/************************************************************
二叉排序树的查找与删除
    Designed BY LU  2014.12.12
************************************************************/

#include<iostream>
#include<malloc.h>
using namespace std;
#define TRUE 1
#define FALSE 0
#define EQ(a,b) ((a)==(b))
#define LT(a,b) ((a)<(b))
#define LQ(a,b) ((a)<=(b))
#define N 10
typedef int KeyType;
struct ElemType
{
    KeyType key;
    int others;
};
typedef ElemType TElemType;
typedef int Status;
typedef struct BiTNode
{
    TElemType data;
    BiTNode *lchild,*rchild; // 左右孩子指针
} BiTNode,*BiTree;

void InitBiTree(BiTree &T)
{
    T=NULL;
}

Status SearchBST(BiTree T, KeyType key, BiTree f, BiTree &p)
{
    if(!T)
    {
        p = f;
        return FALSE;
    }
    else if EQ(key, T->data.key)
    {
        p = T;
        return TRUE;
    }
    else if LT(key, T->data.key)
        return SearchBST(T->lchild, key, T, p);
    else
        return SearchBST(T->rchild, key, T, p);
}

Status InsertBST(BiTree &T, ElemType e)
{
    BiTree p,s;
    if(!SearchBST(T, e.key, NULL, p))
    {
        s = (BiTree)malloc(sizeof(BiTree));
        s->data = e;
        s->lchild = s->rchild = NULL;
        if(!p)
            T = s;
        else if LT(e.key, p->data.key)
            p->lchild = s;
        else
            p->rchild = s;
        return TRUE;
    }
    else return FALSE;
}

Status Delete(BiTree &p)
{
    BiTree q, s;
    if(!p->rchild)
    {
        q = p;
        p = p->lchild;
        free(q);
    }
    else if(!p->lchild)
    {
        q = p;
        p = p->rchild;
        free(q);
    }
    else
    {
        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;
}

Status DeleteBST(BiTree &T, KeyType key)
{
    if(!T)
        return FALSE ;
    else
    {
        if(EQ(key, T->data.key))
            return Delete(T);
        else if(LT(key, T->data.key))
            return DeleteBST(T->lchild, key);
        else
            return DeleteBST(T->rchild, key);
    }
}

void InOrderTraverse(BiTree T,void(*Visit)(TElemType))
{
    if(T)
    {
        InOrderTraverse(T->lchild,Visit);
        Visit(T->data);
        InOrderTraverse(T->rchild,Visit);
    }
}

void print(ElemType c)
{
    cout<<"("<<c.key<<","<<c.others<<") ";
}

int main()
{

    BiTree dt=NULL,f,t;
    int i,p;
    KeyType j;
    ElemType r[N] = {{45,1},{12,2},{53,3},{3,4},{37,5},{24,6},{100,7},{61,8},{90,9},{78,10}};
    InitBiTree(dt);
    for(i = 0; i<N; i++)
        InsertBST(dt,r[i]);
    InOrderTraverse(dt,print);
    cout<<endl;
    cout<<"请输入待查找的值: "<<endl;
    cin>>j;
    p = SearchBST(dt, j,NULL,f);
    if(p)
    {
        cout<<"表中存在此值."<<endl;
        DeleteBST(dt,j);
        cout<<"删除此值后: "<<endl;
        InOrderTraverse(dt,print);
        cout<<endl;
    }

}

1
、设计一个读入一串整数构成一棵二叉排序树的算法。

2、试从二叉排序树中删除一个结点，是该二叉树仍为二叉排序树。