Construct the Rectangle — LeetCode 492 Python Solution

The 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.

Example

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].

Python solution

class Solution:
    def constructRectangle(self, area: int) -> List[int]:
        w = int(sqrt(area))
        while area % w != 0:
            w -= 1
        return [area // w, w]

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 492. Construct the Rectangle is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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