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