MinPerimeterRectangle.md

Task description

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:

function solution(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.

Assume that:

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

Complexity:

• expected worst-case time complexity is O(sqrt(N));
• expected worst-case space complexity is O(1).

function solution(N) {
    // write your code in JavaScript (Node.js 6.4.0)
    for (var i = parseInt(Math.sqrt(N), 10); true ; i--)
            if (N % i == 0)
                return 2 * i + 2 * (N / i);
}