数据结构：二叉查找树的相关操作

二叉查找树的相关操作

二叉查找树是专门用于二叉树的查找，一般的二叉树查找都是通过遍历来实现，二叉查找树能有效提高查找效率。

• 构造一个空的二叉查找树
• 二叉查找树T存在，销毁树T
• 在二叉查找树中查找值为e.key的结点
• 往二叉查找树中插入值为e.key的结点
• 删除二叉查找树中值为key的结点

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代码实现

//  Binary_Search_Tree#include<stdio.h>#include<stdlib.h> #define  TRUE   1#define  FALSE  0#define  OK     1#define  ERROR  0#define  OVERFLOW   -1typedef  int  Status;typedef struct {  int key;  } TElemType;typedef struct BSTNode {    TElemType data;    struct BSTNode *lchild, *rchild;} BSTNode, *BSTree;//  构造一个空的二叉查找树 Status InitBST (BSTree &T) {    T = NULL; }//  销毁树 Status DestroyBST(BSTree &T) {    if(T->lchild != NULL)          DestroyBST(T->lchild);      if(T->rchild != NULL)          DestroyBST(T->rchild);      T = NULL;  }// 若二叉查找树 T 中存在值为 key 的结点，则返回该结点指针，否则返回 NULLBSTree SearchBST(BSTree T, int key) {    if(NULL == T) return NULL; // 查找失败    if(T->data.key == key) return T;    if(T->data.key > key) {        return SearchBST(T->lchild, key);    }    return SearchBST(T->rchild, key);}//  若二叉查找树 T 中不存在值为 e.key 的结点，则插入到 T Status InsertBST(BSTree &T,TElemType e) {    if(NULL == T) {        BSTNode *s;        s = (BSTNode*) malloc (sizeof(BSTNode));        if(NULL == s) return OVERFLOW;        s->data = e;         s->lchild = NULL;        s->rchild = NULL;        T = s;        return TRUE;    }    if(e.key < T->data.key) return InsertBST(T->lchild,e);    if(e.key > T->data.key) return InsertBST(T->rchild,e);    return FALSE;} // 删除结点操作 void DeleteNode(BSTree &p) {    BSTNode *q,*s;    q = p;    if(NULL == p->rchild) {        p = p->lchild;        free(q);    }   else if(NULL == p->lchild) {        p = p->rchild;        free(q);    }   else {        s = p->lchild;        while (s->rchild != NULL) {            q = s;            s = s->rchild;        }        p->data = s->data;        if(q == p)            q->lchild = s->lchild;        else q->rchild = s->lchild;        free(s);    }}// 若二叉查找树 T 中存在值为 key 的结点，则删除 Status DeleteBST(BSTree &T,int key) {    if(NULL == T) return FALSE;    if(key == T->data.key) {        DeleteNode(T);        return TRUE;    }    else if(key < T->data.key)        return DeleteBST(T->lchild,key);    return DeleteBST(T->rchild,key);}//  输出树 void puttree(BSTree &t){    if(NULL == t) return ;    else{        puttree(t->lchild);        printf("%d  ",t->data);        puttree(t->rchild);    }} int main() {    TElemType E;    int i;    int key_1, key_2, key_3;    int a[10];     BSTree t, temp_1, temp_2;    Status temp_3;    printf("enter array a[10](integer):\n");    for(i = 0;i < 10;i++) {     //构造数组a[10]         scanf("%d",&a[i]);    }    InitBST(t);     // 构造一个空的二叉查找树    for(i = 0;i<10;i++) {        E.key = a[i];        InsertBST(t,E);     // 插入值为 E.key的结点     }    printf("Tree is made up from array a[10]:\n");    puttree(t);     // 输出树     printf("\n");    printf("enter key_1(for searching), key_2(for searching), key_3(for deleting):\n");    scanf("%d %d %d",&key_1, &key_2, &key_3);    temp_1 = SearchBST(t,key_1);    if(temp_1) {    // 查找是否有存在结点值为key_1         printf("%d\n", temp_1->data.key);    }   else {        printf("%d can't be found\n",key_1);    }    temp_2 = SearchBST(t,key_2);    if(temp_2) {    // 查找是否有存在结点值为key_2         printf("%d\n", temp_2->data.key);    }   else {        printf("%d can't be found\n",key_2);    }    temp_3 = DeleteBST(t,key_3);    if(temp_3 == TRUE) {    //删除值为key_3的结点         printf("%d has been delete\n", key_3);    } else {        printf("%d can't be found\n",key_3);    }}