492. Construct the Rectangle


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:

  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.

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]


  • 1 <= area <= 10^7


func constructRectangle(area int) []int {
    for i:= int(math.Sqrt(float64(arcea))); i>=1; i-- {
        if i * int(area/i) == area {
            ans := []int{i, int(area/i)}
            if ans[1] > ans[0] {
                ans[0], ans[1] = ans[1], ans[0]
            return ans

    return []int{}

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