LeetCode之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.
      
     
   
  

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.

   

    

     

      

     
     

      

       public class Solution {
      
     
    

     

      

     
     

      

        public int[] constructRectangle(int area) {
      
     
    

     

      

     
     

      

        if (area < 0)
      
     
    

     

      

     
     

      

        return null;
      
     
    

     

      

     
     

      

        int[] a = new int[2];
      
     
    

     

      

     
     

      

        if (area == 0) {
      
     
    

     

      

     
     

      

        a[0] = 0;
      
     
    

     

      

     
     

      

        a[1] = 0;
      
     
    

     

      

     
     

      

        return a;
      
     
    

     

      

     
     

      

        }
      
     
    

     

      

     
     

      

        int mid = (int)Math.sqrt(area);
      
     
    

     

      

     
     

      

        if (mid == 1) {
      
     
    

     

      

     
     

      

        a[0] = area;
      
     
    

     

      

     
     

      

        a[1] = 1;
      
     
    

     

      

     
     

      

        return a;
      
     
    

     

      

     
     

      

        }
      
     
    

     

      

     
     

      

        int l1 = 0, l2 = 0;
      
     
    

     

      

     
     

      

        int w1 = 0, w2 = 0;
      
     
    

     

      

     
     

      

        int sub1 = 0, sub2 = 0;
      
     
    

     

      

     
     

      

        //area是平方数的时候
      
     
    

     

      

     
     

      

        if (mid * mid == area) {
      
     
    

     

      

     
     

      

        a[0] = mid;
      
     
    

     

      

     
     

      

        a[1] = mid;
      
     
    

     

      

     
     

      

        return a;
      
     
    

     

      

     
     

      

        } else {
      
     
    

     

      

     
     

      

        for (int i = mid; i > 0; --i) {
      
     
    

     

      

     
     

      

        if (area % i == 0) {
      
     
    

     

      

     
     

      

        l1 = area / i;
      
     
    

     

      

     
     

      

        w1 = i;
      
     
    

     

      

     
     

      

        sub1 = mid - i;
      
     
    

     

      

     
     

      

        break;
      
     
    

     

      

     
     

      

        }
      
     
    

     

      

     
     

      

        }
      
     
    

     

      

     
     

      

        for (int j = mid; j <= area; ++j) {
      
     
    

     

      

     
     

      

        if (area % j == 0) {
      
     
    

     

      

     
     

      

        w2 = area / j;
      
     
    

     

      

     
     

      

        l2 = j;
      
     
    

     

      

     
     

      

        sub2 = j - mid;
      
     
    

     

      

     
     

      

        }
      
     
    

     

      

     
     

      

        }
      
     
    

     

      

     
     

      

        }
      
     
    

     

      

     
     

      

        if (sub1 <= sub2) {
      
     
    

     

      

     
     

      

        a[0] = l1;
      
     
    

     

      

     
     

      

        a[1] = w1;
      
     
    

     

      

     
     

      

        } else {
      
     
    

     

      

     
     

      

        a[0] = l2;
      
     
    

     

      

     
     

      

        a[1] = w2;
      
     
    

     

      

     
     

      

        }
      
     
    

     

      

     
     

      

        return a;
      
     
    

     

      

     
     

      

        }
      
     
    

     

      

     
     

      

       }