POJ【1909】数论

Description

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. 

1/1 1/2 1/3 1/4 1/5 ...2/1 2/2 2/3 2/4 3/1 3/2 3/3 4/1 4/2 5/1 

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

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

Output

You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.

Sample Input

3147

Sample Output

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

对i累积求和，找到最靠近n并且<=n的一个数，判断它的下一条斜线是奇线是偶线，然后开始一个偶{x=i(自增)，y=i（递减）}，奇反之。

code:

#include<stdio.h>int main(){int i,j,k,n;while(scanf("%d",&n)!=EOF){if(n==0){printf("TERM 0 IS 0/0\n");continue;}int sum=0;for(i=1;;i++){sum+=i;if(sum>=n)break;}sum=sum-i;i=i-1;j=n-sum;if(i%2==1){printf("TERM %d IS %d/%d\n",n,j,i-j+2);}else{printf("TERM %d IS %d/%d\n",n,i-j+2,j);}}return 0;}