7/18 每日一題(返回差距最小的乘積)

 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:

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.

Return an array [L, W] where L and W are the length and width of the web page you designed in sequence.

 

Example 1:

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]. 
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.

Example 2:

Input: area = 37
Output: [37,1]

Example 3:

Input: area = 122122
Output: [427,286]

 

Constraints:

• 1 <= area <= 107

class Solution:

    def constructRectangle(self, area: int) -> List[int]:

        diff_a_i=area

        res=[area,1]

        for i in range(1,(area//2)+2):

            a=area//i  

            if area%i==0 :                

               

                if diff_a_i !=min(diff_a_i,a-i)and a>= i:

                    #當出現新的最小值刷新list

                    res=[a,i]              

                diff_a_i=min(diff_a_i,a-i)

                #刷新最小值

            if a-i <0:

                return res #必須符合[L,W], L>=W

        return res

       

------------------ 參考解答 範未進一步限制在 int(area**0.5)+1

class Solution: def constructRectangle(self, area: int) -> List[int]: diff_a_i = area res = [area, 1] for i in range(1, int(area ** 0.5) + 1): if area % i == 0: a = area // i if a >= i and diff_a_i != min(diff_a_i, a - i): res = [a, i] diff_a_i = min(diff_a_i, a - i) return res