[Swift]LeetCode492. 構造矩形 | Construct the Rectangle

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➤微信公衆號：山青詠芝（shanqingyongzhi）
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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:

1. The given area won't exceed 10,000,000 and is a positive integer
2. The web page's width and length you designed must be positive integers.

---

做爲一位web開發者， 懂得怎樣去規劃一個頁面的尺寸是很重要的。 現給定一個具體的矩形頁面面積，你的任務是設計一個長度爲 L 和寬度爲 W 且知足如下要求的矩形的頁面。要求：

1. 你設計的矩形頁面必須等於給定的目標面積。

2. 寬度 W 不該大於長度 L，換言之，要求 L >= W 。

3. 長度 L 和寬度 W 之間的差距應當儘量小。

你須要按順序輸出你設計的頁面的長度 L 和寬度 W。

示例：

輸入: 4
輸出: [2, 2]
解釋: 目標面積是 4， 全部可能的構造方案有 [1,4], [2,2], [4,1]。
可是根據要求2，[1,4] 不符合要求; 根據要求3，[2,2] 比 [4,1] 更能符合要求. 因此輸出長度 L 爲 2， 寬度 W 爲 2。

說明:

1. 給定的面積不大於 10,000,000 且爲正整數。
2. 你設計的頁面的長度和寬度必須都是正整數。

---

 8ms

1 class Solution {
2     func constructRectangle(_ area: Int) -> [Int] {
3         var w = Int(sqrt(Double(area)))
4         while area % w != 0 {
5             w -= 1
6         }
7         return [area / w, w]
8     }
9 }

---

8ms

 1 class Solution {
 2     func constructRectangle(_ area: Int) -> [Int] {
 3         var minDiff = Int.max
 4         var minDiffWidth: Int?
 5         let maxWidth = Int(ceil(sqrt(Double(area))))
 6         
 7         for width in 1 ... maxWidth {
 8             guard area % width == 0 else { continue }
 9             
10             let length = area / width
11             if length >= width, length - width < minDiff {
12                 minDiff = length - width
13                 minDiffWidth = width
14             }
15         }
16         if let minDiffWidth = minDiffWidth {
17             return [area / minDiffWidth, minDiffWidth]
18         } else {
19             return [area, 1]
20         }
21     }
22 }

---

12ms

 1 class Solution {
 2     func constructRectangle(_ area: Int) -> [Int] {
 3          let maxW = Int(sqrt(Double(area)))
 4         var result = [area,1]
 5          if maxW >= 2 {
 6             for i in 2...maxW {
 7                 if area % i == 0 {
 8                     result = [area / i,i]
 9                 }
10             }
11         }
12         return result
13     }
14 }

---

12ms

1 class Solution {
2     func constructRectangle(_ area: Int) -> [Int] {
3         var n = Int(sqrt(Double(area)))
4         while area % n != 0 {
5             n -= 1
6         }
7         return [max(n, area/n), min(n, area/n)]
8     }
9 }

---

20ms

 1 class Solution {
 2     func constructRectangle(_ area: Int) -> [Int] {
 3         var maxW = Int(sqrt(Double(area)))
 4         var result = [area,1]
 5         while maxW >= 2 {
 6             if area % maxW == 0 {
 7                 result = [area / maxW,maxW]
 8                 break
 9             }
10             maxW -= 1
11         }       
12         return result
13     }
14 }

---

116ms

 1 class Solution {
 2     func constructRectangle(_ area: Int) -> [Int] {
 3         guard area > 0 else { return [0, 0] }
 4         let sqr = sqrt(Double(area))
 5         var i = Int(sqr)
 6         var j = Int(sqr)
 7         var prod = i*j
 8         while prod != area {
 9             if prod > area {
10                 i -= 1
11             } else if prod < area {
12                 j += 1
13             }
14             prod = i*j
15         }
16         return [j, i] 
17         
18     }
19 }