d_rbtree.h

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				x = root;
			}
		}

		x->color = BLACK;
}

template <typename T>
rbtree<T>::rbtree()
{
	makeEmptyTree();
}

template <typename T>
rbtree<T>::rbtree(T *first, T *last)
{
	// construct an empty tree
	makeEmptyTree();

	// insert the data into the tree
	while (first != last)
		insert(*first++);
}

template <typename T>
rbtree<T>::rbtree(const rbtree<T>& obj):
		treeSize(obj.treeSize)
{
	// call copyTree(), and assign its return value
	// to the root
	root = copyTree(obj.root);
}

template <typename T>
rbtree<T>::~rbtree()
{
	// erase the nodes in the tree
	deleteTree(root);

	// tree is emtpy
	root = NIL;
	treeSize = 0;
}

template <typename T>
rbtree<T>& rbtree<T>::operator= (const rbtree<T>& rhs)
{
	if (this != &rhs)
	{
		// erase the tree
		deleteTree(root);

		// call copyTree(), and assign its return value
		// to the root
		root = copyTree(rhs.root);
		treeSize = rhs.treeSize;
	}

	return *this;
}

template <typename T>
bool rbtree<T>::empty() const
{
	return treeSize == 0;
}

template <typename T>
int rbtree<T>::size() const
{
	return treeSize;
}

template <typename T>
rbtree<T>::iterator rbtree<T>::find (const T& item)
{
	rbnode<T> *curr;

	// search tree for item
	curr = findNode(item);

	// if item found, return iterator with value current;
	// otherwise, return end()
	if (curr != NIL)
		return iterator(curr, this);
	else
		return end();
}

template <typename T>
rbtree<T>::const_iterator rbtree<T>::find (const T& item) const
{
	rbnode<T> *curr;

	// search tree for item
	curr = findNode(item);

	// if item found, return const_iterator with value current;
	// otherwise, return end()
	if (curr != NIL)
		return const_iterator(curr, this);
	else
		return end();
}

template <typename T>
pair<rbtree<T>::iterator,bool> rbtree<T>::insert (const T& item)
{
	// TOP-DOWN INSERTION

	// declare pointers to the current node and its parent
	rbnode<T> *curr = root, *parent = NIL, *newNode;

	// loop until we find the value in the tree or locate
	// the insertion point
	while (curr != NIL)
	{
		if (curr->nodeValue == item)
		{
			// item is in the tree. return a pair whose first member
			// is an iterator pointing at item and whose second member
			// is false
			return pair<iterator,bool> (iterator(curr,this), false);
		}

		// a node split is required if both children of curr are RED
		if (curr->left->color == RED && curr->right->color == RED)
			split4Node(curr);

		// move down the tree
		parent = curr;
		if (item < curr->nodeValue)
			curr = curr->left;
		else
			curr = curr->right;
	}

	// create the new node
	newNode = getRBNode(item, NIL, NIL, parent, RED);

	// is item the first node inserted into the tree?
	if (parent == NIL)
		// item is at the root of a brand new tree.
		root = newNode;
	else
	{
		// link the new node into its parent
		if (item < parent->nodeValue)
			// insert as left child
			parent->left = newNode;
		else
			// insert as right child
			parent->right = newNode;

		// if the new node's parent is RED, we
		// must perform a rotation
		if (parent->color == RED)
			split4Node(newNode);
	}

	// the color of the root must be BLACK
	root->color = BLACK;

	// the tree has one more node
	treeSize++;

	// we did an insertion. set success to true and return
	// an iterator pointing at item
	return pair<iterator,bool> (iterator(newNode,this),true);
}

template <typename T>
int rbtree<T>::erase(const T& item)
{
	int numberErased = 1;
	// search tree for item
	rbnode<T> *p  = findNode(item);

	// if item found, delete the node
	if (p != NIL)
		erase(iterator(p,this));
	else
		numberErased = 0;

	return numberErased;
}

template <typename T>
void rbtree<T>::erase (iterator pos)
{
	// BOTTOM-UP ERASE

	// dNodePtr = pointer to node D that is deleted
	// pNodePtr = pointer to parent P of node D
	// rNodePtr = pointer to node R that replaces D
	// spliceOut = pointer to the node that is spliced out of the tree
	// childOfSpliceOut = pointer to the child of the node we splice out
	rbnode<T> *dNodePtr = pos.nodePtr, *pNodePtr, *rNodePtr,
				 *spliceOut, *childOfSpliceOut;
	// saves color of node that is spliced out
	colorType spliceoutColor;

	if (dNodePtr == NIL)
 		throw
			referenceError("rbtree erase(): invalid iterator");

