/// <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());
}
