overlapping of 3 intervals: what is the fastest way

Question

Give 3 intervals (a,b) , (c,d) , (e,f), what is the fastest way to detect (i.e. have a yes/no answer) if exists a value t that is at the same time a<=t<b AND c<=t<d AND e<=t<f ? Is it also possible to compute the range of t that satisfies this condition, min(t),max(t) ?

Moreover, is it possible to do the same without any hypotesis about the order? (i.e. it could be also b<a or a<b)

I've found a well known solution for two segments but for three is not trivial.

Any js or python example code is welcome.

EDIT: corrected condition requirements

Answer 1

Python solution for any number of intervals regardless of order of the numbers in the interval. It'll either return True, min t value, max t value or False, t value, t value.

def in_interval(intervals):
    if len(intervals) == 0:
        return False, None, None
    min_t = min(intervals[0])
    max_t = max(intervals[0])
    for interval in intervals[1:]:
        min_t = max(min_t, min(interval))
        max_t = min(max_t, max(interval))
    if min_t > max_t:
        return False, None, None
    else:
        return True, min_t, max_t

Test run:

>>> intervals = [(6,1),(2,20),(8,7)]
>>> in_interval(intervals)
(False, 1, 1)
>>> intervals = [(6,1),(2,20),(4,9)]
>>> in_interval(intervals)
(True, 4, 6)