AvlNode <T> RemoveMin(out AvlNode <T> min)
{
if (IsEmpty)
{
min = Empty;
return(Empty);
}
if (_left.IsEmpty)
{
//We are the minimum:
min = this;
return(_right);
}
//Go down:
var newLt = _left.RemoveMin(out min);
var newRoot = NewOrMutate(Value, newLt, _right);
return(newRoot.FixRootBalance());
}
public AvlNode <T> SetItem(int index, T val)
{
AvlNode <T> newLt = _left;
AvlNode <T> newGt = _right;
if (index < _left._count)
{
newLt = _left.SetItem(index, val);
}
else if (index > _left._count)
{
newGt = _right.SetItem(index - _left._count - 1, val);
}
else
{
return(NewOrMutate(val, newLt, newGt));
}
return(NewOrMutate(Value, newLt, newGt));
}
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 = NewOrMutate(Value, _left, newGt);
return(newRoot.FixRootBalance());
}
}
/// <summary>
/// Return a new tree with the key-value pair inserted
/// If the key is already present, it replaces the value
/// This operation is O(Log N) where N is the number of keys
/// </summary>
public AvlNode <T> InsertIntoNew(int index, T val)
{
if (IsEmpty)
{
return(new AvlNode <T>(val));
}
AvlNode <T> newLt = _left;
AvlNode <T> newGt = _right;
if (index <= _left._count)
{
newLt = _left.InsertIntoNew(index, val);
}
else
{
newGt = _right.InsertIntoNew(index - _left._count - 1, val);
}
var newRoot = NewOrMutate(Value, newLt, newGt);
return(newRoot.FixRootBalance());
}
public virtual AvlNode <T> NewOrMutate(T newValue, AvlNode <T> newLeft, AvlNode <T> newRight)
{
return(new AvlNode <T>(newValue, newLeft, newRight));
}
public AvlNode()
{
_right = Empty;
_left = Empty;
}