MinPerimeterRectangle

An integer N is given, representing the area of some rectangle.

The area of a rectangle whose sides are of length A and B is A * B, and the perimeter is 2 * (A + B).

The goal is to find the minimal perimeter of any rectangle whose area equals N. The sides of this rectangle should be only integers.

For example, given integer N = 30, rectangles of area 30 are:

        (1, 30), with a perimeter of 62,
        (2, 15), with a perimeter of 34,
        (3, 10), with a perimeter of 26,
        (5, 6), with a perimeter of 22.

Write a function:

    int solution(int N);

that, given an integer N, returns the minimal perimeter of any rectangle whose area is exactly equal to N.

For example, given an integer N = 30, the function should return 22, as explained above.

Write an efficient algorithm for the following assumptions:

        N is an integer within the range [1..1,000,000,000].

int solution(int N) {
    // write your code in C++11 (g++ 4.8.2)
    int i = 1;
    
    int A = 1;
    while (i * i < N) {
        if (N % i == 0) {
            A = i;
        }
        i++;
    }
    
    if (i * i == N) {
        A = i;
    }
    
    return (A + (N / A)) * 2;
}