# LeetCode492-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.

Exmaple:

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.

### 分析

1 * 24 –> 23                   1 * 36 –> 35

2 * 12 –> 10                   2 * 18 –>  16

3 * 8  –> 5                      3 * 12 –>   9

4 * 6  –> 2                      4 * 9  –>   5

6 * 4  –> 2                      6 * 6  –>   0

……                                  ……

• 随着宽边w长度逐1增大，长边l长度逐渐减小
• 长边具体减小到多少由l = area / w相除决定
• 宽边w增大到$$\sqrt {area}$$时（即此时w = l），之后将出现w > l（不满足条件）

### 代码

public class Solution {
public int[] constructRectangle(int area) {
int length = area;
int width = 1;
int gap = area - 1;

for (int w = 2; w <= area / 2; w++) {
for (int l = w; l <= area / 2; l++) {
if (l * w == area) {
int newGap = l - w;
if(newGap < gap) {
length = l;
width = w;
gap = newGap;
}
}
}
}

return new int[] {length, width};
}
}

public class Solution {
public int[] constructRectangle(int area) {
int length = area;
int width = 1;
int gap = area - 1;
int sqrt = (int) Math.sqrt(area);

for (int w = 2; w <= sqrt; w++) {
int l = area / w;
if (l * w == area) {
int newGap = l - w;
if(newGap < gap) {
length = l;
width = w;
gap = newGap;
}
}
}

return new int[] {length, width};
}
}