static OrderedTree()
{
// set up the sentinel node. the sentinel node is the key to a successfull
// implementation and for understanding the red-black tree properties.
sentinelNode = new OrderedTreeNode();
sentinelNode.Left = sentinelNode.Right = sentinelNode;
sentinelNode.Parent = null;
sentinelNode.Color = OrderedTreeNode.BLACK;
}
///<summary>
/// RestoreAfterInsert
/// Additions to red-black trees usually destroy the red-black
/// properties. Examine the tree and restore. Rotations are normally
/// required to restore it
///</summary>
private void RestoreAfterInsert(OrderedTreeNode x)
{
// x and y are used as variable names for brevity, in a more formal
// implementation, you should probably change the names
OrderedTreeNode y;
// maintain red-black tree properties after adding x
while(x != rbTree && x.Parent.Color == OrderedTreeNode.RED) {
// Parent node is .Colored red;
if(x.Parent == x.Parent.Parent.Left) { // determine traversal path
// is it on the Left or Right subtree?
y = x.Parent.Parent.Right; // get uncle
if(y!= null && y.Color == OrderedTreeNode.RED) {
// uncle is red; change x's Parent and uncle to black
x.Parent.Color = OrderedTreeNode.BLACK;
y.Color = OrderedTreeNode.BLACK;
// grandparent must be red. Why? Every red node that is not
// a leaf has only black children
x.Parent.Parent.Color = OrderedTreeNode.RED;
x = x.Parent.Parent; // continue loop with grandparent
}
else {
// uncle is black; determine if x is greater than Parent
if(x == x.Parent.Right) {
// yes, x is greater than Parent; rotate Left
// make x a Left child
x = x.Parent;
RotateLeft(x);
}
// no, x is less than Parent
x.Parent.Color = OrderedTreeNode.BLACK; // make Parent black
x.Parent.Parent.Color = OrderedTreeNode.RED; // make grandparent black
RotateRight(x.Parent.Parent); // rotate right
}
}
else {
// x's Parent is on the Right subtree
// this code is the same as above with "Left" and "Right" swapped
y = x.Parent.Parent.Left;
if(y!= null && y.Color == OrderedTreeNode.RED) {
x.Parent.Color = OrderedTreeNode.BLACK;
y.Color = OrderedTreeNode.BLACK;
x.Parent.Parent.Color = OrderedTreeNode.RED;
x = x.Parent.Parent;
}
else {
if(x == x.Parent.Left) {
x = x.Parent;
RotateRight(x);
}
x.Parent.Color = OrderedTreeNode.BLACK;
x.Parent.Parent.Color = OrderedTreeNode.RED;
RotateLeft(x.Parent.Parent);
}
}
}
rbTree.Color = OrderedTreeNode.BLACK; // rbTree should always be black
}
///<summary>
/// RestoreAfterDelete
/// Deletions from red-black trees may destroy the red-black
/// properties. Examine the tree and restore. Rotations are normally
/// required to restore it
///</summary>
private void RestoreAfterDelete(OrderedTreeNode x)
{
// maintain Red-Black tree balance after deleting node
OrderedTreeNode y;
while(x != rbTree && x.Color == OrderedTreeNode.BLACK) {
if(x == x.Parent.Left) { // determine sub tree from parent
y = x.Parent.Right; // y is x's sibling
if(y.Color == OrderedTreeNode.RED) {
// x is black, y is red - make both black and rotate
y.Color = OrderedTreeNode.BLACK;
x.Parent.Color = OrderedTreeNode.RED;
RotateLeft(x.Parent);
y = x.Parent.Right;
}
if(y.Left.Color == OrderedTreeNode.BLACK &&
y.Right.Color == OrderedTreeNode.BLACK) {
// children are both black
y.Color = OrderedTreeNode.RED; // change parent to red
x = x.Parent; // move up the tree
}
else {
if(y.Right.Color == OrderedTreeNode.BLACK) {
y.Left.Color = OrderedTreeNode.BLACK;
y.Color = OrderedTreeNode.RED;
RotateRight(y);
y = x.Parent.Right;
}
y.Color = x.Parent.Color;
x.Parent.Color = OrderedTreeNode.BLACK;
y.Right.Color = OrderedTreeNode.BLACK;
RotateLeft(x.Parent);
x = rbTree;
}
}
else {
// right subtree - same as code above with right and left swapped
y = x.Parent.Left;
if(y.Color == OrderedTreeNode.RED) {
y.Color = OrderedTreeNode.BLACK;
x.Parent.Color = OrderedTreeNode.RED;
RotateRight (x.Parent);
y = x.Parent.Left;
}
if(y.Right.Color == OrderedTreeNode.BLACK &&
y.Left.Color == OrderedTreeNode.BLACK) {
y.Color = OrderedTreeNode.RED;
x = x.Parent;
}
else {
if(y.Left.Color == OrderedTreeNode.BLACK) {
y.Right.Color = OrderedTreeNode.BLACK;
y.Color = OrderedTreeNode.RED;
RotateLeft(y);
y = x.Parent.Left;
}
y.Color = x.Parent.Color;
x.Parent.Color = OrderedTreeNode.BLACK;
y.Left.Color = OrderedTreeNode.BLACK;
RotateRight(x.Parent);
x = rbTree;
}
}
}
x.Color = OrderedTreeNode.BLACK;
}
///<summary>
/// Delete
/// Delete a node from the tree and restore red black properties
///<summary>
private void Delete(OrderedTreeNode z)
{
// A node to be deleted will be:
// 1. a leaf with no children
// 2. have one child
// 3. have two children
// If the deleted node is red, the red black properties still hold.