	// assign pNodePtr the address of P
	pNodePtr = dNodePtr->parent;

	// If D has a NIL pointer, the
	// replacement node is the other child
	if (dNodePtr->right == NIL || dNodePtr->left == NIL)
	{
		if (dNodePtr->right == NIL)
			rNodePtr = dNodePtr->left;
		else
			rNodePtr = dNodePtr->right;

		// the parent of R is now the parent of D
		// NOTE: rNodePtr may be NIL
		rNodePtr->parent = pNodePtr;

		// we are splicing dNodePtr out of the tree
		spliceOut = dNodePtr;
		// save color of dNodePtr
		spliceoutColor = spliceOut->color;
		// record the child of our spliceout node for possible
		// balancing operations
		childOfSpliceOut = rNodePtr;
	}
	// both pointers of dNodePtr are non-NIL.
	else
	{
		// find and unlink replacement node for D.
		// starting at the right child of node D,
		// find the node whose value is the smallest of all
		// nodes whose values are greater than the value in D.
		// unlink the node from the tree.

		// pOfRNodePtr = pointer to parent of replacement node
		rbnode<T> *pOfRNodePtr = dNodePtr;

		// first possible replacement is right child of D
		rNodePtr = dNodePtr->right;

		// descend down left subtree of the right child of D,
		// keeping a record of current node and its parent.
		// when we stop, we have found the replacement
		while(rNodePtr->left != NIL)
		{
			pOfRNodePtr = rNodePtr;
			rNodePtr = rNodePtr->left;
		}

		// we are splicing rNodePtr out of the tree at its
		// current location
		spliceOut = rNodePtr;
		// save color of the node we will splice out
		spliceoutColor = spliceOut->color;
		// we will replace dNodPtr by spliceOut. make the color
		// of spliceOut the color of dNodePtr
		spliceOut->color = dNodePtr->color;
		// record the child of our spliceout node for possible
		// balancing operations
		childOfSpliceOut = rNodePtr->right;

		if (pOfRNodePtr == dNodePtr)
		{
			// right child of deleted node is the replacement.
			// assign left subtree of D to left subtree of R
			rNodePtr->left = dNodePtr->left;
			// assign the parent of D as the parent of R
			rNodePtr->parent = pNodePtr;
			// assign the left child of D to have parent R
			dNodePtr->left->parent = rNodePtr;
			// if the right child of rNodePtr is NIL,
			// make rNodrPtr the parent of NIL, since any
			// required fixup will start with the child
			if (rNodePtr->right == NIL)
				rNodePtr->right->parent = rNodePtr;
		}
		else
		{
			// we moved at least one node down a left branch
			// of the right child of D. unlink R from tree by
			// assigning its right subtree as the left child of
			// the parent of R
			pOfRNodePtr->left = rNodePtr->right;

			// the parent of the right child of R is the
			// parent of R
			// NOTE: rNodePtr may be NIL
			rNodePtr->right->parent = pOfRNodePtr;

			// put replacement node in place of dNodePtr
			// assign children of R to be those of D
			rNodePtr->left = dNodePtr->left;
			rNodePtr->right = dNodePtr->right;
			// assign the parent of R to be the parent of D
			rNodePtr->parent = pNodePtr;
			// assign the parent pointer in the children
			// of R to point at R
			rNodePtr->left->parent = rNodePtr;
			rNodePtr->right->parent = rNodePtr;
		}
	}

	// complete the link to the parent node.

	// deleting the root node. assign new root
	if (pNodePtr == NIL)
		root = rNodePtr;
	// attach R to the correct branch of P
	else if (dNodePtr->nodeValue < pNodePtr->nodeValue)
		pNodePtr->left = rNodePtr;
	else
		pNodePtr->right = rNodePtr;

	// delete the node from memory and decrement tree size
	delete dNodePtr;

	// fixup the tree if the node spliced out is BLACK
	if (spliceoutColor == BLACK)
		rbDeleteFixup(childOfSpliceOut);

	treeSize--;
}

template <typename T>
void rbtree<T>::erase (rbtree<T>::iterator first,
							  rbtree<T>::iterator last)
{
	if (treeSize == 0)
 		throw
			underflowError("rbtree erase(): tree is empty");

	if (first == begin() && last == end())
	{
		// we are asked to erase the entire tree.
		// erase the tree nodes from memory
		deleteTree(root);

