Answer by martineau for I want to calculate the difference between two values in a "distance_table = []" with permutations, how can I use permutations correctly in this case?

You say you want all permutations without any city to appearing twice, yet your example has the starting city (cityA) listed again at the end:

I want for example: cityA-cityB + cityB-cityC + cityC-cityA

So, assuming the first city appearing again at the end is actually what you meant, I think the following shows how you could generate the permutations of cities you want — if that assumption is wrong, simply remove the one line where the first city is duplicated.

In order to get differing total distances (with three it's always the same), I added a fourth city and changed the output format so it's more compact to better accommodate more cities.

Barcelona;Belgrade;Berlin;Brussels0;1528.13;1497.61;1346.01528.13;0;999.25;1723.01497.61;999.25;0;764.01346.0;1723.0;764.0;0

Here's the code:

from __future__ import print_functionimport csvimport functoolstry:    from itertools import izip, imapexcept ImportError:  # Python 3    izip = zip    imap = mapfrom itertools import permutations, repeat# Create a distance dictionary from csv data file with entries like this:#     (city_a, city_b): float(distance-between-city_a-and-city_b)# for all pairs of city names in the file.data_filename = 'european_cities.csv'dist_dict = {}with open(data_filename, 'r') as file:    reader = csv.reader(file, delimiter=';')    cities = next(reader)  # header row    num_cities = len(cities)    for city in cities:  # should be a row of distances for each city        from_city_iter = repeat(city, num_cities)        dist_dict.update((pair for pair in izip(izip(from_city_iter, cities),                                                imap(float, next(reader)))                            if pair[1])) # skip 0 distances (city_a == city_b)def pairwise(iterable):"s -> (s0,s1), (s1,s2), (s2,s3), ..."    a, b = iter(iterable), iter(iterable)    next(b)  # advance second iterator one iteration    return izip(a, b)for tour in permutations(cities, len(cities)):    tour += (tour[0],)  # make round trip by appending starting city    route = '->'.join(tour)    dist = sum(dist_dict[city_a, city_b] for city_a, city_b in pairwise(tour))    print('{:^49}: {:,}'.format(route, dist))

Output:

Barcelona->Belgrade->Berlin->Brussels->Barcelona : 4,637.38Barcelona->Belgrade->Brussels->Berlin->Barcelona : 5,512.74Barcelona->Berlin->Belgrade->Brussels->Barcelona : 5,565.86Barcelona->Berlin->Brussels->Belgrade->Barcelona : 5,512.74Barcelona->Brussels->Belgrade->Berlin->Barcelona : 5,565.86Barcelona->Brussels->Berlin->Belgrade->Barcelona : 4,637.38 Belgrade->Barcelona->Berlin->Brussels->Belgrade : 5,512.74 Belgrade->Barcelona->Brussels->Berlin->Belgrade : 4,637.38 Belgrade->Berlin->Barcelona->Brussels->Belgrade : 5,565.86 Belgrade->Berlin->Brussels->Barcelona->Belgrade : 4,637.38 Belgrade->Brussels->Barcelona->Berlin->Belgrade : 5,565.86 Belgrade->Brussels->Berlin->Barcelona->Belgrade : 5,512.74  Berlin->Barcelona->Belgrade->Brussels->Berlin  : 5,512.74  Berlin->Barcelona->Brussels->Belgrade->Berlin  : 5,565.86  Berlin->Belgrade->Barcelona->Brussels->Berlin  : 4,637.38  Berlin->Belgrade->Brussels->Barcelona->Berlin  : 5,565.86  Berlin->Brussels->Barcelona->Belgrade->Berlin  : 4,637.38  Berlin->Brussels->Belgrade->Barcelona->Berlin  : 5,512.74 Brussels->Barcelona->Belgrade->Berlin->Brussels : 4,637.38 Brussels->Barcelona->Berlin->Belgrade->Brussels : 5,565.86 Brussels->Belgrade->Barcelona->Berlin->Brussels : 5,512.74 Brussels->Belgrade->Berlin->Barcelona->Brussels : 5,565.86 Brussels->Berlin->Barcelona->Belgrade->Brussels : 5,512.74 Brussels->Berlin->Belgrade->Barcelona->Brussels : 4,637.38