| """ |
| 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 |
