"""

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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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def intranges_from_list(list_):

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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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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, end):

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return (start << 32) | end

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def _decode_range(r):

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return (r >> 32), (r & ((1 << 32) - 1))

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def intranges_contain(int_, ranges):

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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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# we could be immediately ahead of a tuple (start, end)

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# with start < int_ <= end

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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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# or we could be immediately behind a tuple (int_, end)

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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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