如果分数无法简化，我将如何制作新分数？

问题描述

因此，我正在为我的OOP类编写一个作业，要求用户输入多个分数，然后随机生成该分数。部分作业指出，如果无法简化分数之一，则跳过它并创建一个可以简化的新分数。但是，不可还原的馏分仍能通过。如果分数的GCD为1，我需要一种方法让程序创建一个新分数。

代码：

import java.util.Random;


 // The class is called Boxes because I'm supposed to print Boxes around the fractions,but I'll 
    implement it later.
    class SimpleFracBoxes{

   private int numberOfFractions = 0;
   private String result = "";  
   Random myRandom = new Random( );
   int min = 1;
   int max = 100000;
  
   public SimpleFracBoxes( )
   {
   }
   
   public SimpleFracBoxes(int nOFracs)
   {
      numberOfFractions = nOFracs;
   }
 
// makes the fractions   
   public void makeTheFractions()
   {
      for (int i = 0; i < numberOfFractions; i++)
      {
         Fraction frac = getAGoodFraction();
         Fraction frac2 = frac.simplify();
         result = result + " "+ (int)(i + 1) + ": " + frac + " simplifies to "+ frac2 + "\n" ;         
     }
 }     
 // creates a fraction that can be divided           
   private Fraction getAGoodFraction()
   {  
      Fraction frac;
         do {                      
            frac = new Fraction (myRandom.nextInt(max-min),myRandom.nextInt(max-min));      
            }      
          while (frac.getNumerator() >= frac.getDenominator());
          int num = frac.getNumerator();
           int denom = frac.getDenominator();
          int gcd = frac.gcd(num,denom);        
               if (gcd == 1)  {                  
                   getAGoodFraction();
                              
                } else if (gcd !=1) {                    
                  frac.simplify();
                }              
      return frac;    
 }
   public String getFractions()
   {
      return result;
   }     
}

分数类代码

public class Fraction{


private int numerator;
private int denominator;

public Fraction(){
    this(0,1);
}

public Fraction(int number) {
    this(number,1);
}

public Fraction(Fraction frac) {
    this(frac.getNumerator(),frac.getDenominator());
}
public Fraction(int num,int denom){
    setNumerator(num);
    setDenominator(denom);
}

public static int gcd(int m,int n) {

    int r = n % m;

    while (r != 0) {

        n = m;

        m = r;

        r = n % m;
    }

    return m;

}

public static Fraction min(Fraction f1,Fraction f2) {

    double f1_dec = f1.decimal();
    double f2_dec = f2.decimal();

    if (f1_dec <= f2_dec) {

        return f1;

    } else {

        return f2;
    }
}

public Fraction add(Fraction frac) {

    int a,b,c,d;

    Fraction sum;

    a = this.getNumerator();
    b = this.getDenominator();
    c = frac.getNumerator();
    d = frac.getDenominator();

    sum = new Fraction(a*d + b*c,b*d);

    return sum;
}

public Fraction add(int number) {

    Fraction frac = new Fraction(number,1);

    Fraction sum = add(frac);

    return sum;
}

public Fraction divide(Fraction frac) {

    int a,d;

    Fraction quotient;

    a = this.getNumerator();
    b = this.getDenominator();
    c = frac.getNumerator();
    d = frac.getDenominator();

    quotient = new Fraction(a*d,b*c);

    return quotient;
}

public Fraction divide(int number) {

    Fraction frac = new Fraction(number,1);

    Fraction quotient = divide(frac);

    return quotient;
}

public boolean equals(Fraction frac) {

    Fraction f1 = simplify();

    Fraction f2 = frac.simplify();

    if (f1.getNumerator() == f2.getNumerator() &&

        f1.getDenominator() == f2.getDenominator()) {

        return true;

    } else {

        return false;
    }
}

public int getDenominator() {

    return denominator;
}

public int getNumerator(){

    return numerator;
}

public Fraction multiply(Fraction frac){

    int a,d;

    Fraction product;

    a = this.getNumerator();
    b = this.getDenominator();
    c = frac.getNumerator();
    d = frac.getDenominator();

    product = new Fraction(a*c,b*d);

    return product;
}

public Fraction multiply(int number){

    Fraction frac = new Fraction(number,1);

    Fraction product = multiply(frac);

    return product;
}

public void setDenominator(int denom){

if (denom == 0) {

    System.err.println("Fatal error");
    System.exit(1);
}

denominator = denom;

}

public void setNumerator(int num) {
    numerator = num;
}

public Fraction simplify(){

    int num = getNumerator();
    int denom = getDenominator();
    int gcd = gcd(num,denom);

    Fraction simp = new Fraction(num/gcd,denom/gcd);

    return simp;

}

public Fraction subtract(Fraction frac) {

    int a,d;

    Fraction diff;

    a = this.getNumerator();
    b = this.getDenominator();
    c = frac.getNumerator();
    d = frac.getDenominator();

    diff = new Fraction(a*d - b*c,b*d);

    return diff;

}

public Fraction subtract(int number) {

    Fraction frac = new Fraction(number,1);

    Fraction difference = subtract(frac);

    return difference;
}

public String toString() {

    return getNumerator() + "/" + getDenominator();
}


private double decimal() {

    return (double) getNumerator() / getDenominator();
}

}

Output:
How many fractions? 3
 1: 28181/38503 simplifies to 28181/38503 // Unsimplified
 2: 75654/99570 simplifies to 12609/16595
 3: 787/31255 simplifies to 787/31255 // Unsimplified

解决方法

听起来您需要分数比较功能。

// returns true if two fractions are identical
public boolean identical(Fraction frac) ...

