首页 > 代码库 > UVA - 264 - Count on Cantor （Cantor的数表！）
UVA - 264 - Count on Cantor （Cantor的数表！）
UVA - 264
| Time Limit: 3000MS | Memory Limit: Unknown | 64bit IO Format: %lld & %llu |
Description
Count on Cantor
| Count on Cantor |
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.
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 
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
有木有很熟悉的感觉，LRJ在UVA上做的第一个题，\(^o^)/~
AC代码：
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
int main()
{
int n;
while(scanf("%d", &n) != EOF)
{
printf("TERM %d IS ", n);
int x = 1;
while(n>(x*(x+1)/2))
{
x++;
}
n -= (x*(x-1)/2);
if(x&1)
{
printf("%d/%d\n", (x+1)-n, n);
}
else
{
printf("%d/%d\n", n, (x+1)-n);
}
}
return 0;
} UVA - 264 - Count on Cantor （Cantor的数表！）