constructRectangle.py

#   -*- coding: utf-8   -*-
'''
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.
'''
"""
        :type area: int
        :rtype: List[int]
        """
import math
class Solution(object):
    def constructRectangle(self, area):
        if int(math.sqrt(area)) == math.sqrt(area):
            return [int(math.sqrt(area)),int(math.sqrt(area))]
        else:
            tmp = int(math.sqrt(area))
            while area%tmp != 0:
                tmp = tmp - 1
            return [area//tmp,tmp]

if __name__ == "__main__":
	sol = Solution()
	print(sol.constructRectangle(int(raw_input('Enter the area: '))))