Leetcode Problem: Construct the Rectangle

In this article I would be going over a solution to leetcode problem 492: Construct the Rectangle,

Two solutions were developed and I will be walking you through them

Solutuion 1

The function accepts a parameter area, in this example we would go with 16
area = 16
Next we create our answer dictionary variable to hold the factors of the target area
ad = {}
Also setup a temp list with maximum and minimum values of infinity
temp = [ float('inf'), float('-inf')]
First we wanna iterate over from 1 till the square root of the target area + 1 to avoid duplicates
for 1,2...sqrt(16)+1 --> 5
For every iteration, if we find a factor of that number then we want to save it to the answer dictionary

 # 16/1
 # 16/2
 # 16/3
 # 16/4
 ad = {'1':'16', '2':'8', '4':'4'}

Now we can iterate through the answer dictionary to select the best length and width combination with the lowest absolute difference

 for k,v in ad:
    if abs(k-v) < abs(temp[0]-temp[1])
    temp[0], temp[1] = min(k, v), max(k,v)
    return temp

At the end of this process we have the answer in temp list

Code Below

import math
class Solution:
    def constructRectangle(self, area: int) -> List[int]:
        answer_dict = {}
        temp = [float('inf'),  float('-inf')]
        for n in range(1, int(math.sqrt(area))+1):
            if area%n == 0:
                answer_dict[n] = area // n
        for k, v in answer_dict.items():
            if abs(temp[0] - temp[1]) > abs(k-v):
                temp[0], temp[1] = max(k, v), min(k, v)
        return temp

The first solution was long and it could be made a lot simpler
This second solution makes use of one list to keep the prospective lengths and breadths
Easy to understand

class Solution:
    def constructRectangle(self, area: int) -> List[int]:
        ans = []
        for i in range(1, int(sqrt(area))+1):
            j = area // i
            if i * j == area:
                if i <= j:
                    ans.append([max(i,j), min(i,j)])
        return ans[-1]

A little task for the readers, what is the time and space complexities of both solutions
Also do let me know if you have a better solution, or any improvements to be made

Happy Cocding :)