_492.java

package com.fishercoder.solutions;

/**
 * 492. Construct the Rectangle
 *
 * For a web developer, it is very important 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.

 You need to output the length L and the width W of the web page you designed in sequence.
 Example:
 Input: 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.

 Note:
 The given area won't exceed 10,000,000 and is a positive integer
 The web page's width and length you designed must be positive integers.

 */
public class _492 {

    public static class Solution1 {
        public int[] constructRectangle(int area) {
            int i = 0;
            int j = area;
            int[] result = new int[2];
            while (i <= j) {
                long product = i * j;
                if (product == area) {
                    result[0] = j--;
                    result[1] = i++;
                } else if (product > area) {
                    j--;
                } else {
                    i++;
                }
            }
            return result;
        }
    }

}