(2011.08.08)二叉查找树

// 二叉查找树

/***************************************************************************************
　　BST（Binary Search Tree）二叉查找树能使记录的插入与检索都能很快地完成。
 　　设二叉树的任一结点为K，则从根结点开始，在BST中检索K，如果根结点存储的值为
 K，则检索结束。如果不是则必须检索树的更深一层。BST的效率在于只需要检索两棵子
 树之一。
 ****************************************************************************************/

// The Dictionary abstract class. KEComp compares a key
// and an element. EEComp compares two elements.
template <class Key, class Elem, class KEComp, class EEComp>
class Dictionary
{
public:
	// Reninitialize dictionary
	virtual void clear() = 0;
	// Insert an element. Return true if insert is successful, false otherwise.
	virtual bool insert(const Elem&) = 0;
	// Remove some element matching Key. Return true if such exists, false otherwise. 
	// If multiple entries match key, an arbitrary one is removed.
	virtual bool remove (const Key&, Elem&) = 0;
	// Remove and return an arbitrary element from dictionary.
	// Return true if some element is found, false otherwise.
	virtual bool removeAny(Elem&) = 0;
	// Return a copy of some elem matching Key. Return true if such exists, false otherwise.
	// If multiple elements match Key, return an arbitrary one.
	virtual bool find(const Key&,  Elem&) const = 0;
	// Return the number of elements in the dictionary. 
	virtual int size() = 0;
};

 // Binary Search Tree implementation for the dictionrary ADT
template <class Key, class Elem, class KEComp, class EEComp>
class BST : public Dictionary <Key, Elem, KEComp, EEComp>
{
private:
	BinNode<Elem>* root;				// Root of the BST
	int nodecount;								// Number of nodes in the BST
	// Private "helper" functions
	void clearhelp(BinNode<Elem>*);
	BinNode<Elem>* inserthelp(BinNode<Elem>*, const Elem&);
	BinNode<Elem>* deletemin(BinNode<Elem>*, BinNode<Elem> *&);
	BinNode<Elem>* removehelp(BinNode<Elem>*, const Key&, BinNode<Elem>*&);
	bool findhelp(BinNode<Elem>*, const Key&, Elem&) const;
	void printhelp(BinNode<Elem>*, int) const;
public:
	BST()									{root = NULL; nodecount = 0; }
	~BST()									{clearhelp(root);}
	void clear()							{clearhelp(root); root = NULL; nodecount = 0;}
	bool insert(const Elem& e)	 {root = inserthelp(root, e);	nodecount++; return true;}
	bool remove(const Key& K, Elem& e)
	{
		BinNode<Elem>* t = NULL;
		root = removehelp(root, K, t);
		if (t == NULL) return false;						// Nothing found
		e = t ->val();
		nodecount--;
		delete t;
		return true;
	}
	bool removeAny(Elem& e)							// Delete min value
	{
		if (root == NULL)				return false;		// empty tree
		BinNode<Elem>* t;
		root = deletemin(root, t);
		e = t -> val();
		delete t;
		nodecount--;
		return true;
	}
	bool find(const Key& K, Elem& e) const
	{
		return findhelp(root, K, e);
	}
	int size()							{return nodecount;}
	void print() const
	{
		if (root == NULL) cout << "The BST is empty". \n";
		else printhelp(root, 0);
	}
};

// 查找的时候，有四种情况，第一，空树，第二，在根结点中，第三，在左树，第四，在右树。
template <class Key, class Elem, class KEComp, class EEComp>
bool BST<Key, Elem, KEComp, EEComp>:: findhelp(BinNode<Elem>* subroot, const Key& K, Elem& e) const
{
	if (subroot == NULL)									// empty tree
		return false;						
	else if (KEComp::lt(K, subroot -> val()))		// Check left
		return findhelp(subroot -> left(), K, e);
	else if (KEComp::gt(K, subroot -> val()))		// Check right
		return findhelp(subroot -> right(), K, e);
	else																// Found It
	{
		e = subroot -> val();
		return true;
	}
}

template <class Key, class Elem, class KEComp, class EEComp>
bool BST<Key, Elem, KEComp, EEComp>:: deletemin(BinNode<Elem>* rubroot, BinNode<Elem>*& min)
{
	if (subroot() == NULL)			// Found min
	{
	min = subroot;
	return subroot -> right();
	}
	else
	{											// Continue left
		subroot -> setLeft(deletemin(subroot -> left(), min));
		return subroot;
	}
}

template <class Key, class Elem, class KEComp, class EEComp>
void BST<Key, Elem, KEComp, EEComp>:: clear help(BinNode<Elem>* subroot)
{
	if (subroot == NULL) return;
	clearhelp(subroot -> left());
	clearhelp(subroot -> right());
	delete subroot;
}

template<class Key, class Elem, class KEComp, class EEComp>
BinNode<Elem>* BST <Key, Elem, KEComp, EEComp> :: removehelp(BinNode<Elem>* subroot, const Key& K, BinNode<Elem>*& t)
{
	if(subroot == NULL) return NULL;				// Val is not in tree
	else if (KEComp::lt(K, subroot -> val()))		// check left
			subroot -> setleft(removehelp(subroot -> left(), K, t));
	else if (KEComp::gt(K, subroot -> val()))		// check right
			subroot -> setRight(removehelp(subroot -> right(), K, t));
	else																// Found it: remove it
	{
		BinNode<Elem> * temp;
		t = subroot;
		if (subroot -> left() == NULL)				// Only a right child
			subroot = subroot -> right();			// So point to right
		else if (subroot -> right() == NULL)		// Only a left child
			subroot = subroot -> left();				// so point to left
		else														// Both children are non-empty
		{
			subroot -> setRight(deletemin(subroot -> right(), temp));
			Elem te = sbroot -> val();
			subroot -> setVal(temp -> val());
			temp -> setVal(te);
			t = temp;
		}
	}
	return subroot;
}

template <class Key, class Elem, class KEComp, class EEComp>
void BST<Key, Elem, KEComp, EEComp>::printhelp(BinNode<Elem>* subroot, int level) const
{
	if (subroot == NULL) return ;					// Empty tree
	print help(subroot -> left(), level + 1);	// Do left subtree
	for (int i = 0; i < level; i++)						// Indent to level
		cout << "  ";
	cout << subroot -> val() << "\n";				// Print node value
	printhelp(subroot -> right(), level + 1);	// Do right subrtree
}