internal AvlTree(ElaValue key, ElaValue value, AvlTree left, AvlTree right)
{
Key = key;
Value = value;
Left = left;
Right = right;
TreeHeight = 1 + Math.Max(Height(left), Height(right));
}
internal virtual AvlTree Add(ElaValue key, ElaValue value)
{
var result = default(AvlTree);
if (key.CompareTo(Key) > 0)
result = new AvlTree(Key, Value, Left, Right.Add(key, value));
else
result = new AvlTree(Key, Value, Left.Add(key, value), Right);
return MakeBalanced(result);
}
internal virtual AvlTree Remove(ElaValue key)
{
var result = default(AvlTree);
var compare = key.CompareTo(Key);
if (compare == 0)
{
if (Right.IsEmpty && Left.IsEmpty)
result = Empty;
else if (Right.IsEmpty && !Left.IsEmpty)
result = Left;
else if (!Right.IsEmpty && Left.IsEmpty)
result = Right;
else
{
var successor = Right;
while (!successor.Left.IsEmpty)
successor = successor.Left;
result = new AvlTree(successor.Key, successor.Value, Left, Right.Remove(successor.Key));
}
}
else if (compare < 0)
result = new AvlTree(Key, Value, Left.Remove(key), Right);
else
result = new AvlTree(Key, Value, Left, Right.Remove(key));
return MakeBalanced(result);
}
private static AvlTree RotateRight(AvlTree tree)
{
if (tree.Left.IsEmpty)
return tree;
return new AvlTree(tree.Left.Key, tree.Left.Value, tree.Left.Left,
new AvlTree(tree.Key, tree.Value, tree.Left.Right, tree.Right));
}
private static AvlTree MakeBalanced(AvlTree tree)
{
var result = default(AvlTree);
if (IsRightHeavy(tree))
{
if (IsLeftHeavy(tree.Right))
result = DoubleLeft(tree);
else
result = RotateLeft(tree);
}
else if (IsLeftHeavy(tree))
{
if (IsRightHeavy(tree.Left))
result = DoubleRight(tree);
else
result = RotateRight(tree);
}
else
result = tree;
return result;
}
private static bool IsRightHeavy(AvlTree tree)
{
return Balance(tree) >= 2;
}
private static bool IsLeftHeavy(AvlTree tree)
{
return Balance(tree) <= -2;
}
private static int Height(AvlTree tree)
{
return tree.IsEmpty ? 0 : tree.TreeHeight;
}
private static AvlTree DoubleRight(AvlTree tree)
{
if (tree.Left.IsEmpty)
return tree;
var rotatedLeftChild = new AvlTree(tree.Key, tree.Value, RotateLeft(tree.Left), tree.Right);
return RotateRight(rotatedLeftChild);
}
private static int Balance(AvlTree tree)
{
if (tree.IsEmpty)
return 0;
return Height(tree.Right) - Height(tree.Left);
}