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Commit | Line | Data |
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e0df8241 JR |
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 | def intranges_from_list(list_: List[int]) -> Tuple[int, ...]: | |
12 | """Represent a list of integers as a sequence of ranges: | |
13 | ((start_0, end_0), (start_1, end_1), ...), such that the original | |
14 | integers are exactly those x such that start_i <= x < end_i for some i. | |
15 | ||
16 | Ranges are encoded as single integers (start << 32 | end), not as tuples. | |
17 | """ | |
18 | ||
19 | sorted_list = sorted(list_) | |
20 | ranges = [] | |
21 | last_write = -1 | |
22 | for i in range(len(sorted_list)): | |
23 | if i+1 < len(sorted_list): | |
24 | if sorted_list[i] == sorted_list[i+1]-1: | |
25 | continue | |
26 | current_range = sorted_list[last_write+1:i+1] | |
27 | ranges.append(_encode_range(current_range[0], current_range[-1] + 1)) | |
28 | last_write = i | |
29 | ||
30 | return tuple(ranges) | |
31 | ||
32 | def _encode_range(start: int, end: int) -> int: | |
33 | return (start << 32) | end | |
34 | ||
35 | def _decode_range(r: int) -> Tuple[int, int]: | |
36 | return (r >> 32), (r & ((1 << 32) - 1)) | |
37 | ||
38 | ||
39 | def intranges_contain(int_: int, ranges: Tuple[int, ...]) -> bool: | |
40 | """Determine if `int_` falls into one of the ranges in `ranges`.""" | |
41 | tuple_ = _encode_range(int_, 0) | |
42 | pos = bisect.bisect_left(ranges, tuple_) | |
43 | # we could be immediately ahead of a tuple (start, end) | |
44 | # with start < int_ <= end | |
45 | if pos > 0: | |
46 | left, right = _decode_range(ranges[pos-1]) | |
47 | if left <= int_ < right: | |
48 | return True | |
49 | # or we could be immediately behind a tuple (int_, end) | |
50 | if pos < len(ranges): | |
51 | left, _ = _decode_range(ranges[pos]) | |
52 | if left == int_: | |
53 | return True | |
54 | return False |