// If the deleted node is black, the tree needs rebalancing
OrderedTreeNode x = new OrderedTreeNode(); // work node to contain the replacement node
OrderedTreeNode y; // work node
// find the replacement node (the successor to x) - the node one with
// at *most* one child.
if(z.Left == sentinelNode || z.Right == sentinelNode)
y = z; // node has sentinel as a child
else {
// z has two children, find replacement node which will
// be the leftmost node greater than z
y = z.Right; // traverse right subtree
while(y.Left != sentinelNode) // to find next node in sequence
y = y.Left;
}
// at this point, y contains the replacement node. it's content will be copied
// to the valules in the node to be deleted
// x (y's only child) is the node that will be linked to y's old parent.
if(y.Left != sentinelNode)
x = y.Left;
else
x = y.Right;
// replace x's parent with y's parent and
// link x to proper subtree in parent
// this removes y from the chain
x.Parent = y.Parent;
if(y.Parent != null)
if(y == y.Parent.Left)
y.Parent.Left = x;
else
y.Parent.Right = x;
else
rbTree = x; // make x the root node
// copy the values from y (the replacement node) to the node being deleted.
// note: this effectively deletes the node.
if(y != z) {
z.Key = y.Key;
z.Data = y.Data;
}
if(y.Color == OrderedTreeNode.BLACK)
RestoreAfterDelete(x);
lastNodeFound = sentinelNode;
}
///<summary>
/// RotateRight
/// Rebalance the tree by rotating the nodes to the right
///</summary>
public void RotateRight(OrderedTreeNode x)
{
// pushing node x down and to the Right to balance the tree. x's Left child (y)
// replaces x (since x < y), and y's Right child becomes x's Left child
// (since it's < x but > y).
OrderedTreeNode y = x.Left; // get x's Left node, this becomes y
// set x's Right link
x.Left = y.Right; // y's Right child becomes x's Left child
// modify parents
if(y.Right != sentinelNode)
y.Right.Parent = x; // sets y's Right Parent to x
if(y != sentinelNode)
y.Parent = x.Parent; // set y's Parent to x's Parent
if(x.Parent != null) { // null=rbTree, could also have used rbTree
// determine which side of it's Parent x was on
if(x == x.Parent.Right)
x.Parent.Right = y; // set Right Parent to y
else
x.Parent.Left = y; // set Left Parent to y
}
else
rbTree = y; // at rbTree, set it to y
// link x and y
y.Right = x; // put x on y's Right
if(x != sentinelNode) // set y as x's Parent
x.Parent = y;
}
///<summary>
/// GetMinKey
/// Returns the minimum key value
///<summary>
public IComparable GetMinKey()
{
OrderedTreeNode treeNode = rbTree;
if(treeNode == null || treeNode == sentinelNode)
throw(new InvalidOperationException("Tree is empty"));
// traverse to the extreme left to find the smallest key
while(treeNode.Left != sentinelNode)
treeNode = treeNode.Left;
lastNodeFound = treeNode;
return treeNode.Key;
}
///<summary>
/// Delete
/// Delete a node from the tree and restore red black properties
///<summary>
private void Delete(OrderedTreeNode z)
{
// A node to be deleted will be:
// 1. a leaf with no children
// 2. have one child
// 3. have two children
// If the deleted node is red, the red black properties still hold.
