【LeetCode】Construct the Rectangle 解题报告
2017-04-03 11:45
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【LeetCode】Construct the Rectangle 解题报告
标签(空格分隔): LeetCode题目地址:https://leetcode.com/problems/construct-the-rectangle/#/description
题目描述:
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.
Ways
这个题目的意思其实就是找出指定数的约数,并且约数尽量靠近平方根,第一个约数的值大于第二个约数。给定的数字可以很大,千万量级,那么只能用O(n)量级的算法了。我的想法就是首先找出平方根,因为约数肯定尽量靠近了平方根。用到了数学运算sqrt,这个平方根是个double型的,转换成int型会舍去末尾小数。这样,如果强转之后的int的平方等于area,说明area能是个完全平方数,直接把平方根返回就好。否则,说明area不是平方数,只能进行遍历了。遍历的方法是从平方根强转后的int开始越来越小的遍历,这样,保证了尽量靠近了平方根。因为强转是丢失小数的,所以只能往小了遍历,才不会出现错误。然后如果能整除area,计算响应的长宽即可。注意此时的i是小的,那么应该对应宽。
循环的过程中一定不要忘记break,否则会在遍历完到1才停止。
public class Solution { public int[] constructRectangle(int area) { double sqrt = Math.sqrt(area); int int_sqrt = (int) sqrt; int []answer = new int[2]; if(int_sqrt * int_sqrt == area){ answer[0] = int_sqrt; answer[1] = int_sqrt; }else{ for(int i= int_sqrt; i >= 1; i--){ if(area % i == 0){ answer[0] = area / i; answer[1] = i; break;//不要忘记 } } } return answer; } }
我的上面的想法是可行的,但是有点麻烦。可以这么简化,不用判断强转之后是否是平方根,直接循环判断。
public class Solution { public int[] constructRectangle(int area) { int w = (int) Math.sqrt(area); while(area % w != 0){ w--; } return new int[]{area / w, w}; } }
Date
2017 年 4 月 3 日相关文章推荐
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