class TimeSpan:

def __init__(self, begin, end):

self.begin = begin

self.end = end

def is_valid(self):

return self.begin <= self.end

@classmethod

def from_timespans(cls, timespans):

assert timespans

begin = min(ts.begin for ts in timespans)

end = max(ts.end for ts in timespans)

return cls(begin, end)

def covers(self, other):

""" The if this timespan fully covers the other timespan.

"""

assert self.is_valid()

assert other.is_valid()

return (self.begin <= other.begin) and (other.end <= self.end)

def overlaps(self, other):

""" Test if this span overlaps the other span.

"""

assert self.is_valid()

assert other.is_valid()

return (self.begin <= other.end) and (other.begin <= self.end)

def contains_timestamp(self, timestamp):

""" Test if this timespan contains the given timestamp. """

return self.begin <= timestamp <= self.end

def central_timestamp(self):

""" Retrieve the timestamp in the middle of this timespan. """

return (self.begin + self.end) / 2.0