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.
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 {
public int[] ConstructRectangle(int area) {
int min = int.MaxValue;
var res = new int[2];
var sqrt = Math.Sqrt(area);
for(int W = 1;W<=sqrt;W++){
if(area%W!=0){
continue;
}
int L = area/W;
if(min>(L-W)){
min = L-W;
res[0]=L;
res[1]=W;
}
}
return res;
}
}
Time Complexity: O(n*m)
Space Complexity: O(1)
Here n is the input number and m is the time take to compute square root of each number.