| | """ |
| | 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_) |
| | |
| | |
| | if pos > 0: |
| | left, right = _decode_range(ranges[pos-1]) |
| | if left <= int_ < right: |
| | return True |
| | |
| | if pos < len(ranges): |
| | left, _ = _decode_range(ranges[pos]) |
| | if left == int_: |
| | return True |
| | return False |
| |
|
