查找二：二叉排序树查找

//二叉排序树
#include<iostream>
using namespace std;

typedef struct BiTNode
{
    int data;  //结点数据
    BiTNode *lchild, *rchild; //左右孩子指针
}*BiTree;

//递归查找二叉排序树T中是否存在key
//指针f指向T的双亲，初始值为NULL
//若查找成功，指针p指向该数据元素结点并返回true
//否则指针p指向查找路径上访问的最后一个结点并返回false
bool SearchBT(BiTree T, int key, BiTree f, BiTree *p)
{
    if(!T)
    {
        *p = f;
        return false;
    }

    if(key==T->data)
    {
        *p = T;
        return true;
    }
    else if(key<T->data)
    {
        return SearchBT(T->lchild, key, T, p);
    }
    else
    {
        return SearchBT(T->rchild, key, T, p);
    }
}

//当二叉排序树T中不存在关键字等于key的数据元素时
//插入key并返回true，否则返回false
bool InsertBST(BiTree *T, int key)
{
    BiTree p, s;
    if(SearchBT(*T,key,NULL,&p))
        return false;
    else
    {
        s = new BiTNode;
        s->data = key;
        s->lchild = s->rchild = NULL;
        if(!p)
            *T = s;  //插入s为新的根结点
        else if(key<p->data)
            p->lchild = s; //插入s为左孩子
        else
            p->rchild = s; //插入为s的右孩子
        return true;
    }
}

//从二叉排序树中删除结点p，并重接它的左右子树
bool Delete(BiTree *p)
{
    BiTree q, s;
    if((*p)->rchild==NULL) //若右子树为空
    {
        q = *p;
        *p = (*p)->lchild;
        delete q;
    }
    else if((*p)->lchild==NULL) //若左子树为空
    {
        q = *p;
        *p = (*p)->rchild;
        delete q;
    }
    else //左右子树均不为空
    {
        q = *p;
        s = (*p)->lchild;
        while(s->rchild)
        {
            q = s;
            s = s->rchild;
        }
        (*p)->data = s->data;
        if(q!=*p)
            q->rchild = s->lchild;
        else
            q->lchild = s->lchild;
        delete s;
    }
    return true;
}

//若二叉排序树T存在关键字等于key的数据元素时，删除该结点
bool DeleteBST(BiTree *T, int key)
{
    if(!*T)
        return false;
    else
    {
        if(key==(*T)->data)
            return Delete(T);
        else if(key<(*T)->data)
            return DeleteBST(&(*T)->lchild, key);
        else
            return DeleteBST(&(*T)->rchild,key);
    }
}

void PreOrderPrint(BiTree T)
{
    if(T==NULL)
        return; 
    cout<<T->data<<" ";
    PreOrderPrint(T->lchild);
    PreOrderPrint(T->rchild);
}

int main()
{
    int a[10] = {62,88,58,47,35,73,51,99,37,93};
    BiTree T = NULL;

    for(int i=0;i<10;i++)
        InsertBST(&T,a[i]);
    PreOrderPrint(T);
    cout<<endl;
    DeleteBST(&T,93);
    PreOrderPrint(T);
    cout<<endl;
    DeleteBST(&T,47);
    PreOrderPrint(T);
    cout<<endl;
    
    system("pause");
    return 0;
}