// If the deleted node is black, the tree needs rebalancing
OrderedTreeNode x = new OrderedTreeNode(); // work node to contain the replacement node
OrderedTreeNode y; // work node
// find the replacement node (the successor to x) - the node one with
// at *most* one child.
if (z.Left == sentinelNode || z.Right == sentinelNode)
{
y = z; // node has sentinel as a child
}
else
{
// z has two children, find replacement node which will
// be the leftmost node greater than z
y = z.Right; // traverse right subtree
while (y.Left != sentinelNode) // to find next node in sequence
{
y = y.Left;
}
}
// at this point, y contains the replacement node. it's content will be copied
// to the valules in the node to be deleted
// x (y's only child) is the node that will be linked to y's old parent.
if (y.Left != sentinelNode)
{
x = y.Left;
}
else
{
x = y.Right;
}
// replace x's parent with y's parent and
// link x to proper subtree in parent
// this removes y from the chain
x.Parent = y.Parent;
if (y.Parent != null)
{
if (y == y.Parent.Left)
{
y.Parent.Left = x;
}
else
{
y.Parent.Right = x;
}
}
else
{
rbTree = x; // make x the root node
}
// copy the values from y (the replacement node) to the node being deleted.
// note: this effectively deletes the node.
if (y != z)
{
z.Key = y.Key;
z.Data = y.Data;
}
if (y.Color == OrderedTreeNode.BLACK)
{
RestoreAfterDelete(x);
}
lastNodeFound = sentinelNode;
}
public OrderedTree()
{
rbTree = sentinelNode;
lastNodeFound = sentinelNode;
}
///<summary>
/// Clear
/// Empties or clears the tree
///<summary>
public void Clear()
{
rbTree = sentinelNode;
intCount = 0;
}
///<summary>
/// Add
/// args: ByVal key As IComparable, ByVal data As Object
/// key is object that implements IComparable interface
/// performance tip: change to use use int type (such as the hashcode)
///</summary>
public void Add(IComparable key, object data)
{
if(key == null)
throw(new ArgumentNullException("Key is null"));
// traverse tree - find where node belongs
int result = 0;
// create new node
OrderedTreeNode node = new OrderedTreeNode();
OrderedTreeNode temp = rbTree; // grab the rbTree node of the tree
while(temp != sentinelNode) {
// find Parent
node.Parent = temp;
result = key.CompareTo(temp.Key);
if(result == 0)
throw new ArgumentException("Key duplicated");
if(result > 0)
temp = temp.Right;
else
temp = temp.Left;
}
// setup node
node.Key = key;
node.Data = data;
node.Left = sentinelNode;
node.Right = sentinelNode;
// insert node into tree starting at parent's location
if(node.Parent != null) {
result = node.Key.CompareTo(node.Parent.Key);
if(result > 0)
node.Parent.Right = node;
else
node.Parent.Left = node;
}
else
rbTree = node; // first node added
RestoreAfterInsert(node); // restore red-black properities
lastNodeFound = node;
intCount = intCount + 1;
}
///<summary>
/// NextElement
///</summary>
public object NextElement()
{
if (stack.Count == 0)
{
throw new InvalidOperationException("Element not found");
}
// the top of stack will always have the next item
// get top of stack but don't remove it as the next nodes in sequence
// may be pushed onto the top
// the stack will be popped after all the nodes have been returned
OrderedTreeNode node = (OrderedTreeNode)stack.Peek(); //next node in sequence
if (ascending)
{
if (node.Right == OrderedTree.sentinelNode)
{
// yes, top node is lowest node in subtree - pop node off stack
OrderedTreeNode tn = (OrderedTreeNode)stack.Pop();
// peek at right node's parent
// get rid of it if it has already been used
while (HasMoreElements() && ((OrderedTreeNode)stack.Peek()).Right == tn)
{
tn = (OrderedTreeNode)stack.Pop();
}
}
else
{
// find the next items in the sequence
// traverse to left; find lowest and push onto stack
OrderedTreeNode tn = node.Right;
while (tn != OrderedTree.sentinelNode)
