（欧几里得算法）Rational API实现（1216）

有理数：正整数、负整数、正分数、负分数以及零的统称。

有理数是一个整数a和一个正整数b的比，例如3/8，通则为a/b。0也是有理数。有理数是整数和分数的集合，整数也可看做是分母为一的分数。

有理数与分数的区别，分数是一种比值的记法。可以是无理数，例如根号2/1。

有理数的小数部分是有限或为无限循环的数。不是有理数的实数称为无理数，即无理数的小数部分是无限不循环的数。

Arithmetic 数学

numerator 分子

denominator 分母

Divisor 因数

assert:断言

格式：    assert <布尔表达式> ： <错误信息表达式>

这里主要是考虑了加法plus和乘法times的溢出overflow问题：

1.加法plus： a >= 0 就要考虑 a + b < MAX ;   

                     a < 0 就要考虑 a + b > MIN;

2.乘法times：主要是考虑分母一定要为正数，不可以为负数。

代码如下：

---

package chapter1.a2;

import edu.princeton.cs.algs4.StdIn;

/**

* Created by fengjw on 2017/7/29.

*/

public class Rational {

private int numerator;

private int denominator;

private int MAX =2147483647;

private int MIN = -2147483648;

public Rational(int numerator, int denominator)throws ArithmeticException{

if (denominator == 0){

throw new ArithmeticException("Divide by zero.");

}

//分母不能为0

if (denominator < 0){

denominator = -denominator;

numerator = -numerator;

}

/*

这里是求分子和分母去掉公因子的最简形式

(保证分子分母没有公因子)

*/

int commonDivisor = Enclid(numerator,denominator);// 最大公约数Divisor

this.numerator = numerator / commonDivisor;

this.denominator = denominator / commonDivisor;

}

//plus

public Rational plus(Rational b){ //assert 断言 assert <boolean表达式> : <错误信息表达式>

assert isPlusOverflow(numerator * b.denominator, b.numerator *denominator) : "Plus overflow";

assert isTimesOverflow(denominator, b.denominator) :"Times overflow";

int n = numerator * b.denominator +denominator * b.numerator;

int d = denominator * b.denominator;

return new Rational(n,d);

}

//minus

public Rational minus(Rational b){

return new Rational(numerator * b.denominator - b.numerator *denominator,denominator * b.denominator);

}

//times

public Rational times(Rational b){

assert isTimesOverflow(numerator, b.numerator) :"Times overflow";

assert isTimesOverflow(denominator, b.denominator) :"Times overflow";

return new Rational(numerator * b.numerator,denominator * b.denominator);

}

public Rational divides(Rational b){

return new Rational(numerator * b.denominator,denominator * b.numerator);

}

public boolean equlas(Object object){

if (this == object){

return true;

}

if (object == null){

return false;

}

if (this.getClass() != object.getClass()){

return false;

}

Rational that = (Rational) object;

if (this.numerator != that.numerator){

return false;

}

if (this.denominator != that.denominator){

return false;

}

return true;

}

//默认一定会执行的方法。

public String toString(){

if (Math.abs(numerator) % Math.abs(denominator) ==0){

return String.valueOf(numerator /denominator);

}else {

return numerator +"/" + denominator;

}

}

private int Enclid(int p, int q){

if (p == 0 || q ==0)

return 1;

p = Math.abs(p);

q = Math.abs(q);

if(p < q){

int temp = q;

q = p;

p = temp;

}

if (p % q == 0){

return q;

}else {

return Enclid(q, p % q);

}

}

private boolean isPlusOverflow(int a, int b){

return a >= 0 ? a + b <MAX : a + b > MIN;

}

private boolean isTimesOverflow(int a, int b){

if (a < 0)

a = -a;

if (b < 0)

b = -b;

if (a == 0 || b ==0){

return false;

}else {

return a * b < MAX;

}

}

public static void main(String [] args){

System.out.println("Rational a:");

System.out.print("numerator: ");

int numerator = StdIn.readInt();

System.out.print("denominator: ");

int denominator = StdIn.readInt();

Rational a = new Rational(numerator, denominator);

System.out.println("Rational b:");

System.out.print("numerator: ");

numerator = StdIn.readInt();

System.out.print("denominator: ");

denominator = StdIn.readInt();

Rational b = new Rational(numerator, denominator);

System.out.println("a plus b: " + a.plus(b));

System.out.println("a minus b: " + a.minus(b));

System.out.println("a times b: " + a.times(b));

System.out.println("a divides b: " + a.divides(b));

System.out.println("a equals b: " + a.equals(b));

}

}