class_docstr: Queue with Binary Indexed Tree cache
  
  queue-like data structure
  append, update are O(log n)
  reduction over an interval is O(log n) per query
class_docstr_tok: ["Queue","with","Binary","Indexed","Tree","cache","queue-like","data","structure","append",",","update","are","O","(","log","n",")","reduction","over","an","interval","is","O","(","log","n",")","per","query"]
code: def _write(self, ix: int, val: Optional[V]) -> Optional[V]:
      ixl, ixr = self.bounds
      return _write(ixl, ixr, self.root, ix, val, self.op)
  
imports: import collections
  from typing import Any, Callable, Deque, Generic, List, Optional, Sequence, Tuple, TypeVar
  import numpy
  from pfrl.utils.random import sample_n_k
label_desc: Use image node_id 3 for calling the TreeQueue obj's underlying member method code with example usage: obj._write(ix, val) and returns: _write