usaco2.1.2（frac1）

题目：

Ordered Fractions

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

One line with a single integer N.

SAMPLE INPUT (file frac1.in)

5

OUTPUT FORMAT

One fraction per line, sorted in order of magnitude.

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

题意是说输入N，输出分母小于N的所有真分数，见样例
题目分类是图论，但始终想不通与图论有毛线关系
代码：

/*
ID:614433244
PROG: frac1
LANG: C++
*/
#include"iostream"
#include"cstdio"
#include"algorithm"
#include"cstring"
using namespace std;
struct M
{
    int fenzi,fenmu;
}fenshu[160*160];
bool cmp( M a,M b )
{
    return a.fenzi*b.fenmu < b.fenzi*a.fenmu;
}
int gcd(int a,int b)
{
    if( b==0 )
        return a;
    else
        return gcd( b,a%b );
}
int t;
bool vis[160][160];
int main()
{
    freopen("frac1.in","r",stdin);
    freopen("frac1.out","w",stdout);
    memset(vis,0,sizeof(vis));
    int n;
    scanf("%d",&n);
    int i,j;
    t=0;
    for( i=1;i<=n;i++ )
        for( j=i+1;j<=n;j++ )
        {
            if( vis[ i/gcd(i,j) ][ j/gcd(i,j) ] )
                continue;
            else
            {
                fenshu[t].fenzi=i/gcd(i,j);
                fenshu[t].fenmu=j/gcd(i,j);
                vis[i/gcd(i,j)][j/gcd(i,j)]=1;
                t++;
            }
        }
    sort( fenshu,fenshu+t,cmp );
    printf("0/1\n");
    for( i=0;i<t;i++ )
        printf("%d%c%d\n",fenshu[i].fenzi,'/',fenshu[i].fenmu);
    printf("1/1\n");
    return 0;
}