示例#1
0
 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;
 }
示例#2
0
        ///<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
        }
示例#3
0
        ///<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;
        }
示例#4
0
        ///<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;
        }
示例#5
0
        ///<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;
        }
示例#6
0
        ///<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;
        }
示例#7
0
        ///<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;
        }
示例#8
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 public OrderedTree()
 {
     rbTree = sentinelNode;
     lastNodeFound = sentinelNode;
 }
示例#9
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 ///<summary>
 /// Clear
 /// Empties or clears the tree
 ///<summary>
 public void Clear()
 {
     rbTree = sentinelNode;
     intCount = 0;
 }
示例#10
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        ///<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;
        }
示例#11
0
        ///<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);
        }
示例#12
0
 ///<summary>
 /// Clear
 /// Empties or clears the tree
 ///<summary>
 public void Clear()
 {
     rbTree   = sentinelNode;
     intCount = 0;
 }
示例#13
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;
            }
        }
示例#14
0
 public OrderedTree()
 {
     rbTree        = sentinelNode;
     lastNodeFound = sentinelNode;
 }
示例#15
0
        ///<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;
        }
示例#16
0
 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;
 }
示例#17
0
 ///<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();
 }
示例#18
0
        ///<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;
        }
示例#19
0
 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;
         }
     }
 }
示例#20
0
        ///<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
        }