LeetCode Construct the Rectangle

Posted 2020-08-29 Dylan_Java_NYC

原题链接在这里：https://leetcode.com/problems/construct-the-rectangle/

题目：

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:

1. The given area won‘t exceed 10,000,000 and is a positive integer
2. The web page‘s width and length you designed must be positive integers.

题解：

从Math.sqrt(area) 开始往下一个一个试width, 看能否让area被width整除.

Time Complexity: O(Math.sqrt(area)). Space: O(1).

AC Java:

 1 public class Solution {
 2     public int[] constructRectangle(int area) {
 3         if(area == 0){
 4             return new int [] {0,0};
 5         }
 6         int w = (int)Math.sqrt(area);
 7         while(area%w != 0){
 8             w--;
 9         }
10         return new int [] {area/w, w};
11     }
12 }