jpayne@7: """
jpayne@7: Given a list of integers, made up of (hopefully) a small number of long runs
jpayne@7: of consecutive integers, compute a representation of the form
jpayne@7: ((start1, end1), (start2, end2) ...). Then answer the question "was x present
jpayne@7: in the original list?" in time O(log(# runs)).
jpayne@7: """
jpayne@7: 
jpayne@7: import bisect
jpayne@7: from typing import List, Tuple
jpayne@7: 
jpayne@7: def intranges_from_list(list_: List[int]) -> Tuple[int, ...]:
jpayne@7:     """Represent a list of integers as a sequence of ranges:
jpayne@7:     ((start_0, end_0), (start_1, end_1), ...), such that the original
jpayne@7:     integers are exactly those x such that start_i <= x < end_i for some i.
jpayne@7: 
jpayne@7:     Ranges are encoded as single integers (start << 32 | end), not as tuples.
jpayne@7:     """
jpayne@7: 
jpayne@7:     sorted_list = sorted(list_)
jpayne@7:     ranges = []
jpayne@7:     last_write = -1
jpayne@7:     for i in range(len(sorted_list)):
jpayne@7:         if i+1 < len(sorted_list):
jpayne@7:             if sorted_list[i] == sorted_list[i+1]-1:
jpayne@7:                 continue
jpayne@7:         current_range = sorted_list[last_write+1:i+1]
jpayne@7:         ranges.append(_encode_range(current_range[0], current_range[-1] + 1))
jpayne@7:         last_write = i
jpayne@7: 
jpayne@7:     return tuple(ranges)
jpayne@7: 
jpayne@7: def _encode_range(start: int, end: int) -> int:
jpayne@7:     return (start << 32) | end
jpayne@7: 
jpayne@7: def _decode_range(r: int) -> Tuple[int, int]:
jpayne@7:     return (r >> 32), (r & ((1 << 32) - 1))
jpayne@7: 
jpayne@7: 
jpayne@7: def intranges_contain(int_: int, ranges: Tuple[int, ...]) -> bool:
jpayne@7:     """Determine if `int_` falls into one of the ranges in `ranges`."""
jpayne@7:     tuple_ = _encode_range(int_, 0)
jpayne@7:     pos = bisect.bisect_left(ranges, tuple_)
jpayne@7:     # we could be immediately ahead of a tuple (start, end)
jpayne@7:     # with start < int_ <= end
jpayne@7:     if pos > 0:
jpayne@7:         left, right = _decode_range(ranges[pos-1])
jpayne@7:         if left <= int_ < right:
jpayne@7:             return True
jpayne@7:     # or we could be immediately behind a tuple (int_, end)
jpayne@7:     if pos < len(ranges):
jpayne@7:         left, _ = _decode_range(ranges[pos])
jpayne@7:         if left == int_:
jpayne@7:             return True
jpayne@7:     return False