*sigh*

gistfile1.txt

import datetime

p1_meetings = [
  (1230, 1300),
  (845, 900),
  (1300, 1500),
]

p2_meetings = [
  (930, 1200),
  (1600, 2359),
]

p3_meetings = [
  (845, 915),
  (1515, 1545),
]

schedules = [p1_meetings, p2_meetings, p3_meetings]


def find_intervals(meetings):

    reformatted_intervals = []

    for meeting_group in meetings:
        for start, end in meeting_group:
            start_hour, start_minutes = int(str(start)[:-2]), int(str(start)[-2:])
            end_hour, end_minutes = int(str(end)[:-2]), int(str(end)[-2:])

            reformatted_intervals.append([60 * start_hour + start_minutes,
                                          60 * end_hour + end_minutes])

    reformatted_intervals.sort(key=lambda x: x[0])
    merged = [[None, 0]] + merge_intervals(reformatted_intervals) + [[24*60-1]]

    open_slots = []
    for idx in xrange(len(merged)-1):
        if merged[idx+1][0] > merged[idx][1]:
            open_slots.append([merged[idx][1], merged[idx+1][0]])

    ans = []
    for start, end in open_slots:
        start_str = str(datetime.timedelta(seconds=start))
        end_str = str(datetime.timedelta(seconds=end))
        ans.append((start_str[2:4] + start_str[5:],
                    end_str[2:4] + end_str[5:]))
    return ans


def merge_intervals(intervals):

    merged = []
    for interval in intervals:
        if not merged or interval[0] > merged[-1][1]:
            merged.append(interval)
            continue
        else:
            merged[-1][1] = max(interval[1], merged[-1][1])
    return merged


find_intervals(schedules)