P1014 Cantor表

Cantor表

思路

见代码

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner cin = new Scanner(System.in);

        int n = cin.nextInt();
        
        int num = 1; //在第几条斜线上
        int sum = 1; //前num条斜线时数的个数总和
        int t = 1;
        while(sum < n){
        	num ++;
        	t ++;
        	sum += t;
        }
        sum -= t; //前num-1条斜线时数的个数总和
        
        /**
         * 沿斜线从上到下
         * 偶斜线：分子递增，分母递减
         * 奇斜线：相反
         * 且最大值为斜线号
         */
        int x = 1; //分子
        int y = 1; //分母
        if((num & 1) == 0){
        	x = n - sum; 
        	y = (num + 1) - x;
        }else{
        	y = n - sum; 
        	x = (num + 1) - y;
        }
    	System.out.println(x + "/" + y);
    }

}