		// tree is emtpy
		root = NIL;
		treeSize = 0;
	}
	else
		// erase each item in a subrange of the tree
		while (first != last)
			erase(first++);
}

template <typename T>
rbtree<T>::iterator rbtree<T>::begin()
{
	rbnode<T> *curr = root;

	// if the tree is not empty, the first node
	// inorder is the farthest node left from root
	if (curr != NIL)
		while (curr->left != NIL)
			curr = curr->left;

	// build return value using private constructor
	return iterator(curr, this);
}

template <typename T>
rbtree<T>::const_iterator rbtree<T>::begin() const
{
	const rbnode<T> *curr = root;

	// if the tree is not empty, the first node
	// inorder is the farthest node left from root
	if (curr != NIL)
		while (curr->left != NIL)
			curr = curr->left;

	// build return value using private constructor
	return const_iterator(curr, this);
}

template <typename T>
rbtree<T>::iterator rbtree<T>::end()
{
	// end indicated by an iterator with NIL stnode pointer
	return iterator(NIL, this);
}

template <typename T>
rbtree<T>::const_iterator rbtree<T>::end() const
{
	// end indicated by an iterator with NIL stnode pointer
	return const_iterator(NIL, this);
}

// recursive inorder scan used to build the shadow tree
template <typename T>
rbnodeShadow *rbtree<T>::buildShadowTree(rbnode<T> *t, int level, int& column) const
{
	// pointer to new shadow tree node
	rbnodeShadow *newNode = NULL;

	// text and ostr used to perform format conversion
	char text[80];
	ostrstream ostr(text,80);

	if (t != NIL)
	{
		// create the new shadow tree node
		newNode = new rbnodeShadow;

		// allocate node for left child at next level in tree; attach node
		rbnodeShadow *newLeft = buildShadowTree(t->left, level+1, column);
		newNode->left = newLeft;

		// initialize data members of the new node
		if (t->color == RED)
			ostr << t->nodeValue << '*' << ends;
		else
			ostr << t->nodeValue << ends;

		newNode->nodeValueStr = text;
		newNode->level = level;
		newNode->column = column;

		// update column to next cell in the table
		column++;

		// allocate node for right child at next level in tree; attach node
		rbnodeShadow *newRight = buildShadowTree(t->right, level+1, column);
		newNode->right = newRight;
	}

	return newNode;
}

template <typename T>
void rbtree<T>::displayTree(int maxCharacters) const
{
	string label;
	int level = 0, column = 0;
	int colWidth = maxCharacters + 1;
	//
	int currLevel = 0, currCol = 0;

	if (treeSize == 0)
		return;

	// build the shadow tree
	rbnodeShadow *shadowRoot = buildShadowTree(root, level, column);

	// use during the level order scan of the shadow tree
	rbnodeShadow *currNode;

   // store siblings of each rbnodeShadow object in a queue so that
	// they are visited in order at the next level of the tree
   queue<rbnodeShadow *> q;

   // insert the root in the queue and set current level to 0
   q.push(shadowRoot);

   // continue the iterative process until the queue is empty
   while(!q.empty())
   {
      // delete front node from queue and make it the current node
      currNode = q.front();
		q.pop();

		// if level changes, output a newline
		if (currNode->level > currLevel)
		{
			currLevel = currNode->level;
			currCol = 0;
			cout << endl;
		}

		// if a left child exists, insert the child in the queue
      if(currNode->left != NULL)
			q.push(currNode->left);

		// if a right child exists, insert the child in the queue
      if(currNode->right != NULL)
			q.push(currNode->right);

		// output formatted node label
		if (currNode->column > currCol)
		{
			cout << setw((currNode->column-currCol)*colWidth) << ' ';
			currCol = currNode->column;
		}
		cout << setw(colWidth) << currNode->nodeValueStr;
		currCol++;
   }
	cout << endl;

	// delete the shadow tree
	deleteShadowTree(shadowRoot);
}

template <typename T>
void rbtree<T>::deleteShadowTree(rbnodeShadow *t) const
{
	// if current root node is not NULL, delete its left subtree,
	// its right subtree and then the node itself
	if (t != NULL)
	{
		deleteShadowTree(t->left);
		deleteShadowTree(t->right);
		delete t;
	}
}

#endif	// RED_BLACK_TREE_CLASS