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