helpers.py

def build_combinations(k, n):
    assert n > k > 1
    to_process = [[i] for i in range(1, n + 1)]
    while to_process:
        l = to_process.pop()
        s = sum(l)
        le = len(l)
        # There are three main variations you can use for the loop, from here.
        # To distinguish permutations: range(1, n - s + 1)
        # To avoid repeated cases    : range(l[-1], n - s + 1)
        # Or to number repetitions   : range(l[-1] + 1, n - s + 1)
        for i in range(l[-1], n - s + 1):
            news = s + i
            if news <= n:
                newl = list(l)
                newl.append(i)
                if le == k - 1 and news == n:
                    yield tuple(newl)
                elif le <= k - 2 and news < n:
                    to_process.append(newl)


def manhattan_distance(p1, p2):
    return sum(abs(pa - pb) for pa, pb in zip(p1, p2))