[100%] MinPerimeterRectangle (codility lessons)

Lesson10

Prime and composite numbers

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Easy

MinPerimeterRectangle

Find the minimal perimeter of any rectangle whose area equals N.

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:

class Solution { public 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].

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Code Walkthrough

class Solution {
    public int solution(int N) {
        int i = 1;
        int minPerimeter  = Integer.MAX_VALUE;
        while (i * i <= N) {
            if (N % i == 0) {
                int A = i;
                int B = N / i;
                minPerimeter = Math.min(minPerimeter, 2 * (A + B));
            }
            i++;
        }

        return minPerimeter;
    }
}

Conclusion

• Detected time complexity: O(sqrt(N))
• Detected space complexity: O(log N)

Codility Report

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See also: CodilityのLessonsをすべて解く（更新中）