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:
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].