二叉查找树类的C++实现

　　二叉查找树或者是一棵空树；或者是具有下列性质的二叉树： （1）若左子树不空，则左子树上所有结点的值均小于它的根结点的值； （2）若右子树不空，则右子树上所有结点的值均大于它的根结点的值； （3）左、右子树也分别为二叉排序树。

　　下面的二叉查找树类主要实现了二叉查找树的以下操作：查找结点、插入结点、构造二叉查找树、查找指定结点的前驱和后继、删除结点。

template <typename T>
struct BiNode{
    T k_data;
    BiNode<T> *LChild, *RChild;
    BiNode<T> *Parent;
    BiNode(T element, BiNode<T> *lt, BiNode<T> *rt, BiNode<T> *pt):k_data(element), LChild(lt), RChild(rt), Parent(pt){}
};


//打印节点
template <typename T>
void PrintNode(BiNode<T> node)
{
    cout<<node.k_data<<" ";
}

template <typename T>
class BiSearchTree
{
public:
    BiSearchTree(BiNode<T>* pRoot = NULL)
    {
        root = pRoot;
    }

    ~BiSearchTree()
    {
        ReleaseBiTree(&root);
    }

    void ReleaseBiTree(BiNode<T> **pRoot)
    {
        if (*pRoot != NULL)
        {
            ReleaseBiTree(&(*pRoot)->LChild);
            ReleaseBiTree(&(*pRoot)->RChild);
            delete (*pRoot);
        }
    }

    //前序遍历二叉树
    void VisitBiTreePreOrder(void(*Visit)(BiNode<T>)) const
    {
        VisitBiTreePreOrder(root, Visit);
    }

    //后序遍历二叉树
    void VisitBiTreeInOrder(void(*Visit)(BiNode<T>)) const
    {
        VisitBiTreeInOrder(root, Visit);
    }

    //查找，找到则返回节点，否则返回空
    BiNode<T>* Search(T key) const
    {
        return Search(root, key);
    }

    //插入，如果已经有此节点，则返回false，否则插入节点，返回true
    bool Insert(T key)
    {
        BiNode<T>* p_newNode = new BiNode<T>(key, NULL, NULL, NULL);
        if (root == NULL)//空树
        {
            root = p_newNode;
        }
        BiNode<T>* p = root;
        BiNode<T>* location = NULL;//key的插入位置
        while(p != NULL)//查找key
        {
            location = p;
            if (p->k_data > key)
            {
                p = p->LChild;
            } 
            else if(p->k_data < key)
            {
                p = p->RChild;
            }
            else
            {
                break;
            }
        }

        if (p == NULL)//未找到key
        {
            p_newNode->Parent = location;
            if (location->k_data > key)
            {
                location->LChild = p_newNode;
            } 
            else if(location->k_data < key)
            {
                location->RChild = p_newNode;
            }

            return true;
        }
        else//找到key
        {
            return false;
        }
    }

    //创建二叉查找树
    void CreatBiSearchTree(T a[], int n)
    {
        for (int i = 0; i < n; i++)
        {
            Insert(a[i]);
        }
    }

    //求一个节点的后继节点
    BiNode<T>* bst_successor(BiNode<T> *node)
    {
        if (node->RChild != NULL)//右子树不为空，后继节点即为右子树的最小值节点
        {
            BiNode<T>* p_node = node->RChild;
            while(p_node->LChild != NULL){p_node = p_node->LChild;}
            return p_node;
        }
        else//右子树为空，则那么node的直接后继节点就是从node向上的路径中第一次右转后遇到的节点。
        {
            BiNode<T>* p_node = node->Parent;
            while(p_node != NULL && p_node->RChild == node)
            {
                node = p_node;
                p_node = p_node->Parent;
            }
            return p_node;
        }
    }

    //删除节点
    //1. 结点Z没有孩子结点，那么直接删除Z就行了。
    //2. 结点Z有一个孩子结点，那么删除Z，将Z的父结点与此孩子结点（子树）关联就可以了。
    //3. 结点Z有两个孩子结点，实现方法就是将后继从二叉树中删除（适用第一、二种情况），将后继的数据覆盖到Z中。
    bool Delete(T key)
    {
        if (root == NULL)
        {
            return false;
        }
        BiNode<T>* p = root;
        while(p != NULL)//查找key
        {
            if (p->k_data > key)
            {
                p = p->LChild;
            } 
            else if(p->k_data < key)
            {
                p = p->RChild;
            }
            else
            {
                break;
            }
        }

        if (p != NULL)//查找到k
        {
            //求真正被删除的节点
            BiNode<T>* p_real;  
            if (p->LChild && p->RChild)  
                p_real = bst_successor(p);//此真正被删除的节点一定满足条件1.或者条件2.
            else  
                p_real = p;

