2.1 frac1

Ordered Fractions

Consider the set of all reduced fractions between 0 and 1 inclusivewith 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

/*ID: xdzhbin1LANG: C++TASK: frac1*/#include <fstream>#include <vector>#include <algorithm>#include <iostream>using namespace std;typedef struct fraction  //表示分数{int numerator; //分子int denominator;//分母fraction(int a,int b): //构造函数numerator(a),denominator(b){}}fraction;//小于操作bool cmp(fraction f1, fraction f2){int ret = f1.numerator*f2.denominator - f2.numerator*f1.denominator;if (ret >= 0){return false;}else{return true;}}//判断两个分数是否相等bool equal(fraction f1, fraction f2){int ret = f1.numerator*f2.denominator - f2.numerator*f1.denominator;if (ret == 0){return true;}else{return false;}}//辗转相减，求最大公约数int gcd(int a,int b){/*int ret = a<b?a:b;while (ret != 1){if (a%ret==0 && b%ret==0){return ret;}ret--;}return 1;*/while (a!=b){if (a>b){a -= b;}else{b -= a;}}return a;}class Frac{private:int n;vector<fraction> v;ofstream out;public:Frac(int a):  n(a){out.open("frac1.out");}void calculate();void display();};//枚举产生所有分数，放入向量v中void Frac::calculate(){int i,j;for(i=0; i<n; i++){for (j=i+1; j<=n; j++){v.push_back(fraction(i,j));}}v.push_back(fraction(1,1));sort(v.begin(),v.end(),cmp); //根据分数大小排序}void Frac::display(){int i;fraction f = v[0];out<<0<<"/"<<1<<endl;//输出第一个for (i=1; i<v.size(); i++){if (equal(f,v[i])) //如果跟前一个大小相等则不输出{continue;}else{//输出最简形式int gcdnum = gcd(v[i].numerator,v[i].denominator);out<<v[i].numerator/gcdnum<<"/"<<v[i].denominator/gcdnum<<endl;f = v[i];}}}int main(){ifstream in("frac1.in");int n;in>>n;Frac f(n);f.calculate();f.display();in.close();return 0;}