{
stack.Push(tn);
tn = tn.Left;
}
}
}
else // descending, same comments as above apply
{
if (node.Left == OrderedTree.sentinelNode)
{
// walk the tree
OrderedTreeNode tn = (OrderedTreeNode)stack.Pop();
while (HasMoreElements() && ((OrderedTreeNode)stack.Peek()).Left == tn)
{
tn = (OrderedTreeNode)stack.Pop();
}
}
else
{
// determine next node in sequence
// traverse to left subtree and find greatest node - push onto stack
OrderedTreeNode tn = node.Left;
while (tn != OrderedTree.sentinelNode)
{
stack.Push(tn);
tn = tn.Right;
}
}
}
// the following is for .NET compatibility (see MoveNext())
Key = node.Key;
Value = node.Data;
// ******** testing only ********
return(keys == true ? node.Key : node.Data);
}
///<summary>
/// Clear
/// Empties or clears the tree
///<summary>
public void Clear()
{
rbTree = sentinelNode;
intCount = 0;
}
public object this[IComparable key] {
get {
return(GetData(key));
}
set {
if (key == null)
{
throw new ArgumentNullException("Key is null");
}
// traverse tree - find where node belongs
int result = 0;
// create new node
OrderedTreeNode node = new OrderedTreeNode();
OrderedTreeNode temp = rbTree; // grab the rbTree node of the tree
while (temp != sentinelNode)
{
// find Parent
node.Parent = temp;
result = key.CompareTo(temp.Key);
if (result == 0)
{
lastNodeFound = temp;
temp.Data = value;
return;
}
if (result > 0)
{
temp = temp.Right;
}
else
{
temp = temp.Left;
}
}
// setup node
node.Key = key;
node.Data = value;
node.Left = sentinelNode;
node.Right = sentinelNode;
// insert node into tree starting at parent's location
if (node.Parent != null)
{
result = node.Key.CompareTo(node.Parent.Key);
if (result > 0)
{
node.Parent.Right = node;
}
else
{
node.Parent.Left = node;
}
}
else
{
rbTree = node; // first node added
}
RestoreAfterInsert(node); // restore red-black properities
lastNodeFound = node;
intCount = intCount + 1;
}
}
public OrderedTree()
{
rbTree = sentinelNode;
lastNodeFound = sentinelNode;
}
///<summary>
/// RestoreAfterDelete
/// Deletions from red-black trees may destroy the red-black
/// properties. Examine the tree and restore. Rotations are normally
/// required to restore it
///</summary>
private void RestoreAfterDelete(OrderedTreeNode x)
{
// maintain Red-Black tree balance after deleting node
OrderedTreeNode y;
while (x != rbTree && x.Color == OrderedTreeNode.BLACK)
{
if (x == x.Parent.Left) // determine sub tree from parent
{
y = x.Parent.Right; // y is x's sibling
if (y.Color == OrderedTreeNode.RED)
{
// x is black, y is red - make both black and rotate
y.Color = OrderedTreeNode.BLACK;
x.Parent.Color = OrderedTreeNode.RED;
RotateLeft(x.Parent);
y = x.Parent.Right;
}
if (y.Left.Color == OrderedTreeNode.BLACK &&
y.Right.Color == OrderedTreeNode.BLACK)
{
// children are both black
y.Color = OrderedTreeNode.RED; // change parent to red
x = x.Parent; // move up the tree
}
else
{
if (y.Right.Color == OrderedTreeNode.BLACK)
{
y.Left.Color = OrderedTreeNode.BLACK;
y.Color = OrderedTreeNode.RED;
RotateRight(y);
y = x.Parent.Right;
}
y.Color = x.Parent.Color;
x.Parent.Color = OrderedTreeNode.BLACK;
y.Right.Color = OrderedTreeNode.BLACK;
RotateLeft(x.Parent);
x = rbTree;
}
}
else
{
// right subtree - same as code above with right and left swapped
y = x.Parent.Left;
if (y.Color == OrderedTreeNode.RED)
{
y.Color = OrderedTreeNode.BLACK;
x.Parent.Color = OrderedTreeNode.RED;
RotateRight(x.Parent);
y = x.Parent.Left;
}
if (y.Right.Color == OrderedTreeNode.BLACK &&
y.Left.Color == OrderedTreeNode.BLACK)
{
y.Color = OrderedTreeNode.RED;
x = x.Parent;
}
else
{
if (y.Left.Color == OrderedTreeNode.BLACK)
{
y.Right.Color = OrderedTreeNode.BLACK;
y.Color = OrderedTreeNode.RED;
RotateLeft(y);
y = x.Parent.Left;
}
y.Color = x.Parent.Color;
x.Parent.Color = OrderedTreeNode.BLACK;
