"""
Given a list of integers, made up of (hopefully) a small number of long runs
of consecutive integers, compute a representation of the form
((start1, end1), (start2, end2) ...). Then answer the question "was x present
in the original list?" in time O(log(# runs)).
"""

import bisect

def intranges_from_list(list_):
    """Represent a list of integers as a sequence of ranges:
    ((start_0, end_0), (start_1, end_1), ...), such that the original
    integers are exactly those x such that start_i <= x < end_i for some i.
    """

    sorted_list = sorted(list_)
    ranges = []
    last_write = -1
    for i in range(len(sorted_list)):
        if i+1 < len(sorted_list):
            if sorted_list[i] == sorted_list[i+1]-1:
                continue
        current_range = sorted_list[last_write+1:i+1]
        range_tuple = (current_range[0], current_range[-1] + 1)
        ranges.append(range_tuple)
        last_write = i

    return tuple(ranges)


def intranges_contain(int_, ranges):
    """Determine if `int_` falls into one of the ranges in `ranges`."""
    tuple_ = (int_, int_)
    pos = bisect.bisect_left(ranges, tuple_)
    # we could be immediately ahead of a tuple (start, end)
    # with start < int_ <= end
    if pos > 0:
        left, right = ranges[pos-1]
        if left <= int_ < right:
            return True
    # or we could be immediately behind a tuple (int_, end)
    if pos < len(ranges):
        left, _ = ranges[pos]
        if left == int_:
            return True
    return False