将小数转换为小数c ++

Question

我可以使用什么算法将十进制数转换并输入到c ++中的分数形式.例如,如果我输入1.25,我希望转换为输出为1 1/4.

Answer 1

首先得到小数部分,然后取gcd.使用欧几里德算法http://en.wikipedia.org/wiki/Euclidean_algorithm

void foo(double input)
{
    double integral = std::floor(input);
    double frac = input - integral;

    const long precision = 1000000000; // This is the accuracy.

    long gcd_ = gcd(round(frac * precision), precision);

    long denominator = precision / gcd_;
    long numerator = round(frac * precision) / gcd_;

    std::cout << integral << " + ";
    std::cout << numerator << " / " << denominator << std::endl;
}

long gcd(long a, long b)
{
    if (a == 0)
        return b;
    else if (b == 0)
        return a;

    if (a < b)
        return gcd(a, b % a);
    else
        return gcd(b, a % b);
}

Answer 2

#include <iostream>
#include <valarray> 

using namespace std;

void as_fraction(double number, int cycles = 10, double precision = 5e-4){
    int sign  = number > 0 ? 1 : -1;
    number = number * sign; //abs(number);
    double new_number,whole_part;
    double decimal_part =  number - (int)number;
    int counter = 0;
    
    valarray<double> vec_1{double((int) number), 1}, vec_2{1,0}, temporary;
    
    while(decimal_part > precision & counter < cycles){
        new_number = 1 / decimal_part;
        whole_part = (int) new_number;
        
        temporary = vec_1;
        vec_1 = whole_part * vec_1 + vec_2;
        vec_2 = temporary;
        
        decimal_part = new_number - whole_part;
        counter += 1;
    }
    cout<<"x: "<< number <<"\tFraction: " << sign * vec_1[0]<<'/'<< vec_1[1]<<endl;
}

int main()
{
    as_fraction(3.142857);
    as_fraction(0.1);
    as_fraction(0.333333);
    as_fraction(514.0/37.0);
    as_fraction(1.17171717);
    as_fraction(-1.17);
}


x: 3.14286      Fraction: 22/7                                                                                                                
x: 0.1          Fraction: 1/10                                                                                                                        
x: 0.333333     Fraction: 1/3                                                                                                                 
x: 13.8919      Fraction: 514/37                                                                                                              
x: 1.17172      Fraction: 116/99                                                                                                              
x: 1.17         Fraction: -117/100

有时您想近似十进制，而不需要等价。例如，pi=3.14159 近似为 22/7 或 355/113。我们可以使用循环参数来获得这些：

as_fraction(3.14159, 1);
as_fraction(3.14159, 2);
as_fraction(3.14159, 3);

x: 3.14159      Fraction: 22/7                                                                                                                
x: 3.14159      Fraction: 333/106                                                                                                             
x: 3.14159      Fraction: 355/113