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

這個網誌中的熱門文章

2018年5月繳106年度綜合所得稅信用卡優惠整理!

最新106年度綜合所得稅計算教學!教你看懂稅率級距表/免稅額/扣除額!今年新增基本生活費不課稅也更新囉~

綜合所得稅節稅攻略:列舉扣除額保險費篇!

證件遺失補辦身分證/健保卡/駕照/行照/信用卡總整理

國泰Koko combo icash網購/超商/icash/繳費5%!

綜合所得稅節稅攻略:列舉扣除額房貸房租篇!

2018最新博客來100,50,25折價券序號e-coupon分享

7-11/全家/萊爾富刷信用卡/icash繳費賺回饋攻略!

繳納2018/107年度房屋稅信用卡回饋/分期整理!

繳納2018/107年度牌照稅信用卡回饋/分期整理!