二叉排序树的实现

1. 编写SearchBST(T, key)与InsertBST(T, key)的伪代码，并实现

查找

//伪代码
SearchBST(T, key)
{
    if (T为空 || T->key == key)
        return T;
    if (key > T->key)
        return SearchBST(T->rchild, key);
    else
        return SearchBST(T->lchild, key);
}
//代码实现
BSTree SearchBST(BSTree T,int key)
{
    if (T == NULL || T->key == key)
        return T;
    if (key > T->key)
        return SearchBST(T->rchild, key);
    else
        return SearchBST(T->lchild, key);
}

插入

//伪代码
InsertBST(T, key)
{
    if(T为空)
    {
        T->key = key;
        T->lchild = T->rchild = NULL;
    }
    else if (key == T->key)
        return;
    else if(key > T->key)
        Insert(T->rchild, key);
    else
        Insert(T->lchild, key);
}

//代码实现
void InsertBST(BSTree &T,int key)
{
    if(T == NULL)
    {
        T = new BSTNode;
        T->key = key;
        T->lchild = T->rchild = NULL;
    }
    else if (key == T->key)
        return;
    else if(key > T->key)
        InsertBST(T->rchild, key);
    else
        InsertBST(T->lchild, key);
}

2. 编写CreateBST(T)的伪代码实现从控制台输入创建BST树。最后使用代码实现。使用“50 30 80 20 40 90 10 25 35 85 23 88”创建BST，并中序输出该BST

创建

//伪代码
CreateBST(n) //n为输入的数据量
{
    for (i = 0; i<n; i++)
    {
        cin >> key;
        InsertBST(T, key);
    }
    return T;
}

//代码实现
BSTree CreateBST(int n)
{
    BSTree T = NULL;
    int key;
    for (int i = 0; i<n; i++)
    {
        cin >> key;
        InsertBST(T, key);
    }
    return T;
}

输出效果：

3. 编写DeleteBST(T, key)的伪代码实现从T中删除关键字key。如果无法编写出来，请写出在BST中删除关键字key所需注意的事项。

//伪代码
DeleteBST(T, key)
{
    if (T为空)
    {
        return;
    }else
    {
        if (key < T->key)
        {
            DeleteBST(T->lchild, key);
        }
        else if (key > T->key)
        {
            DeleteBST(T->rchild, key);
        }else
        {
            DeleteT(T); //调用删除结点函数
        }
    }
}
DeleteT(T)
{
    if (T->rchild 为空)
    {
        p = T;
        T = T->lchild;
        删除结点p;
    }else if (T->lchild 为空)
    {
        p = T;
        T = T->rchild;
        删除结点p;
    }else
    {
        DeleteTree(T,T->lchild); //结点p左右子树均存在时，调用另一删除函数
    }
}
DeleteTree(T,r)
{
    if (r->rchild 不为空)
    {
        DeleteTree(T,r->rchild); //找到最右结点
    }else
    {
        T->key = r->key;
        p = r;
        r = r->lchild;
        删除结点p;
    }
}

4. 选做：使用代码实现DeleteBST(T, key)

//代码实现
void DeleteBST(BSTree &T,int key)
{
    if (T == NULL)
    {
        return;
    }else
    {
        if (key < T->key)
        {
            DeleteBST(T->lchild, key);
        }
        else if (key > T->key)
        {
            DeleteBST(T->rchild, key);
        }else
        {
            DeleteT(T); //调用删除结点函数
        }
    }
}
void DeleteT(BSTree &T)
{
    BSTree p;
    if (T->rchild == NULL)
    {
        p = T;
        T = T->lchild;
        delete p;
    }else if (T->lchild == NULL)
    {
        p = T;
        T = T->rchild;
        delete p;
    }else
    {
        DeleteTree(T,T->lchild); //结点p左右子树均存在时，调用另一删除函数
    }
}
void DeleteTree(BSTree &T,BSTree &r)
{
    BSTree p;
    if (r->rchild)
    {
        DeleteTree(T,r->rchild);
    }else
    {
        T->key = r->key;
        p = r;
        r = r->lchild;
        delete p;
    }
}

效果（删除30）：