264 - Count on Cantor

UVa網站題目連結
My Solved Problems Performance

One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.

displaymath27

In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.

Input and Output

You are to write a program that will read a list of numbers in the range from 1 to tex2html_wrap_inline29 and will print for each number the corresponding term in Cantor's enumeration as given below. No blank line should appear after the last number.

The input list contains a single number per line and will be terminated by end-of-file.

Sample input

3
14
7

Sample output

TERM 3 IS 2/1
TERM 14 IS 2/4
TERM 7 IS 1/4

Solution

  1. import java.io.BufferedInputStream;
  2. import java.util.Scanner;

  3. public class Main {

  4. public static void main(String args[]) {

  5. int n, loopCounter, sum;
  6. Scanner in = new Scanner(new BufferedInputStream(System.in));

  7. while (in.hasNext()) {

  8. n = in.nextInt();
  9. for (loopCounter=1, sum = 0;(sum+=loopCounter)<n;loopCounter++) {}
  10. if ((loopCounter&1)==1)
  11. System.out.println("TERM " + n + " IS " +(1+(sum-n))+"/" + (
  12. loopCounter-(sum-n)));
  13. else
  14. System.out.println("TERM " + n + " IS " + (loopCounter-(sum-n))+
  15. "/" +(1+(sum-n)));
  16. }
  17. }
  18. }
關鍵字:UVa Online Judge, ACM. Java


留言

相關文章

這個網誌中的熱門文章

【玉山U Bear卡】2019必辦神卡!網購5%超商8%電影20%!

【證件遺失補辦】身分證/健保卡/駕照/行照/信用卡總整理

【玉山卡攻略】神卡雲集,依序辦卡拿新舊戶首刷最佳解!

【地價稅繳納攻略】2019/108年度信用卡回饋/分期整理!

【信用卡排行榜】最新現金回饋信用卡排行榜(含2020可用)!

【博客來折價券】博客來免費序號e-coupon分享(持續更新)

【全家FamiPay】新光寰宇10%/玉山UBear 8%/台新Fish 8%!

【永豐大戶DAWHO】現金回饋信用卡國內2%國外3%最高8%!

【聯邦+LINE一卡通2%】不必自己算!繳費條碼產生器上線!

【統一發票】獎金儲值加碼,7-11送中熱美/全聯享贈點!