10. Prime and composite numbers. CountFactors.swift

import Foundation
import Glibc

// Solution @ Sergey Leschev, Belarusian State University

// 10. Prime and composite numbers. CountFactors.

// 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:
// class Solution { public int solution(int 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.

// Write an efficient algorithm for the following assumptions:
// N is an integer within the range [1..2,147,483,647].

public func solution(_ N: Int) -> Int {
    if N == 1 { return 1 }
    var factorsCount = 0
    let maxValue = Int(sqrt(Double(N)))
    
    for i in 1 ... maxValue where N % i == 0 { factorsCount += 2 }
    if maxValue * maxValue == N { factorsCount -= 1 }
    return factorsCount
}