Introduction

In this blog post, we will explore how to solve the LeetCode problem "492" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

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: 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

Explanation

Here's the breakdown of the solution:

• Start from the middle: Begin checking for factors of the area from the square root down. This ensures that we find the pair of factors that are closest together first.
• Check for factors: Iterate downwards from the integer square root of the area. If i is a factor, then area / i is also a factor.

• Return the factors: As soon as a factor is found, the factors are length and width and satisfy the conditions.

• Runtime Complexity: O(sqrt(area)), Storage Complexity: O(1)

Code

    import math

def constructRectangle(area: int) -> list[int]:
    """
    Designs a rectangular web page with the given area, minimizing the difference
    between length and width.

    Args:
        area: The target area of the web page.

    Returns:
        A list [L, W] representing the length and width of the web page.
    """

    w = int(math.sqrt(area))
    while area % w != 0:
        w -= 1
    return [area // w, w]