Construct intervals from a sequence of numbers and vice versa

Question

What is a Pythonic way to construct intervals from a sequence of integer numbers? E.g. sequence [1, 2, 3, 6, 7, 9] could be converted to ['1-3', '6-7', '9']. I have implemented it like this:

def sequence_to_intervals(seq):
    intervals = []
    interval_start = None
    interval_end = None
    for i in sorted(seq):
        if interval_start is None:
            interval_start = i
            interval_end = i
        elif interval_end + 1 >= i:
            interval_end = i
        else:
            if interval_start == interval_end:
                intervals.append(str(interval_start))
            else:
                intervals.append(f'{interval_start}-{interval_end}')
            interval_start = i
            interval_end = i
    else:
        if interval_start == interval_end:
            intervals.append(str(interval_start))
        else:
            intervals.append(f'{interval_start}-{interval_end}')
    return intervals

Simple test:

seq = [1, 2, 3, 6, 7, 9]
sequence_to_intervals(seq)
['1-3', '6-7', '9']

Converting intervals back to sequence:

def intervals_to_sequence(intervals):
    seq = []
    for interval in intervals:
        if '-' in interval:
            start, stop = interval.split('-')
            seq += list(range(int(start), int(stop) + 1))
        else:
            seq += [int(interval)]
    return seq

Simple test:

intervals = ['1-3', '6-7', '9']
intervals_to_sequence(intervals)
[1, 2, 3, 6, 7, 9]

Answer 1

For the first part of making sequence to intervals, you could do this instead (prob. more Pythonic?) (This can be converted to a function easier - leave for the exercise)

>>> # if x-1 not in seq:  x becomes start point
>>> # if y+1 not in seq:  y becomes end point
>>> starts = [x for x in seq if x-1 not in seq]
>>> ends =  [y for y in seq if y+1 not in seq]
>>> ends
[3, 7, 9]
>>> intervals = [str(a)+'-'+str(b) for a, b in zip(starts, ends)]
>>> intervals
['1-3', '6-7', '9-9']
>>> 

[Note - last interval could be 'fixed' too - if we see start_point == end_point. Leave as an exercise.]

Then for the second part, it would be quite similar:

>>> seq = []
>>> for inter in intervals:
    s, e = inter.split('-')
    seq += list(range(int(s), int(e)+1))
>>> seq
[1, 2, 3, 6, 7, 9]