/// <summary>
/// Function that balance the tree after having updated its height
/// </summary>
/// <param name="node">the root of the tree to balance </param>
private void Balance(ref AvlTreeNode <T> node)
{
// Left Heavy Tree
if (GetBalanceFactor(node) == 2)
{
if (GetBalanceFactor(node.Left) > -1) // Left Heavy Left Subtree or zero balance factor
{
SingleRightRotation(ref node);
}
else // Right Heavy Left Subtree
{
DoubleLeftRightRotation(ref node);
}
} // Right Heavy Tree
else if (GetBalanceFactor(node) == -2)
{
if (GetBalanceFactor(node.Right) < 1) // Right Heavy Right Subtree or zero balance factor
{
SingleLeftRotation(ref node);
}
else // Left Heavy Right SubTree
{
DoubleRightLeftRotation(ref node);
}
}
}
/// <summary>
/// Get the maximum value of a tree
/// </summary>
/// <param name="avlTreeNode">the root of the tree</param>
/// <returns>the maximum value of the tree</returns>
private static T FindMaxValue(AvlTreeNode <T> avlTreeNode)
{
while (avlTreeNode.Right != null)
{
avlTreeNode = avlTreeNode.Right;
}
return(avlTreeNode.Value);
}
/// <summary>
/// A Single rotation composed of a left rotation and a right rotation.
/// </summary>
/// <param name="node">The pivoting node involved in rotations.</param>
private void SingleRightRotation(ref AvlTreeNode <T> node)
{
AvlTreeNode <T> node1 = node.Left;
node.Left = node1.Right;
node1.Right = node;
AdjustHeight(node);
AdjustHeight(node1);
node = node1;
}
/// <summary>
/// Inserts a new node with the specified value at the appropriate location in the <see cref="AvlTree{T}"/>.
/// </summary>
/// <remarks>
/// This method is an O(log n) operation plus constant time due to rebalancing.
/// </remarks>
/// <param name="item">Value to insert.</param>
public override void Add(T item)
{
if (Root == null)
{
Root = new AvlTreeNode <T>(item);
}
else
{
AvlTreeNode <T> root = Root;
InsertNode(ref root, item, true);
Root = root;
}
Count++;
}
/// <summary>
/// Called by the Add method. Finds the location where to put the node in the <see cref="AvlTree{T}"/> and if
/// necessary rebalance.
/// </summary>
/// <param name="avlNode">Node to start searching from.</param>
/// <param name="value">Value to insert into the tree.</param>
/// <param name="insertDuplicates">if set to <c>true</c>, inserts value if it is a duplicate.</param>
/// <returns><c>true</c> if a new node was added, <c>false</c> otherwise</returns>
private bool InsertNode(ref AvlTreeNode <T> avlNode, T value, bool insertDuplicates)
{
int compareResult = Comparer.Compare(value, avlNode.Value);
if (!insertDuplicates && (compareResult == 0))
{
return(false);
}
bool newNodeAdded = true;
if (compareResult < 0)
{
if (avlNode.Left == null)
{
avlNode.Left = new AvlTreeNode <T>(value);
}
else
{
AvlTreeNode <T> left = avlNode.Left;
newNodeAdded = InsertNode(ref left, value, insertDuplicates);
avlNode.Left = left;
}
}
else
{
if (avlNode.Right == null)
{
avlNode.Right = new AvlTreeNode <T>(value);
}
else
{
AvlTreeNode <T> right = avlNode.Right;
newNodeAdded = InsertNode(ref right, value, insertDuplicates);
avlNode.Right = right;
}
}
if (newNodeAdded)
{
if ((GetBalanceFactor(avlNode) == 2) || (GetBalanceFactor(avlNode) == -2))
{
Balance(ref avlNode);
}
else
{
AdjustHeight(avlNode);
}
}
return(newNodeAdded);
}
/// <summary>
/// Called by remove public method. This removal helper method find the item to
/// remove and if present remove it rebalancing in case the avl tree
