分数拆分(Fractions Again?!)

sadness安全宇航员 lv.1

发布时间：2022-12-10 21:36:49 310

Time Limit:3000MS		Memory Limit:Unknown		64bit IO Format:%lld & %llu

Input

Input contains no more than 100 lines, each giving a value of k (0 < k ≤ 10000).

Output

For each k, output the number of corresponding (x, y) pairs, followed by a sorted list of the values of x and y, as shown in the sample output.

Sample Input

212

Sample Output

21/2 = 1/6 + 1/3
1/2 = 1/4 + 1/4
8
1/12 = 1/156 + 1/13
1/12 = 1/84 + 1/14
1/12 = 1/60 + 1/15
1/12 = 1/48 + 1/16
1/12 = 1/36 + 1/18
1/12 = 1/30 + 1/20
1/12 = 1/28 + 1/21
1/12 = 1/24 + 1/24

【分析】

当 x 和 y 满足题意时，由于 x >= y，则 1/x <= 1/y，又因为1/k = 1/x + 1/y，所以 1/x = 1/k - 1/y <= 1/y 即 y <= 2k。通过枚举 y，算出 x 的值，那么x 和 y 便满足题意要求。 x = ( k * y) / (y - k)，因为 x 为正整数，所以 y - k > 0 即 y > k。综上，y 枚举的范围为 [k + 1, 2k]。

用java语言编写程序，代码如下：

import java.io.BufferedInputStream;
import java.util.ArrayList;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner input = new Scanner(new BufferedInputStream(System.in));
    while(input.hasNext()) {
      int k = input.nextInt();
      
      ArrayList list = new ArrayList();
      for(int y = k + 1; y <= 2 * k; y++) {
        if((k * y) % (y - k) == 0) {
          int x = (k * y) / (y - k);
          list.add(new FA(x, y));
        }
      }
      int n = list.size();
      System.out.println(n);
      for(int i = 0; i < n; i++)
        System.out.println("1/" + k + " = " + "1/" + 
            list.get(i).x + " + " + "1/" + list.get(i).y);
    }
  }
  
  static class FA {
    int x, y;
    public FA(int x, int y) {
      this.x = x;
      this.y = y;
    }
  }
}

文章来源： https://blog.51cto.com/u_15894233/5893533

特别声明：以上内容（图片及文字）均为互联网收集或者用户上传发布，本站仅提供信息存储服务！如有侵权或有涉及法律问题请联系我们。

分数拆分(Fractions Again?!)

​​Input​​

​​Output​​

​​Sample Input​​

​​Sample Output​​

Input

Output

Sample Input

Sample Output