USACO 2.2.2 Ordered Fractions

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

题目大意：

　　这道题是说，让你输出0~1之间的所有真分式。给你了一个n，这个n表示的最大的分母。

解题思路：

　　由于n最大只有160，那么直接O（n^2）暴力就可以了，把所有的分子和分母满足条件的组合全部记录下来，然后，从小到大排序后，在一个一个输出就OK了。

代码：

/*
    ID:wikioi_2
    PROG:frac1
    LANG:C++
*/

# include<cstdio>
# include<iostream>
# include<algorithm>

using namespace std;

# define MAX 12345

struct node
{
    int x,y;// x/y;
}a[MAX];

int gcd ( int a,int b )
{
    if ( b==0 )
        return a;
    else
        return gcd(b,a%b);
}

int cmp ( const struct node & a,const struct node & b )
{
    return ( (double)a.x/a.y < (double)b.x/b.y );
}

int main(void)
{
    freopen("frac1.in","r",stdin);
    freopen("frac1.out","w",stdout);
    int n;
    scanf("%d",&n);
    int cnt = 0;
    for ( int i = 1;i <= n;i++ )
    {
        for ( int j = 0;j <= i;j++ )
        {
            int t1 = j;
            int t2 = i;
            if ( gcd(t1,t2)==1 )
            {
                a[cnt].x = j;
                a[cnt].y = i;
                cnt++;
            }
        }
    }
    sort(a,a+cnt,cmp);
    for ( int i = 0;i < cnt;i++ )
    {
        printf("%d/%d
",a[i].x,a[i].y);
    }


    return 0;
}