            BiNode<T>* p_parent = p_real->Parent;
            if (p_real->LChild == NULL && p_real->RChild == NULL)//1.左右都空
            {
                if (p_parent == NULL)//需要删除的是根节点
                    root = NULL;
                else 
                    if (p_parent->LChild == p_real) {p_parent->LChild = NULL;}
                    else {p_parent->RChild = NULL;}
            } 
            else if (p_real->LChild == NULL  && p_real->RChild != NULL)//2.左空，右不空
            {
                if (p_parent == NULL)//需要删除的是根节点
                    {root = p_real->RChild; p_real->RChild->Parent = NULL;}
                else 
                    if (p_parent->LChild == p_real) {p_parent->LChild = p_real->RChild; p_real->RChild->Parent = p_parent;}
                    else {p_parent->RChild = p_real->RChild; p_real->RChild->Parent = p_parent;}
            }
            else if (p_real->LChild != NULL  && p_real->RChild == NULL)//3.左不空，右空
            {
                if (p_parent == NULL)//需要删除的是根节点
                    {root = p_real->LChild; p_real->LChild->Parent = NULL;}
                else 
                    if (p_parent->LChild == p_real) {p_parent->LChild = p_real->LChild; p_real->LChild->Parent = p_parent;}
                    else {p_parent->RChild = p_real->LChild; p_real->LChild->Parent = p_parent;}
            }

            if (p_real != p)//如果是有双子树的节点，则覆盖原应被删除节点
            {
                p->k_data = p_real->k_data;
            }

            delete p_real;//删除节点
            return true;
        }
        return false;
    }


protected:
private:
    //查找节点
    BiNode<T>* Search(BiNode<T>* pRoot, T key) const
    {
        if (pRoot == NULL)
        {
            return NULL;//查找失败
        }
        if (pRoot->k_data == key)
        {
            return pRoot;//查找成功
        }
        else if (pRoot->k_data > key)
        {
            return Search(pRoot->LChild, key);
        } 
        else if(pRoot->k_data < key)
        {
            return Search(pRoot->RChild, key);
        }
    }

    void VisitBiTreePreOrder(BiNode<T> *pRoot, void(*Visit)(BiNode<T>)) const
    {
        if (pRoot != NULL)
        {
            Visit(*pRoot);
            VisitBiTreePreOrder(pRoot->LChild, Visit);
            VisitBiTreePreOrder(pRoot->RChild, Visit);
        } 
    }

    void VisitBiTreeInOrder(BiNode<T> *pRoot, void(*Visit)(BiNode<T>)) const
    {
        if (pRoot != NULL)
        {
            VisitBiTreeInOrder(pRoot->LChild, Visit);
            Visit(*pRoot);
            VisitBiTreeInOrder(pRoot->RChild, Visit);
        } 
    }

    BiNode<T> *root;
};

int main()
{
    int keys[] = {8, 5, 2, 1, 4, 7, 3, 6, 9};
    BiSearchTree<int>* p_BiSearchTree = new BiSearchTree<int>();
    p_BiSearchTree->CreatBiSearchTree(keys, sizeof(keys)/sizeof(keys[0]));
    cout<<"前序遍历二叉树：";
    p_BiSearchTree->VisitBiTreePreOrder(PrintNode);
    cout<<endl<<"中序遍历二叉树：";
    p_BiSearchTree->VisitBiTreeInOrder(PrintNode);
    cout<<endl;

    while (0)
    {
        int k;
        cin.clear();
        cin.sync();
        cout<<"请输入要查找的节点值：";
        cin>>k;
        cout<<p_BiSearchTree->Search(k)->k_data<<endl;
    }

    int i = 4;
    while (i)
    {
        int k;
        cin.clear();
        cin.sync();
        cout<<"请输入要删除的节点值：";
        cin>>k;
        p_BiSearchTree->Delete(k);
        cout<<"前序遍历二叉树：";
        p_BiSearchTree->VisitBiTreePreOrder(PrintNode);
        cout<<endl<<"中序遍历二叉树：";
        p_BiSearchTree->VisitBiTreeInOrder(PrintNode);
        cout<<endl;
        i--;
    }

    delete p_BiSearchTree;
    system("pause");
    return 0;
}