g0401_0500.s0492_construct_the_rectangle.Solution Maven / Gradle / Ivy

Go to download

Show more of this group Show more artifacts with this name
Show all versions of leetcode-in-java21 Show documentation

Java-based LeetCode algorithm problem solutions, regularly updated

There is a newer version: 1.38

package g0401_0500.s0492_construct_the_rectangle;

// #Easy #Math #2022_07_21_Time_1_ms_(74.88%)_Space_42_MB_(8.37%)

/**
 * 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
**/
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};
    }
}