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1 """
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2 Given a list of integers, made up of (hopefully) a small number of long runs
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3 of consecutive integers, compute a representation of the form
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4 ((start1, end1), (start2, end2) ...). Then answer the question "was x present
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5 in the original list?" in time O(log(# runs)).
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6 """
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7
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8 import bisect
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9 from typing import List, Tuple
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10
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11
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12 def intranges_from_list(list_: List[int]) -> Tuple[int, ...]:
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13 """Represent a list of integers as a sequence of ranges:
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14 ((start_0, end_0), (start_1, end_1), ...), such that the original
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15 integers are exactly those x such that start_i <= x < end_i for some i.
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16
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17 Ranges are encoded as single integers (start << 32 | end), not as tuples.
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18 """
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19
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20 sorted_list = sorted(list_)
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21 ranges = []
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22 last_write = -1
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23 for i in range(len(sorted_list)):
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24 if i + 1 < len(sorted_list):
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25 if sorted_list[i] == sorted_list[i + 1] - 1:
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26 continue
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27 current_range = sorted_list[last_write + 1 : i + 1]
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28 ranges.append(_encode_range(current_range[0], current_range[-1] + 1))
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29 last_write = i
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30
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31 return tuple(ranges)
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32
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33
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34 def _encode_range(start: int, end: int) -> int:
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35 return (start << 32) | end
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36
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37
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38 def _decode_range(r: int) -> Tuple[int, int]:
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39 return (r >> 32), (r & ((1 << 32) - 1))
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40
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41
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42 def intranges_contain(int_: int, ranges: Tuple[int, ...]) -> bool:
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43 """Determine if `int_` falls into one of the ranges in `ranges`."""
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44 tuple_ = _encode_range(int_, 0)
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45 pos = bisect.bisect_left(ranges, tuple_)
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46 # we could be immediately ahead of a tuple (start, end)
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47 # with start < int_ <= end
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48 if pos > 0:
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49 left, right = _decode_range(ranges[pos - 1])
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50 if left <= int_ < right:
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51 return True
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52 # or we could be immediately behind a tuple (int_, end)
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53 if pos < len(ranges):
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54 left, _ = _decode_range(ranges[pos])
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55 if left == int_:
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56 return True
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57 return False
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