y.Left.Color = OrderedTreeNode.BLACK;
RotateRight(x.Parent);
x = rbTree;
}
}
}
x.Color = OrderedTreeNode.BLACK;
}
public bool ContainsKey(IComparable key)
{
OrderedTreeNode treeNode = rbTree; // begin at root
int result = 0;
// traverse tree until node is found
while(treeNode != sentinelNode) {
result = key.CompareTo(treeNode.Key);
if(result == 0) {
lastNodeFound = treeNode;
return true;
}
if(result < 0)
treeNode = treeNode.Left;
else
treeNode = treeNode.Right;
}
return false;
}
///<summary>
/// Determine order, walk the tree and push the nodes onto the stack
///</summary>
public OrderedTreeEnumerator(OrderedTreeNode tnode, bool keys, bool ascending)
{
stack = new Stack();
this.keys = keys;
this.ascending = ascending;
this.tnode = tnode;
Reset();
}
///<summary>
/// GetData
/// Gets the data object associated with the specified key
///<summary>
public object GetData(IComparable key)
{
if(key == null)
throw new ArgumentNullException("Key is null");
int result;
OrderedTreeNode treeNode = rbTree; // begin at root
// traverse tree until node is found
while(treeNode != sentinelNode) {
result = key.CompareTo(treeNode.Key);
if(result == 0) {
lastNodeFound = treeNode;
return treeNode.Data;
}
if(result < 0)
treeNode = treeNode.Left;
else
treeNode = treeNode.Right;
}
return null;
}
public void Reset()
{
pre = true;
stack.Clear();
// use depth-first traversal to push nodes into stack
// the lowest node will be at the top of the stack
if(ascending) {
// find the lowest node
while(tnode != OrderedTree.sentinelNode) {
stack.Push(tnode);
tnode = tnode.Left;
}
}
else {
// the highest node will be at top of stack
while(tnode != OrderedTree.sentinelNode) {
stack.Push(tnode);
tnode = tnode.Right;
}
}
}
///<summary>
/// RestoreAfterInsert
/// Additions to red-black trees usually destroy the red-black
/// properties. Examine the tree and restore. Rotations are normally
/// required to restore it
///</summary>
private void RestoreAfterInsert(OrderedTreeNode x)
{
// x and y are used as variable names for brevity, in a more formal
// implementation, you should probably change the names
OrderedTreeNode y;
// maintain red-black tree properties after adding x
while (x != rbTree && x.Parent.Color == OrderedTreeNode.RED)
{
// Parent node is .Colored red;
if (x.Parent == x.Parent.Parent.Left) // determine traversal path
// is it on the Left or Right subtree?
{
y = x.Parent.Parent.Right; // get uncle
if (y != null && y.Color == OrderedTreeNode.RED)
{
// uncle is red; change x's Parent and uncle to black
x.Parent.Color = OrderedTreeNode.BLACK;
y.Color = OrderedTreeNode.BLACK;
// grandparent must be red. Why? Every red node that is not
// a leaf has only black children
x.Parent.Parent.Color = OrderedTreeNode.RED;
x = x.Parent.Parent; // continue loop with grandparent
}
else
{
// uncle is black; determine if x is greater than Parent
if (x == x.Parent.Right)
{
// yes, x is greater than Parent; rotate Left
// make x a Left child
x = x.Parent;
RotateLeft(x);
}
// no, x is less than Parent
x.Parent.Color = OrderedTreeNode.BLACK; // make Parent black
x.Parent.Parent.Color = OrderedTreeNode.RED; // make grandparent black
RotateRight(x.Parent.Parent); // rotate right
}
}
else
{
// x's Parent is on the Right subtree
// this code is the same as above with "Left" and "Right" swapped
y = x.Parent.Parent.Left;
if (y != null && y.Color == OrderedTreeNode.RED)
{
x.Parent.Color = OrderedTreeNode.BLACK;
y.Color = OrderedTreeNode.BLACK;
x.Parent.Parent.Color = OrderedTreeNode.RED;
x = x.Parent.Parent;
}
else
{
if (x == x.Parent.Left)
{
x = x.Parent;
RotateRight(x);
}
x.Parent.Color = OrderedTreeNode.BLACK;
x.Parent.Parent.Color = OrderedTreeNode.RED;
RotateLeft(x.Parent.Parent);
}
}
}
rbTree.Color = OrderedTreeNode.BLACK; // rbTree should always be black
}