492 - Construct the Rectangle

492. Construct the Rectangle

Problem Statement

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]

 

Constraints:

• 1 <= area <= 107

Click to open Hints

• The W is always less than or equal to the square root of the area, so we start searching at sqrt(area) till we find the result.

Solutions

Rust

impl Solution {
    pub fn construct_rectangle(area: i32) -> Vec<i32> {
        let mut w = (area as f64).sqrt() as i32;

        // until the remainder is 0, decrement w
        // this will find the largest w that is a factor of area
        while area % w != 0 {
            w -= 1;
        }

        // return the result
        vec![area / w, w]
    }
}

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