然后您可以编写一个if语句

if (!frac.identical(frac.reduce())) {
   ... print fraction ...
}

此外，我会考虑将分数缩减逻辑移至分数中，因为这样将来可以在不复制逻辑的情况下对其进行重用。通过在“分数的用户”中使用它，您将获得一个“数据结构”，其中“相关逻辑”在其他位置。一类的最基本定义是“逻辑紧密相关的数据”，其减少的分数与分数非常相关，而与将分数存储在数据库中并没有那么紧密的联系。

,

• 类decimal()中的方法Fraction未使用，因此我将其删除。
• 当GCD值为1时，不要递归调用方法getAGoodFraction()，而要使用循环。
• 使用方法Fraction和setNumerator()，而不是每次随机生成的分子大于随机生成的分母时都创建一个新的setDenominator()对象。那就是他们的目的。
• 无需在方法simplify()中调用方法getAGoodFraction()。只需返回分数。因为GCD不等于1，所以您知道它可以简化。

将以下代码与您的代码进行比较。
请注意，我在类main()中添加了Fraction方法，以便能够运行代码。另外，由于来自{KevinAnderson的问题，comment，我还更改了方法gcd()。

import java.util.Random;

public class Fraction {
    private int numerator;
    private int denominator;

    public Fraction() {
        this(0,1);
    }

    public Fraction(int number) {
        this(number,1);
    }

    public Fraction(Fraction frac) {
        this(frac.getNumerator(),frac.getDenominator());
    }

    public Fraction(int num,int denom) {
        setNumerator(num);
        setDenominator(denom);
    }

    public static int gcd(int m,int n) {
        int factor = m;
        int r = n % factor;
        while (r != 0  &&  factor > 1) {
            r = n % --factor;
            if (r == 0) {
                r = m % factor;
            }
        }
        return factor;
    }

    public int getDenominator() {
        return denominator;
    }

    public int getNumerator() {
        return numerator;
    }

    public void setDenominator(int denom) {
        if (denom == 0) {
            System.err.println("Fatal Error");
            System.exit(1);
        }
        denominator = denom;
    }

    public void setNumerator(int num) {
        numerator = num;
    }

    public Fraction simplify() {
        int num = getNumerator();
        int denom = getDenominator();
        int gcd = gcd(num,denom);

        Fraction simp = new Fraction(num / gcd,denom / gcd);
        return simp;
    }

    public String toString() {
        return getNumerator() + "/" + getDenominator();
    }

    public static void main(String[] args) {
        SimpleFracBoxes sfb = new SimpleFracBoxes(10);
        sfb.makeTheFractions();
        System.out.println(sfb.getFractions());
    }
}

class SimpleFracBoxes {
    private int numberOfFractions = 0;
    private String result = "";
    Random myRandom = new Random();
    int min = 1;
    int max = 100000;

    public SimpleFracBoxes() {
    }

    public SimpleFracBoxes(int nOFracs) {
        numberOfFractions = nOFracs;
    }

//makes the fractions   
    public void makeTheFractions() {
        for (int i = 0; i < numberOfFractions; i++) {
            Fraction frac = getAGoodFraction();
            Fraction frac2 = frac.simplify();
            result += String.format("%" + String.valueOf(numberOfFractions).length() + "d. %5d/%5d simplifies to %5d/%5d%n",(i + 1),frac.getNumerator(),frac.getDenominator(),frac2.getNumerator(),frac2.getDenominator());
        }
    }

// creates a fraction that can be divided           
    private Fraction getAGoodFraction() {
        int gcd = 1;
        Fraction frac = new Fraction();
        while (gcd == 1) {
            do {
                frac.setNumerator(myRandom.nextInt(max - min));
                frac.setDenominator(myRandom.nextInt(max - min));
            } while (frac.getNumerator() >= frac.getDenominator());
            int num = frac.getNumerator();
            int denom = frac.getDenominator();
            gcd = Fraction.gcd(num,denom);
        }
        return frac;
    }

    public String getFractions() {
        return result;
    }
}

这是运行上述代码时产生的示例输出。

 1. 64480/84728 simplifies to  8060/10591
 2. 33376/79317 simplifies to  4768/11331
 3. 50944/97026 simplifies to 25472/48513
 4. 21339/45510 simplifies to  7113/15170
 5. 35884/38628 simplifies to  8971/ 9657
 6. 15148/17199 simplifies to  2164/ 2457
 7. 72670/95005 simplifies to 14534/19001
 8. 19810/44730 simplifies to   283/  639
 9. 61790/63956 simplifies to 30895/31978
10.  4824/ 5352 simplifies to   201/  223