/// <summary>
/// Return a new dict with the root key-value pair removed
/// </summary>
AvlNode <T> RemoveRoot()
{
if (IsEmpty)
{
return(this);
}
if (left.IsEmpty)
{
return(right);
}
if (right.IsEmpty)
{
return(left);
}
//Neither are empty:
if (left._count < right._count)
{
//LTDict has fewer, so promote from GTDict to minimize depth
AvlNode <T> min;
var newgt = right.RemoveMin(out min);
var newroot = new AvlNode <T> (min.Value, left, newgt);
return(newroot.FixRootBalance());
}
else
{
AvlNode <T> max;
var newlt = left.RemoveMax(out max);
var newroot = new AvlNode <T> (max.Value, newlt, right);
return(newroot.FixRootBalance());
}
}
AvlNode <T> RemoveMax(out AvlNode <T> max)
{
if (IsEmpty)
{
max = Empty;
return(Empty);
}
if (right.IsEmpty)
{
//We are the max:
max = this;
return(left);
}
else
{
//Go down:
var newgt = right.RemoveMax(out max);
var newroot = new AvlNode <T> (Value, left, newgt);
return(newroot.FixRootBalance());
}
}
