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

This seems like a reduce operation. The analogy is that each time a call is started, the current number of active calls is increased by 1. Each time a call is ended, the current number of calls drops to zero.

Once you have that stream of active calls all you need is to apply a max operation to them. Here is a working python2 example:

from itertools import chain
inp = ((123, 125),
       (123, 130),
       (123, 134),
       (130, 131),
       (130, 131),
       (130, 132),)

# technical: tag each point as start or end of a call
data = chain(*(((a, 'start'), (b, 'end')) for a, b in inp))

def r(state, d):
    last = state[-1]
    # if a call is started we add one to the number of calls,
    # if it ends we reduce one
    current = (1 if d[1] == 'start' else -1)
    state.append(last + current)
    return state

max_intersect = max(reduce(r, sorted(data), [0]))

print max_intersect