POJ ACM习题【No.1969】

Count on Canton

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions: 5589		Accepted: 3228

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

3
14
7

Sample Output

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

 

此题最大的难点在于需要区分左右方向。

 

 

import java.util.*;

public class Main {

	public static void main(String[] args) {
		Scanner cin = new Scanner(System.in);
		
		while(cin.hasNext())
		{
			int num = cin.nextInt();
			int index = 1;
			int result = 0;
			while(result <= num)
			{
				result += index;
				index ++;
			}
			result -= (index-1);
			
			int layer = index - 1;
			int offset = num - result;
			int up, down = 0;
			
			if(layer % 2 == 0)
			{
				if(offset == 0)
				{
					up = 1;
					down = layer - 1;
				}
				else
				{
					up = offset;
					down = layer + 1 - offset; 
				}
			}
			else
			{
				if(offset == 0)
				{
					up = layer - 1;
					down = 1;
				}
				else
				{
					up = layer + 1 - offset;
					down = offset;	
				}
			}
			System.out.println("TERM " + num + " IS " + up + "/" + down);
		}
	}
}