二叉搜索树的建立

二叉搜索树最大特征是：左边子结点的值<当前结点的值，右边子结点的值＞当前结点的值。

依照这个特征，可以使用递归和非递归两种方式建立一颗二叉搜索树。

下面是我的代码，分明列举了递归和非递归的建立方式。最初写的代码与正确版本大致相同，但程序总是运行不通过，debug后发现问题在于指针操作错误。自以为对c语言非常熟稔了，但还是犯下如此幼稚的错误，所以贴出这个错误，作为一个警示。

2014/5/24 ps:原来二叉搜索树最难的地方在于删除操作，所以补充一个删除操作。此外，还明白了书本介绍二叉搜索树的原因，因为很多更复杂的树结构，是以此为基础的，如b树，b+树，avl树等等。

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

typedef struct NODE
{
    NODE * pleft;
    NODE * pright;
    int ivalue;
} node;

/*  错误示例，实际上这个函数并没有连接起新建的结点

void insert_bitree(node *pt, int value)
{

    if(pt == NULL)
    {
        pt = (node *) malloc ( sizeof(node) );
        pt->ivalue = value;
        pt->pleft = NULL;
        pt->pright = NULL;
        return ;
    }
    else if( value < pt->ivalue)
    {
        insert_bitree(pt->pleft, value);   
    }
    else
    {
        insert_bitree(pt->pright, value);
    }

}

*/



void insert_bitree(node **ppt, int value) //递归方式1
{

    if(*ppt == NULL)
    {
        *ppt = (node *) malloc ( sizeof(node) );
        (*ppt)->ivalue = value;
        (*ppt)->pleft = NULL;
        (*ppt)->pright = NULL;
        return ;
    }
    else if( value < (*ppt)->ivalue)
    {
        insert_bitree(&((*ppt)->pleft), value); //将指向指针的指针重定位到当前结点的pleft
    }
    else
    {
        insert_bitree(&((*ppt)->pright), value); //将指向指针的指针重定位到当前结点的pright
    }

}







node* create_searchtree(node *t, int  temp)   //递归方式2
{  
    if (t == NULL) {    // 若当前树为空  
        t = (node *)malloc(sizeof(node) * 1);  
        if (t == NULL) {  
            printf("内存分配失败!
");  
            exit(EXIT_FAILURE);  
        }  
        t->ivalue = temp;  
        t->pleft = NULL;  
        t->pright = NULL;  
    }else if (t->ivalue  > temp) {   // 如果比当前结点小，则插入左子树  
        t->pleft = create_searchtree(t->pleft, temp);  
    }else if (t->ivalue < temp){    // 如果比当前结点大，则插入右子树  
        t->pright = create_searchtree(t->pright, temp);  
    }  
   
    return t;  
} 



node * creat_bitree(int value[], int len) //非递归方式
{
    int i, flag;

    node *before;
    node *tmp;
    node *pt = (node *)malloc( sizeof(node) );

    
    
    pt->ivalue = value[0];
    pt->pleft = pt->pright = NULL;
    
    

    flag = 0;
    for(i = 1; i < len; i++)
    {
        tmp = pt;
        while(tmp != NULL)
        {
            if ( value[i] < (tmp)->ivalue)
            {
                before = tmp; // 存储当前结点的位置
                flag = -1;  //标志位，表明向左子树探索
                tmp = (tmp)->pleft;
                
                
            }
            else
            {
                before = tmp;
                flag = 1;
                tmp = tmp->pright;
            }



        }
        
            if(flag == -1) //将输入值插入当前结点的左子树
            {
                before->pleft = (node *) malloc (sizeof(node) );
                before->pleft->ivalue = value[i];
                before->pleft->pleft = before->pleft->pright = NULL;
            }
            else if( flag == 1)
            {

                before->pright = (node *) malloc (sizeof(node) );
                before->pright->ivalue = value[i];
                before->pright->pleft = before->pright->pright = NULL;
            }
        
        
    }

    return pt;

}


void preorder(node *pt)  //先序访问二叉树
{
    if(pt != NULL)
    {
        printf("%d
", pt->ivalue);
        preorder(pt->pleft);
        preorder(pt->pright);
    }
}

void postorder(node *pt)
{
    if(pt != NULL)
    {
        postorder(pt->pleft);
        postorder(pt->pright);
        printf("%d
", pt->ivalue);
    }
}


int main()
{

    
    int a[8] = {1, 2, 7, 4, 5, 19, 9, 3};
    int len = sizeof(a) / sizeof(int);





#if 1
    int i;
    node *pt = (node *)malloc(sizeof(node));
    assert(pt != NULL);
    pt->ivalue = a[0];
    pt->pleft = pt->pright = NULL;
    for(i = 1; i < 8; i++)
    {

        //pt = create_searchtree(pt, a[i]);
        insert_bitree(&pt, a[i]);


    }
#else 

    node *pt = creat_bitree(a, len);

#endif


    preorder(pt);

    return 0;
}

node * find_elem(int x, node * t)
{
    if( t == NULL)
        return NULL;
    if( x < t->ivalue)
        return find_elem(x, t->pleft);
    else if ( x > t->ivalue)
        return find_elem(x, t->pright);
    else
        return t;
}
 
node * find_min(node *t)
{
    if( t == NULL)
        return NULL;
    else if( t->pleft == NULL)
        return t;
    else
        return find_min(t->pleft);
}
 
node * delete_elem(int x, node *t)
{
    node * tmp;
 
    if( t == NULL) // 已到树底，并且树中不存在该元素
    {
        printf("element: %d doesn't exist
", x);
        exit(-1);
    }
    else if( x < t->ivalue ) // 进入左子树
        t->pleft = delete_elem(x, t->pleft );
    else  if( x > t->ivalue )
        t->pright = delete_elem(x, t->pright);
    else if( t->pleft && t->pright) // 找到该元素，但该元素还有两个子节点，从最右端节点找到最小点，进行替换该元素所在节点，替换后该树仍为二叉搜索树
    {
        tmp  = find_min(t->pright);
        t->ivalue = tmp->ivalue;
        t->pright = delete_elem(t->ivalue, t->pright);
    }
    else // 找到该元素，但该元素仅有一个子节点
    {
        tmp = t;
        if( t->pleft == NULL)
            t = t->pright;
        else if( t->pright == NULL)
            t = t->pleft;
        free(tmp);
    }
    return t;
}