Finding (number of) overlaps in a list of time ranges

Question

Given a list of time ranges, I need to find the maximum number of overlaps.

Following is a dataset showing a 10 minute interval of calls, from which I am trying to f

Answer 1

Here is a working algorithm in Python

def maximumOverlap(calls):
    times = []
    for call in calls:
        startTime, endTime = call
        times.append((startTime, 'start'))
        times.append((endTime, 'end'))
    times = sorted(times)

    count = 0
    maxCount = 0
    for time in times:
        if time[1] == 'start':
            count += 1    # increment on arrival/start
        else:
            count -= 1    # decrement on departure/end
        maxCount = max(count, maxCount)  # maintain maximum
    return maxCount

calls = [
('2:22:22 PM', '2:22:33 PM'),
('2:22:35 PM', '2:22:42 PM'),
('2:22:36 PM', '2:22:43 PM'),
('2:22:46 PM', '2:22:54 PM'),
('2:22:49 PM', '2:27:21 PM'),
('2:22:57 PM', '2:23:03 PM'),
('2:23:29 PM', '2:23:40 PM'),
('2:24:08 PM', '2:24:14 PM'),
('2:27:37 PM', '2:39:14 PM'),
('2:27:47 PM', '2:27:55 PM'),
('2:29:04 PM', '2:29:26 PM'),
('2:29:31 PM', '2:29:43 PM'),
('2:29:45 PM', '2:30:10 PM'),
]
print(maximumOverlap(calls))