LeetCode-in-Java

492. Construct the Rectangle

Easy

A web developer needs to know how to design a web page’s size. So, given a specific rectangular web page’s area, your job by now is to design a rectangular web page, whose length L and width W satisfy the following requirements:

1. The area of the rectangular web page you designed must equal to the given target area.
2. The width W should not be larger than the length L, which means L >= W.
3. The difference between length L and width W should be as small as possible.

Return an array [L, W] where L and W are the length and width of the web page you designed in sequence.

Example 1:

Input: area = 4

Output: [2,2]

Explanation: The target area is 4, and all the possible ways to construct it are [1,4], [2,2], [4,1]. But according to requirement 2, [1,4] is illegal; according to requirement 3, [4,1] is not optimal compared to [2,2]. So the length L is 2, and the width W is 2.

Example 2:

Input: area = 37

Output: [37,1]

Example 3:

Input: area = 122122

Output: [427,286]

Constraints:

• 1 <= area <= 107

Solution

public class Solution {
    /*
      Algorithm:
     - start with an index i from the square root all the way to 1;
     - if at any time, area % i == 0 (so i is a divisor of area), then it's the closest solution.
    */
    public int[] constructRectangle(int area) {
        int low = (int) Math.sqrt(area);
        while (low > 0) {
            if (area % low == 0) {
                return new int[] {area / low, low};
            }
            low--;
        }
        return new int[] {0, 0};
    }
}

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