Sample solution: Parametrise those tests

test_times.py

from times import compute_overlap_time, time_range


@pytest.mark.parametrize("first_range, second_range, expected_overlap",
[(time_range("2010-01-12 10:00:00", "2010-01-12 12:00:00"),
  time_range("2010-01-12 10:30:00", "2010-01-12 10:45:00", 2, 60),
  [("2010-01-12 10:30:00","2010-01-12 10:37:00"), ("2010-01-12 10:38:00", "2010-01-12 10:45:00")]),
  (time_range("2010-01-12 10:00:00", "2010-01-12 11:00:00"),
  time_range("2010-01-12 12:30:00", "2010-01-12 12:45:00", 2, 60),
  []),
  (time_range("2010-01-12 10:00:00", "2010-01-12 13:00:00", 3, 900),
  time_range("2010-01-12 10:40:00", "2010-01-12 11:20:00", 2, 120),
  [("2010-01-12 10:40:00","2010-01-12 10:50:00"), ("2010-01-12 11:05:00", "2010-01-12 11:20:00")]),
  (time_range("2010-01-12 10:00:00", "2010-01-12 11:00:00"),
  time_range("2010-01-12 11:00:00", "2010-01-12 12:45:00"),
  [])
])
def test_time_range_overlap(first_range, second_range, expected_overlap):
    assert compute_overlap_time(first_range, second_range) == expected_overlap

times.py

import datetime


def time_range(start_time, end_time, number_of_intervals=1, gap_between_intervals_s=0):
    start_time_s = datetime.datetime.strptime(start_time, "%Y-%m-%d %H:%M:%S")
    end_time_s = datetime.datetime.strptime(end_time, "%Y-%m-%d %H:%M:%S")
    d = (end_time_s - start_time_s).total_seconds() / number_of_intervals + gap_between_intervals_s * (1 / number_of_intervals - 1)
    sec_range = [(start_time_s + datetime.timedelta(seconds=i * d + i * gap_between_intervals_s),
                  start_time_s + datetime.timedelta(seconds=(i + 1) * d + i * gap_between_intervals_s))
                 for i in range(number_of_intervals)]
    return [(ta.strftime("%Y-%m-%d %H:%M:%S"), tb.strftime("%Y-%m-%d %H:%M:%S")) for ta, tb in sec_range]


def compute_overlap_time(range1, range2):
    overlap_time = []
    for start1, end1 in range1:
        for start2, end2 in range2:
            # both ranges need to start before the other ends, otherwise there is no overlap!
            if start1 <= end2 and start2 <= end1: 
                low = max(start1, start2)
                high = min(end1, end2)
                if high == low:
                    continue
                overlap_time.append((low, high))
    return overlap_time