task28.java

/*	CountFactors
	Count factors of given number n.
	Task Score 100%, Correctness 100%, Performance 100%

	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.

	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).	*/
	
class Solution {
    /*  Factor and divisor are the same thing.
        So we just iterate from 1 till sqrt(N)
        to find first divisor of a pair. For ex.,
        if i * j = N, where i <= sqrt(N) and
        j >= sqrt(N), then we find i and don't search
        for j. The separate case if sqrt of N is
        an integer number: this case adds only
        one divisor */
    public int solution(int N) {
        long n = N;
        long i, counter = 0;
        for (i = 1; i * i < n; i++)
            if (n % i == 0)
                counter += 2;
        if (i * i == n)
            counter++;
        return (int)counter;
    }
}