magic_4x4.py

from itertools import combinations, permutations, chain
import sys, time

try:
    inputs = input()
except EOFError:
    pass

#inputs = '1 2 3 4 5 6 7 8 9 10 10 11 13 14 14 15'
if len(inputs.split()) != 16:
    print('Error', file=sys.stderr)
    exit()

start_time = time.time()
inputs = list(map(int, inputs.split()))
ns = inputs


def get_removed_list(l, removings):
    removed = l.copy()
    list(map(lambda x: removed.remove(x), removings))
    return removed

magic_row_squares = []
for partition1 in combinations(ns, 4):
    magic_sum = sum(partition1)
    remain_partition1 = get_removed_list(ns, partition1)
    for partition2 in combinations(remain_partition1, 4):
        if sum(partition2) != magic_sum: continue
        remain_partition2 = get_removed_list(remain_partition1, partition2)
        for partition3 in combinations(remain_partition2, 4):
            if sum(partition3) != magic_sum: continue
            remain_partition3 = get_removed_list(remain_partition2, partition3)
            for partition4 in combinations(remain_partition3, 4):
                if sum(partition4) != magic_sum: continue
                magic_row_squares.append([partition1, partition2, partition3, partition4])
                
c = 0
magic_squares = []
for magic_row_square in magic_row_squares:
    for row1 in permutations(magic_row_square[0]):
        magic_sum = sum(row1)
        for row2 in permutations(magic_row_square[1]):
            if not sum(row1[:2] + row2[:2]) == sum(row1[2:] + row2[2:]) == magic_sum: continue
            for row3 in permutations(magic_row_square[2]):
                for row4 in permutations(magic_row_square[3]):
                    if not sum(row3[:2] + row4[:2]) == sum(row3[2:] + row4[2:]) == magic_sum: continue
                    
                    if not (row1[0] + row2[1] + row3[2] + row4[3] == magic_sum and \
                            row1[3] + row2[2] + row3[1] + row4[0] == magic_sum): continue
                    end = 0 
                    for i in range(len(magic_row_square)):
                        if row1[i] + row2[i] + row3[i] + row4[i] != magic_sum:
                            end = 1
                            break
                    if end:
                        continue
                    
                    magic_squares.append(row1 + row2 + row3 + row4)
                    c+=1

for magic_square in magic_squares:
    print(' '.join(map(str, magic_square)), file=sys.stdout)
elapsed_time = time.time() - start_time
print(f'총 {len(magic_squares)} 개의 답이 있습니다. 계산시간은 총 {elapsed_time:.2f} 초 입니다. ', file=sys.stderr)