Construct the Rectangle

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- Tag: #rectangle, sqrt

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:

- 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.

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.

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

## https://code.dennyzhang.com/construct-the-rectangle ## Basic Ideas: ## ## Complexity: Time O(sqrt(n)), Space O(1) class Solution: def constructRectangle(self, area): """ :type area: int :rtype: List[int] """ import math for num in range(int(math.sqrt(area)), 0, -1): if area % num == 0: return [int(area/num), num]