/// </summary>
/// <param name="avlNode">root subtree node to start deleting </param>
/// <param name="item">value to delete</param>
/// <returns>the root of the tree with value removed</returns>
private AvlTreeNode <T> RemoveNode(AvlTreeNode <T> avlNode, T item)
{
if (avlNode == null)
{
throw new Exception("item not found");
}
if (item.IsLessThan(avlNode.Value, Comparer))
{
avlNode.Left = RemoveNode(avlNode.Left, item);
}
else if (item.IsGreaterThan(avlNode.Value, Comparer))
{
avlNode.Right = RemoveNode(avlNode.Right, item);
}
else if (item.IsEqual(avlNode.Value, Comparer))
{
if (avlNode.Right == null && avlNode.Left == null)
{
// node to remove is a leaf, we simply delete node
return(null);
}
if (avlNode.Left == null)
{
// node to remove has only a right subtree, we link it with its parent
return(avlNode.Right);
}
if (avlNode.Right == null)
{
// node to remove has only a left subtree, we link it with its parent
return(avlNode.Left);
}
// node to remove has both childs
T newValue = FindMaxValue(avlNode.Left);
avlNode.Value = newValue;
avlNode.Left = RemoveNode(avlNode.Left, newValue);
}
// Checking for unbalance, if detected, balance (include also height update)
// otherwise only Adjust height
if ((GetBalanceFactor(avlNode) == 2) || (GetBalanceFactor(avlNode) == -2))
{
Balance(ref avlNode);
}
else
{
AdjustHeight(avlNode);
}
return(avlNode);
}
/// <summary>
/// A Double rotation composed of a right rotation and a left rotation.
/// </summary>
/// <param name="node">The pivoting node involved in rotations.</param>
private void DoubleRightLeftRotation(ref AvlTreeNode <T> node)
{
AvlTreeNode <T> node1 = node.Right.Left;
node.Right.Left = node1.Right;
node1.Right = node.Right;
AdjustHeight(node.Right);
AdjustHeight(node1);
node.Right = node1.Left;
node1.Left = node;
AdjustHeight(node);
AdjustHeight(node1);
node = node1;
}
/// <summary>
/// Inserts a new node with the specified value at the appropriate location in the <see cref="AvlTree{T}"/>
/// if it does not already exist within the tree. Does nothing otherwise.
/// </summary>
/// <remarks>
/// This method is an O(log n) operation plus constant time due to rebalancing.
/// </remarks>
/// <param name="item">The item.</param>
/// <returns>true if node was unique and added.</returns>
public bool AddUnique(T item)
{
if (Root == null)
{
Root = new AvlTreeNode <T>(item);
Count++;
return(true);
}
AvlTreeNode <T> root = Root;
bool newNodeAdded = InsertNode(ref root, item, false);
Root = root;
if (newNodeAdded)
{
Count++;
}
return(newNodeAdded);
}
/// <summary>
/// Set the proper height of a node
/// </summary>
/// <param name="avlNode">the node needing a height fix </param>
private void AdjustHeight(AvlTreeNode <T> avlNode)
{
avlNode.Height = Math.Max(Height(avlNode.Left), Height(avlNode.Right)) + 1;
}
/// <summary>
/// Retrieves the height of the specified node.
/// </summary>
/// <param name="node">Node to obtain depth.</param>
/// <returns>If the node is null 0; otherwise its proper height.</returns>
public int Height(AvlTreeNode <T> node)
{
return((node == null) ? 0 : node.Height);
}
/// <summary>
/// Get the balance factor for the node
/// Balance factor is defined as the height difference
/// between left and right subtree if subtrees exist otherwise
/// for a null node as 0
/// </summary>
public int GetBalanceFactor(AvlTreeNode <T> node)
{
return((node == null) ? 0 : Height(node.Left) - Height(node.Right));
}