count_factors.py

"""
A positive integer D is a factor of a positive integer N.

if there exists an integer M such that N = D * M.

For example, 6 is a factor of 24, because M = 4 satisfies
the above condition (24 = 6 * 4).

Write a function:

    def solution(N)

that, given a positive integer N, returns the number of its factors.

For example, given N = 24, the function should return 8, because 24 has 8 factors,
namely 1, 2, 3, 4, 6, 8, 12, 24. There are no other factors of 24.

Assume that:

N is an integer within the range [1..2,147,483,647].
Complexity:
    expected worst-case time complexity is O(sqrt(N));
    expected worst-case space complexity is O(1).
"""


def solution(N):
    result = 0
    if N > 0:
        i = 1
        factors = []
        while i**2 <= N:
            if N % i == 0:
                if (N / i) != i:
                    factors.append(i)
                    factors.append(N / i)
                else:
                    factors.append(i)
            i += 1
        result = len(factors)
    return result