List comprehension to find all multiples of each number in list less than a number

Question

I'm trying to write a function that will find all numbers that are a multiple of at least one number in a list where the multiple is less than a certain number. Here's what I've tried so far:

def MultiplesUnderX(MultArray,X):
    '''
    Finds all the multiples of each value in MultArray that
    are below X.
    MultArray: List of ints that multiples are needed of
    X: Int that multiples will go up to
    '''
    return [i if (i % x == 0 for x in MultArray) else 0 for i in range(X)]

For example, MultiplesUnderX([2,3],10) would return [2,3,4,6,8,9]. I'm a little unsure how to do this with the for loop inside of the list comprehension.

Answer 1

You can use the Python any() function to check if there is at least one instance of a divider in MultArray:

def MultiplesUnderX(MultArray,X):

    return [i for i in range(X) if any(i % x == 0 for x in MultArray)]

Answer 2

You can use the Python built-in function any which returns True if the iterable passed in contains any truth-y values in combination with a conditional at the end of the list comprehension limiting the list to only elements that satisfy the any call.

def get_multiples_under(factors, max):
    return [i for i in xrange(1, max) if any(i % factor == 0 for factor in factors)]

Your desired output is shown as such:

multiples = [2, 3]
print get_multiples_under(multiples, 10)
# [2, 3, 4, 6, 8, 9]

Answer 3

Another version of this algorithm which may be more efficient if the list is mostly co-prime, you can just use range(i, X, i) to generate only the multiples of i , then use heapq.merge to merge the iterators such that the iterator returned is sorted.

The last step is to eliminate duplicates as you go:

import heapq

def all_multiples(multi_list, max_N):
    gens = []
    for fac in sorted(set(multi_list)):
        # In Python 3 this is a generator of all multiples of "fac" less
        # than max_N. In Python 2 use xrange
        gens.append(range(fac, max_N, fac))

    # This will do a heap merge on the generators (which are already sorted)
    o = heapq.merge(*gens)
    last = None
    for val in o:
        if val != last:
            yield val
            last = val


if __name__ == "__main__":
    multi_list = [2, 4, 7]
    print(list(all_multiples(multi_list, 12)))
    # [2, 4, 6, 7, 8, 10]