04-树7 二叉搜索树的操作集（30 分）

Posted 2020-10-29 思而不学

本题要求实现给定二叉搜索树的5种常用操作。

函数接口定义：

BinTree Insert( BinTree BST, ElementType X );
BinTree Delete( BinTree BST, ElementType X );
Position Find( BinTree BST, ElementType X );
Position FindMin( BinTree BST );
Position FindMax( BinTree BST );

其中BinTree结构定义如下：

typedef struct TNode *Position;
typedef Position BinTree;
struct TNode{
    ElementType Data;
    BinTree Left;
    BinTree Right;
};

• 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。

裁判测试程序样例：

#include <stdio.h>
#include <stdlib.h>

typedef int ElementType;
typedef struct TNode *Position;
typedef Position BinTree;
struct TNode{
    ElementType Data;
    BinTree Left;
    BinTree Right;
};

void PreorderTraversal( BinTree BT ); /* 先序遍历，由裁判实现，细节不表 */
void InorderTraversal( BinTree BT );  /* 中序遍历，由裁判实现，细节不表 */

BinTree Insert( BinTree BST, ElementType X );
BinTree Delete( BinTree BST, ElementType X );
Position Find( BinTree BST, ElementType X );
Position FindMin( BinTree BST );
Position FindMax( BinTree BST );

int main()
{
    BinTree BST, MinP, MaxP, Tmp;
    ElementType X;
    int N, i;

    BST = NULL;
    scanf("%d", &N);
    for ( i=0; i<N; i++ ) {
        scanf("%d", &X);
        BST = Insert(BST, X);
    }
    printf("Preorder:"); PreorderTraversal(BST); printf("\n");
    MinP = FindMin(BST);
    MaxP = FindMax(BST);
    scanf("%d", &N);
    for( i=0; i<N; i++ ) {
        scanf("%d", &X);
        Tmp = Find(BST, X);
        if (Tmp == NULL) printf("%d is not found\n", X);
        else {
            printf("%d is found\n", Tmp->Data);
            if (Tmp==MinP) printf("%d is the smallest key\n", Tmp->Data);
            if (Tmp==MaxP) printf("%d is the largest key\n", Tmp->Data);
        }
    }
    scanf("%d", &N);
    for( i=0; i<N; i++ ) {
        scanf("%d", &X);
        BST = Delete(BST, X);
    }
    printf("Inorder:"); InorderTraversal(BST); printf("\n");

    return 0;
}
/* 你的代码将被嵌在这里 */

输入样例：

10
5 8 6 2 4 1 0 10 9 7
5
6 3 10 0 5
5
5 7 0 10 3

输出样例：

Preorder: 5 2 1 0 4 8 6 7 10 9
6 is found
3 is not found
10 is found
10 is the largest key
0 is found
0 is the smallest key
5 is found
Not Found
Inorder: 1 2 4 6 8 9

main.c:

  1 #include <stdio.h>
  2 #include <stdlib.h>
  3 
  4 #include "03_01_PTA.h"
  5 #include "stack.h"
  6 
  7 int main()
  8 {
  9     BinTree BST, MinP, MaxP, Tmp;
 10     ElementType X;
 11     int N, i;
 12 
 13     BST = NULL;
 14     scanf("%d", &N);
 15     for(i=0;i<N;i++) {
 16         scanf("%d", &X);
 17         BST = Insert(BST, X);
 18     }
 19     printf("Preorder:"); PreorderTraversal(BST); printf("\n");
 20     MinP = FindMin(BST);
 21     MaxP = FindMax(BST);
 22     scanf("%d", &N);
 23     for(i=0;i<N;i++) {
 24         scanf("%d", &X);
 25         Tmp = Find(BST, X);
 26         if(Tmp == NULL) printf("%d is not found\n", X);
 27         else {
 28             printf("%d is found\n", Tmp->Data);
 29             if(Tmp == MinP) printf("%d is the smallest key\n", Tmp->Data);
 30             if(Tmp == MaxP) printf("%d is the largest key\n", Tmp->Data);
 31         }
 32     }
 33     scanf("%d", &N);
 34     for(i=0;i<N;i++) {
 35         scanf("%d", &X);
 36         BST = Delete(BST, X);
 37     }
 38     printf("Inorder:"); InorderTraversal(BST); printf("\n");
 39 
 40     return 0;
 41 }
 42 
 43 void PreorderTraversal(BinTree BT)
 44 {
 45     BinTree T = BT;
 46     Stack S = CreateStack();
 47     while(T || !IsEmpty(S)) {
 48         while(T) {
 49             printf(" %d", T->Data);
 50             StackPush(T, S);
 51             T = T->Left;
 52         }
 53         if(!IsEmpty(S)) {
 54             T = StackPop(S);
 55             T = T->Right;
 56         }
 57     }
 58 }
 59 
 60 void InorderTraversal(BinTree BT)
 61 {
 62     BinTree T = BT;
 63     Stack S = CreateStack();
 64     while(T || !IsEmpty(S)) {
 65         while(T) {
 66             StackPush(T, S);
 67             T = T->Left;
 68         }
 69         if(!IsEmpty(S)) {
 70             T = StackPop(S);
 71             printf(" %d", T->Data);
 72             T = T->Right;
 73         }
 74     }
 75 }
 76 
 77 BinTree Insert(BinTree BST, ElementType X)
 78 {
 79     if(!BST) {
 80         BST = (BinTree)malloc(sizeof(struct TNode));
 81         BST->Data = X;
 82         BST->Left = BST->Right = NULL;
 83     } else {
 84         if(X < BST->Data) {
 85             BST->Left = Insert(BST->Left, X);
 86         } else if(X > BST->Data) {
 87             BST->Right = Insert(BST->Right, X);
 88         }
 89     }
 90     return BST;
 91 }
 92 
 93 
 94 BinTree Delete(BinTree BST, ElementType X)
 95 {
 96     BinTree Tmp;
 97     if(!BST) printf("Not Found\n");
 98     else {
 99         if(X < BST->Data)
100             BST->Left = Delete(BST->Left, X);           /* 左子树递归删除 */
101         else if(X > BST->Data)
102             BST->Right = Delete(BST->Right, X);         /* 右子树递归删除 */
103         else {                                          /* 找到需要删除的结点 */
104             if(BST->Left && BST->Right) {               /* 被删除的结点有左右子结点 */
105                 Tmp = FindMin(BST->Right);                 /* 在右子树中找到最小结点填充删除结点 */
106                 BST->Data = Tmp->Data;
107                 BST->Right = Delete(BST->Right, BST->Data); /* 递归删除要删除结点的右子树中最小元素 */
108             } else {                                    /* 被删除结点有一个或没有子结点 */
109                 Tmp = BST;
110                 if(!BST->Left)                          /* 有右孩子或者没有孩子 */
111                     BST = BST->Right;
112                 else if(!BST->Right)                    /* 有左孩子，一定要加else，不然BST可能是NULL */
113                     BST = BST->Left;
114                 free(Tmp);                              /* 如无左右孩子直接删除 */
115             }
116         }
117     }
118     return BST;
119 }
120 
121 Position Find(BinTree BST, ElementType X)
122 {
123     if(!BST)
124         return NULL;
125     if(X == BST->Data)
126         return BST;
127     if(X < BST->Data)
128         return Find(BST->Left, X);
129     if(X > BST->Data)
130         return Find(BST->Right, X);
131 }
132 
133 Position FindMin(BinTree BST)
134 {
135     if(BST) {
136         while(BST->Left) {
137             BST = BST->Left;
138         }
139     }
140     return BST;
141 }
142 
143 Position FindMax(BinTree BST)
144 {
145     if(BST) {
146         while(BST->Right) {
147             BST = BST->Right;
148         }
149     }
150     return BST;
151 }

