pitch.py

from itertools import combinations, chain


__author__ = 'josebermudez'


def calculate_divisors(num):
    """
    Get the divisors from a num
    :param num: number
    :return: set of divisors
    """
    return set(reduce(list.__add__, ([i, num//i] for i in range(1, int(num**0.5) + 1) if num % i == 0)))


def calculate_sum(nums):
    """
    Get sum of a list, 0 if the list is empty.
    :param nums: list
    :return: sum
    """
    return sum(nums) if len(nums) > 0 else 0


def check_subsets(divisors, num):
    """
    Check subsets and compare the sum of subset with number, return True if sum
    is equal to the number.
    :param divisors: divisors of a number
    :param num: number
    :return: boolean
    """
    # check all combinations
    for comb in chain(*map(lambda x: combinations(divisors, x), range(1, len(divisors)))):
        if sum(comb) == num:
            return False

    return True


if __name__ == "__main__":
    # loop from 1 to 553
    for x in xrange(1, 554):
        # divisor of x, excluding x
        divisors = list(calculate_divisors(x))
        divisors.remove(x)

        # check conditions
        if calculate_sum(divisors) > x and check_subsets(divisors, x):
            print 'Pitch finded:', x