C++ binary search tree

#include <iostream>

using namespace std;



template <class T> class BST;

template <class T>
class Element
{
public :
	T key;
};


template <class T>
class BstNode
{
	friend  class BST<T>;
public:

//private:
	Element<T> data;
	BstNode * leftChild;
	BstNode * rightChild;
	void display(int i);

};


template <class T>
class BST
{
public:
	BST(BstNode<T>* init = 0) :root(init) {}
	bool Insert(Element<T> const &x);       //二叉查找树插入节点
	BstNode<T>* Search(Element<T> const &x);  //二叉查找树递归查找节点
	BstNode<T>* Search(BstNode<T>*, Element<T> const &x);
	BstNode<T>* IterSearch(Element<T> const &x); //

	void display()
	{
		cout << "\n";
		if (root)
			root->display(1);
		else
			cout << "empty tree\n";
	}

private:
	BstNode<T> * root;

};


template<class T>
void BstNode<T>::display(int i)
{
	cout << "Position:" << i << ":data.key:" << data.key << "\n";

	if (leftChild) leftChild->display(2*i);  //左边的是2*i
	if (rightChild) rightChild->display(2*i+1); //右边的是2*i +1

}

template <class T>
bool BST<T>::Insert(Element<T> const &x)
{
	BstNode<T> *p = root;
	BstNode<T> *q = p;

	while (p)
	{
		q = p;
		if (x.key == p->data.key)
		{
			cout << "already in tree" << endl;
			return false;
		}
		else if (x.key < p->data.key)
			p = p->leftChild;
		else if (x.key > p->data.key)
			p = p->rightChild;
	}

	//找到的位置的上个节点就是q，下个节点就是p，p是q的子节点
	p = new BstNode<T>;
	p->data = x;
	p->leftChild = p->rightChild = 0;

	if (root == 0) root = p;
	else if (q->data.key > x.key) q->leftChild = p;
	else if (q->data.key < x.key) q->rightChild = p;

	return true;
}

template <class T>
BstNode<T>* BST<T>::Search(Element<T> const &x)
{
	return Search(root,x);
}

template <class T>
BstNode<T>* BST<T>::Search(BstNode<T>* node, Element<T> const & ele)
{
	if (node == 0) return 0;

	if (node->data.key == ele.key) return node;
	if (node->data.key < ele.key) return Search(node->rightChild,ele);
	else return Search(node->leftChild,ele);
}

template <class T>
BstNode<T>* BST<T>::IterSearch(Element<T> const &x)
{
	for (BstNode<T>* p = root;p!= 0;)
	{
		if (p->data.key == x.key) return p;

		if (p->data.key < x.key)
			p = p->rightChild;
		else
			p = p->leftChild;
	}
}

int main()
{
	BST<int> bst;
	Element<int> a, b, c, d, e, f, g, h, i, j, k, l;

	a.key = 5;
	b.key = 3;
	c.key = 11;
	d.key = 3;
	e.key = 15;
	f.key = 2;
	g.key = 8;
	h.key = 22;
	i.key = 20;
	j.key = 9;

	cout<<bst.Insert(a)<<endl;
	cout << bst.Insert(b)<<endl;
	cout << bst.Insert(c)<<endl;
	cout << bst.Insert(d) << endl;
	cout << bst.Insert(e) << endl;
	cout << bst.Insert(f) << endl;
	cout << bst.Insert(g) << endl;
	cout << bst.Insert(h) << endl;
	cout << bst.Insert(i) << endl;
	cout << bst.Insert(j) << endl;
	
	bst.display();

	BstNode<int>* p = bst.Search(c);

	if (p != 0)
	{
		cout << "Search 找到了:" << p->data.key << endl;
	}
	else
	{
		cout << "Search 没找到" << endl;
	}

	p = bst.IterSearch(c);
	if (p != 0)
	{
		cout << "IterSearch 找到了:" << p->data.key << endl;
	}
	else
	{
		cout << "IterSearch 没找到" << endl;
	}
	return 0;
}

operation result: