variants.py

import sys

numbers = [2, 0, 1, 5, 2, 0, 1, 5]
k = len(numbers) - 1
indexed_tail = list(zip(range(k), numbers[1:]))

to_bin = 2 ** k - 1

variants = []

for n in range(to_bin):
    s = numbers[0] + sum([(((n >> i) & 1) * 2 - 1) * x for (i, x) in indexed_tail])

    if s == 0:
        variants.append(n)

if not variants:
    print('No variants')
    sys.exit(0)

def calc_minus_signs(n, k):
    signs = 0
    for i in range(k):
        if (n >> i) & 1 == 0:
            signs += 1
    return signs

# warning: mutation of variants
minimum = [variants.pop()]
minimum_signs = calc_minus_signs(minimum[0], k)

for n in variants:
    signs = k - calc_minus_signs(n, k)
    if signs < minimum_signs:
        minimum = [n]
        minimum_signs = signs
    elif signs == minimum_signs:
        minimum.append(n)

for n in minimum:
    string = str(numbers[0])
    for i in range(k):
        sign = '-' if (n >> i) & 1 == 0 else '+'
        string += ' ' + sign + ' '
        string += str(numbers[i + 1])
    string += ' = 0'
    print(string)