Fix Overlaps | Python Fiddle

import random

def fix_overlaps(l):
    """
    Fixes the overlaps
    Note: Needs to be a list of pairs (start, end) sorted by start
    """
    res = list()
    if len(l) == 0:
        return res
    cur = l[0]
    for pair in l:
        if cur[1] > pair[0]:
            if cur[1] < pair[1]:
                cur = (cur[0], pair[1])
        else:
            res.append(cur)
            cur = pair
    res.append(cur)
    return res

def random_integer(a, b):
    return random.randint(a, b)

def random_range_list(count, a, b):
    res = list()
    for i in range(count):
        start = random_integer(a, b - 1) # Obviously a real value goes here
        end = random_integer(start, b) # Obviously a real value goes here
        pair = (start, end)
        res.append(pair)
    return res

busy_times = random_range_list(10, 0, 1000)
print "Random: ", busy_times

sorted_times = sorted(busy_times, key= lambda pair: pair[0])
print "Sorted: ", sorted_times

unioned_times = fix_overlaps(sorted_times)
print "Unioned: ", unioned_times

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