1  """
   2  Given a list of integers, made up of (hopefully) a small number of long runs
   3  of consecutive integers, compute a representation of the form
   4  ((start1, end1), (start2, end2) ...). Then answer the question "was x present
   5  in the original list?" in time O(log(# runs)).
   6  """
   7  
   8  import bisect
   9  from typing import List, Tuple
  10  
  11  
  12  def intranges_from_list(list_: List[int]) -> Tuple[int, ...]:
  13      """Represent a list of integers as a sequence of ranges:
  14      ((start_0, end_0), (start_1, end_1), ...), such that the original
  15      integers are exactly those x such that start_i <= x < end_i for some i.
  16  
  17      Ranges are encoded as single integers (start << 32 | end), not as tuples.
  18      """
  19  
  20      sorted_list = sorted(list_)
  21      ranges = []
  22      last_write = -1
  23      for i in range(len(sorted_list)):
  24          if i + 1 < len(sorted_list):
  25              if sorted_list[i] == sorted_list[i + 1] - 1:
  26                  continue
  27          current_range = sorted_list[last_write + 1 : i + 1]
  28          ranges.append(_encode_range(current_range[0], current_range[-1] + 1))
  29          last_write = i
  30  
  31      return tuple(ranges)
  32  
  33  
  34  def _encode_range(start: int, end: int) -> int:
  35      return (start << 32) | end
  36  
  37  
  38  def _decode_range(r: int) -> Tuple[int, int]:
  39      return (r >> 32), (r & ((1 << 32) - 1))
  40  
  41  
  42  def intranges_contain(int_: int, ranges: Tuple[int, ...]) -> bool:
  43      """Determine if `int_` falls into one of the ranges in `ranges`."""
  44      tuple_ = _encode_range(int_, 0)
  45      pos = bisect.bisect_left(ranges, tuple_)
  46      # we could be immediately ahead of a tuple (start, end)
  47      # with start < int_ <= end
  48      if pos > 0:
  49          left, right = _decode_range(ranges[pos - 1])
  50          if left <= int_ < right:
  51              return True
  52      # or we could be immediately behind a tuple (int_, end)
  53      if pos < len(ranges):
  54          left, _ = _decode_range(ranges[pos])
  55          if left == int_:
  56              return True
  57      return False
  58