492. Construct the Rectangle
1. Description
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:
- The area of the rectangular web page you designed must equal to the given target area.
- The width W should not be larger than the length L, which means L >= W.
- 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.
2. Example
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]
3. Constraints
- 1 <= area <= $10^7$
4. Solutions
My Accepted Solution
n = area
Time complexity: O($\sqrt{n}$)
Space complexity: O(1)
class Solution
{
public:
// vector<int> constructRectangle(int area)
vector<int> constructRectangle(int area)
{
int width = sqrt(area);
for ( ; width >= 1; width--)
{
if (area % width == 0)
break;
}
return vector<int>{area / width, width};
}
};