main.c

03_01_PTA.h

 1 #ifndef __03_01_PTA_H_
 2 #define __03_01_PTA_H_
 3 
 4 typedef int ElementType;
 5 typedef struct TNode *Position;
 6 typedef Position BinTree;
 7 struct TNode {
 8     ElementType Data;
 9     BinTree Left;
10     BinTree Right;
11 };
12 
13 void PreorderTraversal(BinTree BT);
14 void InorderTraversal(BinTree BT);
15 
16 BinTree Insert(BinTree BST, ElementType X);
17 BinTree Delete(BinTree BST, ElementType X);
18 Position Find(BinTree BST, ElementType X);
19 Position FindMin(BinTree BST);
20 Position FindMax(BinTree BST);
21 
22 #endif

03_01_PTA.h

stack.c

 1 #include <stdio.h>
 2 #include <stdlib.h>
 3 #include "stack.h"
 4 
 5 Stack CreateStack()
 6 {
 7     Stack s;
 8     s = (Stack)malloc(sizeof(struct SNode));
 9     s->Next = NULL;
10     return s;
11 }
12 
13 int IsEmpty(Stack S)
14 {
15     return (S->Next == NULL);
16 }
17 
18 void StackPush(BinTree X, Stack S)
19 {
20     struct SNode *TmpCell;
21     TmpCell = (Stack)malloc(sizeof(struct SNode));
22     TmpCell->Data = X;
23     TmpCell->Next = S->Next;
24     S->Next = TmpCell;
25 }
26 
27 BinTree StackPop(Stack S)
28 {
29     struct SNode *FirstCell;
30     BinTree TopElem;
31     if(IsEmpty(S)) {
32         printf("Stack Empty");
33         return NULL;
34     } else {
35         FirstCell = S->Next;
36         S->Next = FirstCell->Next;
37         TopElem = FirstCell->Data;
38         free(FirstCell);
39         return TopElem;
40     }
41 }

stack.c

stack.h

 1 #ifndef __STACK_H_
 2 #define __STACK_H_
 3 
 4 #include "03_01_PTA.h"
 5 
 6 //typedef BinTree ElementType;
 7 typedef struct SNode *Stack;
 8 struct SNode {
 9     BinTree Data;
10     Stack Next;
11 };
12 
13 Stack CreateStack();
14 int IsEmpty(Stack S);
15 void StackPush(BinTree X, Stack S);
16 BinTree StackPop(Stack S);
17 
18 #endif

stack.h

Makefile

SOURCE_FILE = stack.c 03_01_PTA.c
STACK_SOURCE_FILE = stack_test.c stack.c

#all: 03_01 stack_test

#stack_test: $(STACK_SOURCE_FILE)
#    gcc $(STACK_SOURCE_FILE) -o stack_test -g -Wall 

03_01:$(SOURCE_FILE)
    gcc $(SOURCE_FILE) -o 03_01 -g -Wall


clean:
    rm -f stack_test 03_01