除节点
112 BinTree Delete( BinTree BST, ElementType X )
113     Position temp;
114     if(BST==NULL)
115         printf("Not Found\\n");
116         return BST;
117     
118     else if(X < BST->Data)
119         BST->Left = Delete(BST->Left,X);
120     else if(X > BST->Data)
121         BST->Right = Delete(BST->Right,X);
122     else
123         if(BST->Left && BST->Right)
124             temp = FindMax(BST->Left);
125             BST->Data = temp->Data;
126             BST->Left = Delete(BST->Left,BST->Data);
127         else
128             temp = BST;
129             if(BST->Left)
130                 BST = BST->Left;
131             else
132                 BST = BST->Right;
133             
134             free(temp);
135         
136         return BST;
137     
138         
139 
140 
141 int main()
142 
143     BinTree BST, MinP, MaxP, Tmp;
144     ElementType X;
145     int N, i;
146     BST = NULL;
147     scanf("%d", &N);
148     for ( i=0; i<N; i++ ) 
149         scanf("%d", &X);
150         //printf("%d",X);
151         BST = Insert(BST, X);
152     
153     printf("Preorder:"); PreorderTraversal(BST); printf("\\n");
154     printf("Inorder:"); InorderTraversal(BST); printf("\\n");
155     MinP = FindMin(BST);
156     MaxP = FindMax(BST);
157     scanf("%d", &N);
158     for( i=0; i<N; i++ ) 
159         scanf("%d", &X);
160         Tmp = Find(BST, X);
161         if (Tmp == NULL) printf("%d is not found\\n", X);
162         else 
163             printf("%d is found\\n", Tmp->Data);
164             if (Tmp==MinP) printf("%d is the smallest key\\n", Tmp->Data);
165             if (Tmp==MaxP) printf("%d is the largest key\\n", Tmp->Data);
166         
167     
168     scanf("%d", &N);
169     for( i=0; i<N; i++ ) 
170         scanf("%d", &X);
171         BST = Delete(BST, X);
172     
173     printf("Inorder:"); InorderTraversal(BST); printf("\\n");
174     return 0;
175