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