Luo Gu P1014.Cantor table

Luo Gu P1014.Cantor table

Title Description

One of the famous proof of modern mathematics is Georg Cantor proved the rational numbers is enumerable. He is following this one table to prove this proposition:

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, …

... Our Z-shape to each number on the table. The first 1/1, then 1 / 2,2 / 1,3 / 1,2 / 2, ...

Input Format

Integer N (1≤N≤10000000)

Output Format

Item table N

Sample input and output

Input Sample # 1

7

Sample Output # 1

1/4

Topic ideas

#include<iostream>
#define ll long long

using namespace std;

int main()
{
    int flag = 1;
    ll n,i=1,j=1,t=1;
    scanf("%lld",&n);
    while(1){
        if(t==n){
            printf("%lld/%lld",i,j);
            return 0;
        }
        switch(flag)
        {
            case 1:
            j++;
            t++;
            flag = 2;
            break;
            case 2:
            i++;
            j--;
            t++;
            if(j==1)flag = 3;
            break;
            case 3:
            i++;
            t++;
            flag = 4;
            break;
            case 4:
            i--;
            j++;
            t++;
            if(i==1)flag = 1;
            break;
        }
    }
    return 0;
}