Construct the Rectangle

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.

For 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.

Default:

func constructRectangle(area int) []int {

}

解答思路:

大致就是做因式分解，找出兩因數差距為最小值，所以如果我們將給予的值從1開始整除，原則上因數間的差距會慢慢變小，而當差距到最小時，下一個差距反而變大的話(或是相減的差距變為負數)，此時前一組就是我們要找的目標，在最後要放的時候記得要將因數較大的放第一個(長度L)，小的擺在第二個(寬度W)，因為結果要的是L, W。

程式碼解說:

一開始先初始化一陣列但長度僅只有2用於存放結果，之後利用回圈將面積從1開始與常數做整除，如果面積與常數相除能完全整除，且商數(比較大)與常數相減大於0，就將商數放入結果陣列的第一個(長度)，至於常數則是放第二個(寬度)，一直到發現商數減去常數時為負，表示常數(寬度)已經比商數(長度)大，此時便跳離回圈將前一組因數結果做回傳

var tmp int
result := make([]int, 2)
for i := 1; i <= area; i++ {
	if area%i == 0 {
		tmp = area / i
		if tmp-i >= 0 {
			result[0] = tmp
			result[1] = i
		} else {
			break
		}
	}
}
return result

完整程式碼:

func constructRectangle(area int) []int {
	var tmp int
	result := make([]int, 2)
	for i := 1; i <= area; i++ {
		if area%i == 0 {
			tmp = area / i
			if tmp-i >= 0 {
				result[0] = tmp
				result[1] = i
			} else {
				break
			}
		}
	}
	return result
}

總結:

給予一長方形的面積，找出長與寬且兩者差距需為最小值，將給予的面積從1開始整除，因數間的差距會慢慢變小，當差距到最小時，下一個差距反而變大的話(或是相減的差距變為負數)，此時前一組因數就是我們要找的目標。