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USACO Ordered Fractions

2024-10-08 19:34:38   213人阅读

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)

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



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: njuwz151
TASK: frac1
LANG: 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);
}

 

USACO Ordered Fractions


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