Complexity of IntervalTree.{begin,end} is O(1), not O(n).

They call self.boundary_table.iloc[0] (resp. [-1]), and self.boundary_table
is a SortedDict.
SortedDict.iloc is an instance of _IlocWrapper, whose __getitem__ only
does: return self._dict._list[index]
_dict is the SortedDict instance, and _dict._list is an instance of
SortedList.
Finally, SortedList.__item__ has special cases to perform in O(1)
when the index is 0 or -1.

References:
* https://github.com/grantjenks/sorted_containers/blob/ccec8d4/sortedcontainers/sorteddict.py#L34-L40
* https://github.com/grantjenks/sorted_containers/blob/b62fe6a/sortedcontainers/sortedlist.py#L599-L602

Author: progval

intervaltree/intervaltree.py

@@ -818,7 +818,7 @@ def begin(self):
         """
         Returns the lower bound of the first interval in the tree.
         
-        Completes in O(n) time.
+        Completes in O(1) time.
         """
         if not self.boundary_table:
             return 0
@@ -828,7 +828,7 @@ def end(self):
         """
         Returns the upper bound of the last interval in the tree.
         
-        Completes in O(n) time.
+        Completes in O(1) time.
         """
         if not self.boundary_table:
             return 0