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








#include<stdio.h>
void pre(int x1, int x2, int y1, int y2, int n)
{
    if (y1 + y2 > n)
    {
        return;
    }
    pre(x1, x1 + x2, y1, y1 + y2, n);
    printf("%d/%d\n", x1 + x2, y1 + y2);
    pre(x1 + x2, x2, y1 + y2, y2, n);
}
int main()
{
    int n;
    freopen("frac1.in", "r", stdin);
    freopen("frac1.out", "w", stdout);
    scanf("%d", &n);
    printf("0/1\n");
    pre(0, 1, 1, 1, n);
    printf("1/1\n");
    fclose(stdin);
    fclose(stdout);
    return 0;    
}



(n1,n1+n2,d1,d1+d2)后关系n1/(n1+n2) < d1/(d1+d2) <式1>仍然成立，可以通过对式1两边分别乘上(n1+n2)(d1+d2)并移动项得到n1/n2 < d1/d2而得，右子树的也可以这样论证。但我不知道WHY