/// <summary>
/// Recursive add or update used in indexer.
/// </summary>
private AVLTreeMapNode <TKey, TValue> AddOrUpdate(AVLTreeMapNode <TKey, TValue> node, TKey key, TValue value, out bool updated)
{
updated = false;
if (node == null)
{
return(new AVLTreeMapNode <TKey, TValue>(key, value));
}
int cmp = comparer.Compare(key, node.Key);
if (cmp < 0)
{
node.Left = AddOrUpdate(node.Left, key, value, out updated);
}
else if (cmp > 0)
{
node.Right = AddOrUpdate(node.Right, key, value, out updated);
}
else
{
node.Value = value;
updated = true; // mark that value is updated
return(node);
}
if (updated) // if only updated, no need to balance
{
return(node);
}
else
{
return(Balance(node));
}
}
/// <summary>
/// Fixes the node height, calculating it from its children.
/// </summary>
private void FixHeight(AVLTreeMapNode <TKey, TValue> node)
{
var leftHeight = NodeHeight(node.Left);
var rightHeight = NodeHeight(node.Right);
node.Height = (leftHeight > rightHeight ? leftHeight : rightHeight) + 1;
}
/// <summary>
/// Checks if balancing is needed and performs it.
/// </summary>
private AVLTreeMapNode <TKey, TValue> Balance(AVLTreeMapNode <TKey, TValue> node)
{
FixHeight(node);
// if balance factor is -2 the left subtree is smaller than the right
// so we need to perform a left rotation
if (BalanceFactor(node) == -2)
{
if (BalanceFactor(node.Right) > 0)// Right Left Case if true, else Right Right Case
{
node.Right = RotateRight(node.Right);
}
return(RotateLeft(node));
}
// if balance factor is 2 the right subtree is smaller than the left
// so we need to perform a right rotation
if (BalanceFactor(node) == 2)
{
if (BalanceFactor(node.Left) < 0)// Left Right Case if true, else Left Left Case
{
node.Left = RotateLeft(node.Left);
}
return(RotateRight(node));
}
return(node);
}
/// <summary>
/// Finds and removes the min element of the given subtree.
/// </summary>
private AVLTreeMapNode <TKey, TValue> FindAndRemoveMin(AVLTreeMapNode <TKey, TValue> node, ref AVLTreeMapNode <TKey, TValue> min)
{
if (node.Left == null)
{
min = node;
return(node.Right);
}
node.Left = FindAndRemoveMin(node.Left, ref min);
return(Balance(node));
}
/// <summary>
/// Standard right rotation.
/// </summary>
private AVLTreeMapNode <TKey, TValue> RotateRight(AVLTreeMapNode <TKey, TValue> node)
{
AVLTreeMapNode <TKey, TValue> m = node.Left;
node.Left = m.Right;
m.Right = node;
FixHeight(node);
FixHeight(m);
return(m);
}
/// <summary>
/// Recursive removal with balancing on every step.
/// </summary>
private AVLTreeMapNode <TKey, TValue> Remove(AVLTreeMapNode <TKey, TValue> node, TKey key)
{
if (node == null)
{
return(node);
}
int cmp = comparer.Compare(key, node.Key);
if (cmp < 0)
{
node.Left = Remove(node.Left, key);
}
else if (cmp > 0)
{
node.Right = Remove(node.Right, key);
}
else
{
Count--;
AVLTreeMapNode <TKey, TValue> left = node.Left;
AVLTreeMapNode <TKey, TValue> right = node.Right;
node.Invalidate();
if (right == null)
{
return(left);
}
AVLTreeMapNode <TKey, TValue> min = null;
AVLTreeMapNode <TKey, TValue> rightSubtreeRoot = FindAndRemoveMin(right, ref min);
min.Right = rightSubtreeRoot;
min.Left = left;
return(Balance(min));
}
return(Balance(node));
}
/// <summary>
/// Recursive insertion with balancing on every step.
/// </summary>
private AVLTreeMapNode <TKey, TValue> Add(AVLTreeMapNode <TKey, TValue> node, TKey key, TValue value)
{
if (node == null)
{
return(new AVLTreeMapNode <TKey, TValue>(key, value));
}
int cmp = comparer.Compare(key, node.Key);
if (cmp < 0)
{
node.Left = Add(node.Left, key, value);
}
else if (cmp > 0)
{
node.Right = Add(node.Right, key, value);
}
else
{
throw new ArgumentException("Tried to insert duplicate value!");
}
return(Balance(node));
}
/// <summary>
/// Gets the node height. Returns 0 if node is null.
/// </summary>
private int NodeHeight(AVLTreeMapNode <TKey, TValue> node)
{
return(node?.Height ?? 0);
}
/// <summary>
/// Calculates the balance factor.
/// </summary>
private int BalanceFactor(AVLTreeMapNode <TKey, TValue> node)
{
return(NodeHeight(node.Left) - NodeHeight(node.Right));
}