math_marathon_2020_task_1

def sorted_k_partitions(seq, k):
    n = len(seq)
    groups = []  # a list of lists, currently empty

    def generate_partitions(i):
        if i >= n:
            yield list(map(tuple, groups))
        else:
            if n - i > k - len(groups):
                for group in groups:
                    group.append(seq[i])
                    yield from generate_partitions(i + 1)
                    group.pop()

            if len(groups) < k:
                groups.append([seq[i]])
                yield from generate_partitions(i + 1)
                groups.pop()

    result = generate_partitions(0)

    result = [sorted(ps, key=lambda p: (len(p), p)) for ps in result]

    result = sorted(result, key=lambda ps: (*map(len, ps), ps))

    return result


K = 11
P = 1

list_1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]
list_2 = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]

nums = list([i+1 for i in range(K)])

ways = sorted_k_partitions(nums, P)

#for way in ways:
#    print(way)

def check_ans(way):
    summa = sum(way[0])
    for group in way:
        if sum(group) != summa:
            return False
    return True




def get_for_k(k, list):
    nums = list[:k]

    for p in range(1, k+1):
        print("K={} P={}".format(k, p))
        ways = sorted_k_partitions(nums, p)
        for way in ways:
            if check_ans(way):
                print(way)

# первое - K-кол-во чисел, которые мы рассматриваем в последовательности, далее массив - ряд чисел
get_for_k(12, list_1)