# 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:

``````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.
``````

``````class Solution {
public:
vector<int> constructRectangle(int area) {
int r = sqrt(area);
while (area % r != 0) --r;
return {area / r, r};
}
};
``````

``````class Solution {
public:
vector<int> constructRectangle(int area) {
int r = 1;
for (int i = 1; i * i <= area; ++i) {
if (area % i == 0) r = i;
}
return {area / r, r};
}
};
``````

https://discuss.leetcode.com/topic/76469/3ms-concise-c

https://discuss.leetcode.com/topic/76314/3-line-clean-and-easy-understand-solution

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