就是法雷数列。。。

Consider the set of all reduced fractions between 0 and 1 inclusive with denominators less than or equal to N.

Here is the set when N = 5:

0/1 1/5 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 1/1

Write a program that, given an integer N between 1 and 160 inclusive, prints the fractions in order of increasing magnitude.

PROGRAM NAME: frac1

INPUT FORMAT

SAMPLE INPUT (file frac1.in)

5

OUTPUT FORMAT

SAMPLE OUTPUT (file frac1.out)

0/1
1/5
1/4
1/3
2/5
1/2
3/5
2/3
3/4
4/5
1/1

/*
ID: qhn9992
PROG: frac1
LANG: C++11
*/
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

int n;

void getans(int a,int b,int c,int d)
{
    int nc=a+c,tr=b+d;
    if(tr<=n)
    {
        getans(a,b,nc,tr);
        printf("%d/%d\n",nc,tr);
        getans(nc,tr,c,d);
    }
}

int main()
{
    freopen("frac1.in","r",stdin);
    freopen("frac1.out","w",stdout);
    scanf("%d",&n);
    printf("0/1\n");
    getans(0,1,1,1);
    printf("1/1\n");
    return 0;
}

USACO Ordered Fractions