#!/usr/bin/python
# -*- coding: utf-8 -*-
"""See calendarprob.py.

This version is, I think, correct, and only 22 lines of code rather
than 34 lines.  It took me 13 minutes to write, because it was buggy
at first, while the version in calendarprob.py (more straightforward
in my view) only took 11.  But this version is, I think, correct in
handling meetings that cross day boundaries.  Also, it handles
meetings for any number of people.

I feel like this might be simpler with numpy argsort...

"""

def intervals(persons):
    n = 0
    for t, d in sorted(item for meetings, (start, end) in persons
                       for item in [(a, -1) for a, b in meetings]
                       + [(b, +1) for a, b in meetings]
                       + [(start, +1), (end, -1)]):
        n += d             # number of people available from this time
        yield t, n

def allopen(persons, duration):
    times = list(intervals(persons))
    for i, (t, n) in enumerate(times[:-1]):
        u = times[i+1][0]
        if n == len(persons) and midminutes(u) - midminutes(t) >= duration:
            yield t, u

def midminutes(t):
    return t // 100 * 60 + t % 100

if __name__ == '__main__':
    persons = [
        ([(900, 1030), (1200, 1300), (1600, 1800)], (900, 2000)),
        ([(1000, 1130), (1230, 1430), (1430, 1500), (1600, 1700)], (1000, 1830)),
        ]
    #print(list(intervals(persons)))
    print(list(allopen(persons, 30)))