Construct the Rectangle.py

'''

For a web developer, it is very important 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.
You need to output the length L and the width W of the web page you designed in sequence.
Example:
Input: 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.
Note:
The given area won't exceed 10,000,000 and is a positive integer
The web page's width and length you designed must be positive integers.
'''

import math

class Solution(object):
    def constructRectangle(self, area):
        """
        :type area: int
        :rtype: List[int]
        """
        
        for x in reversed(xrange(1, int(math.sqrt(area)) + 1)):
            if area % x == 0:
                return [area // x, x]
            
        return [0, 0]