python - Return numbers that share no common factors

Question

Problem is as follows:

Create a function that takes 2 inputs, a number n and a list lst. The function should return a list of all the numbers in lst that share no common factors with n (other than 1). n and all numbers in lst will be positive integers greater than or equal to 0.

My attempt

def no_common_factors (n, lst):

    def uf(n):  #get a set of factors
        factors = []
        i = 2
        while n > 1: 
            if n % i == 0: 
                factors += [i]
                n = n / i
            else: 
                i += 1
        return set(factors)

    factors_n = uf(n)
    no_common = []

    for i in range(0, len(lst)): 
        factors_i = uf(i)
        if factors_n.isdisjoint(factors_i): 
            no_common += [lst[i]]
        else: 
            continue

    return no_common

doesn't work:

In [41]: no_common_factors(15, [72,27,32,61,77,11,40])
Out[41]: [72, 27, 32, 77]

when it should return [32, 61, 77, 11].

I stare at it but can't see what I'm doing wrong, it's supposed to be really simple. Please help!

You are checking the factors of the iteration variable `i` instead of the actual number. Either do `uf(lst[i])` or better iterate over the numbers themselves `for x in lst:` — Felk, Sep 19 '17 at 15:34
Is that a common thing to have a function within a function? It looks strange to me. — offeltoffel, Sep 19 '17 at 15:37
@offeltoffel, that's the best I could come up with, but I think it's relatively common. :) — P. Prunesquallor, Sep 19 '17 at 15:54
You can move the `def uf(n)` function to the top and it will still work and look a bit nicer. Now that you have your desired answer, this is only maculature ;) — offeltoffel, Sep 19 '17 at 16:21

norok2 · Answer 1 · 2017-09-19T16:16:21.077

I would do it using math.gcd which returns the greatest common divisor of two numbers:

import math

def no_shared_factors(num, items):
    return [item for item in items if math.gcd(item, num) == 1]

which outputs the correct result:

>>> no_shared_factors(15, [72, 27, 32, 61, 77, 11, 40])
[32, 61, 77, 11]

If math.gcd is too much of a black box, you could write your own implementation or peek the math code (see Code for Greatest Common Divisor in Python):

def gcd(a, b):
    """
    Calculate the Greatest Common Divisor of a and b.

    Unless b==0, the result will have the same sign as b (so that when
    b is divided by it, the result comes out positive).
    """
    while b:
        a, b = b, a % b
    return a

Take a look at the GCD page on Wikipedia for many more alternative algorithms.

Thank you for the answer! That's a waaay more elegant solution. — P. Prunesquallor, Sep 19 '17 at 15:56

score 3 · Accepted Answer · answered Sep 19 '17 at 15:34

3

Your bug is in the factors_i calculation.

Replace:

factors_i = uf(i)

By:

factors_i = uf(lst[i])

By the way, you can simplify your code:

def no_common_factors(n, lst):
    factors_n = uf(n)
    no_common = []

    for integer in lst:
        factors_i = uf(integer)
        if factors_n.isdisjoint(factors_i):
            no_common.append(integer)

    return no_common

answered Sep 19 '17 at 15:34

Laurent LAPORTE

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Thank you very much! I couldn't see that. – P. Prunesquallor Sep 19 '17 at 15:55

python - Return numbers that share no common factors

2 Answers2