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