USACO Ordered Fractions

首先看一下题目

 

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)

0/11/51/41/32/51/23/52/33/44/51/1由于数据量很小的缘故，我们可以把所有的分数存下来，然后进行排序。第一步，存下所有的已约分的分数。第二步，对存下来的分数进行排序。至此，此题完成。

/**ID: njuwz151TASK: frac1LANG: C++*/#include <bits/stdc++.h>using namespace std;const int maxn = 165;int n;typedef struct {    int x;    int y;} Frac;Frac frac[maxn*maxn];int cmp(Frac a, Frac b);int gcd(int a, int b);int main() {    freopen("frac1.in", "r", stdin);    freopen("frac1.out", "w", stdout);        cin >> n;        int count = 0;    for(int i = 1; i <= n; i++) {        for(int j = 0; j <= i; j++) {//            cout << i << "   " << j << "    " << gcd(i, j) << endl;            if(gcd(i, j) == 1) {                frac[count].x = j;                frac[count].y = i;                count++;            }        }    }        sort(frac, frac + count, cmp);    for(int i = 0; i < count; i++) {        cout << frac[i].x << "/" << frac[i].y << endl;    }}int cmp(Frac a, Frac b) {    return a.x * b.y < b.x * a.y;}int gcd(int a, int b) {    return b == 0 ? a : gcd(b, a % b);}