492. Construct the Rectangle #

Problem #

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 <= 10000000

Summary #

As a web developer, knowing how to plan a page’s dimensions is very important. Given a specific rectangular page area, your task is to design a rectangular page with length L and width W that satisfies the following requirements:

The rectangular page you design must equal the given target area.
The width W should not be greater than the length L; in other words, L >= W is required.
The difference between length L and width W should be as small as possible.

You need to output the length L and width W of the page you designed in order.

Solution Approach #

Let W be equal to the square root of area
While W is greater than or equal to 1, check whether area%W is equal to 0. If not, decrement W by 1 and continue the loop; if it is, return [area/W, W]

Code #


package leetcode

import "math"

func constructRectangle(area int) []int {
	ans := make([]int, 2)
	W := int(math.Sqrt(float64(area)))
	for W >= 1 {
		if area%W == 0 {
			ans[0], ans[1] = area/W, W
			break
		}
		W -= 1
	}
	return ans
}