PAT-basic-1034 有理数四则运算

一、题目

本题要求编写程序，计算 2 个有理数的和、差、积、商。

输入格式：

输入在一行中按照 a1/b1 a2/b2 的格式给出两个分数形式的有理数，其中分子和分母全是整型范围内的整数，负号只可能出现在分子前，分母不为 0。

输出格式：

分别在 4 行中按照 有理数1 运算符有理数2 = 结果 的格式顺序输出 2 个有理数的和、差、积、商。注意输出的每个有理数必须是该有理数的最简形式 k a/b，其中 k 是整数部分，a/b 是最简分数部分；若为负数，则须加括号；若除法分母为 0，则输出 Inf。题目保证正确的输出中没有超过整型范围的整数。

输入样例 1：

2/3 -4/2

输出样例 1：

2/3 + (-2) = (-1 1/3)
2/3 - (-2) = 2 2/3
2/3 * (-2) = (-1 1/3)
2/3 / (-2) = (-1/3)

输入样例 2：

5/3 0/6

输出样例 2：

1 2/3 + 0 = 1 2/3
1 2/3 - 0 = 1 2/3
1 2/3 * 0 = 0
1 2/3 / 0 = Inf

二、解析

细节题，首先要注意输出格式，这里选择先将每一个有理数转化为要求的格式，然后统一加减乘除。定义加减乘除的时候需要注意除法，分母为0的情况。此外控制负数最好只出现在分子。

三、代码

java :

查看代码

 package shuati;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.Scanner;

public class PAT_BASIC_1034 {
    private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static Scanner input = new Scanner(System.in);
    public static void main(String[] args) throws IOException {
        String str[] = input.nextLine().split("[\\s+/]");
        Rational r1 = new Rational(Long.parseLong(str[0]), Long.parseLong(str[1]));
        Rational r2 = new Rational(Long.parseLong(str[2]), Long.parseLong(str[3]));
        Rational.printRes(r1, r2);

//        Rational r = new Rational(24, 36);
//        long gdb = r.getGdb();
//        System.out.println(gdb);
    }
    private static class Rational{
        long fz;
        long fm;
        public Rational() {}
        public Rational(long fz, long fm) {
            if(fm<0 && fz<0 || fm<0 && fz>0){
                fz = -1 * fz;
                fm = -1 * fm;
            }
            long gcd = getGcd(fz, fm);
            this.fz = fz/gcd;
            this.fm = fm/gcd;
//            System.out.println("gcd: " + gcd +", Rational: " + this.fz +  " " + this.fm);
        }
        public String getString(){
            if(fz == 0 || fm == 0) return "0";
            long num1 = Math.abs(fz);
            long num2 = fm;
            StringBuffer buf = new StringBuffer();
            if(fz < 0)
                buf.append("(-");
            if(num1 >= num2){
                long k = num1/num2;
                long a = num1 - k*num2;
                buf.append(k);
                if(a != 0){
                    buf.append(" ");
                    buf.append(a + "/" + num2);
                }
            }else
                buf.append(num1 + "/" + num2);
            if(fz < 0)
                buf.append(")");
            return buf.toString();
        }
        public long getGcd(long fz, long fm){
            if(fz==0 || fm ==0) return 1;
            long num1 = Math.abs(fz), num2 = Math.abs(fm);
            long temp = num1 % num2;
            while(temp != 0){
                num1 = num2;
                num2 = temp;
                temp = num1 % num2;
            }
            return num2;
        }
        public static void printRes(Rational r1, Rational r2){
            String s1 = r1.getString();
            String s2 = r2.getString();
            System.out.printf("%s + %s = %s\n",s1 , s2, add(r1, r2).getString());
            System.out.printf("%s - %s = %s\n",s1 , s2, sub(r1, r2).getString());
            System.out.printf("%s * %s = %s\n",s1 , s2, mul(r1, r2).getString());
            if(div(r1, r2) == null)
                System.out.printf("%s / %s = Inf\n", s1, s2);
            else
                System.out.printf("%s / %s = %s\n",s1 , s2, div(r1, r2).getString());
        }
        public static Rational add(Rational r1, Rational r2){
            long fz1 = r1.fz, fm1 = r1.fm;
            long fz2 = r2.fz, fm2 = r2.fm;
            long newFm = fm1 * fm2;
            long newFz = fz1*fm2 + fz2*fm1;
            Rational res = new Rational(newFz, newFm);
            return res;
        }
        public static Rational sub(Rational r1, Rational r2){
            long newFm = r1.fm * r2.fm;
            long newFz = r1.fz*r2.fm - r2.fz*r1.fm;
            return new Rational(newFz, newFm);
        }
        public static Rational mul(Rational r1, Rational r2){
            long newFm = r1.fm * r2.fm;
            long newFz = r1.fz * r2.fz;
            return new Rational(newFz, newFm);
        }
        public static Rational div(Rational r1, Rational r2){
            if(r2.getString().equals("0")) return null;
            long newFm = r1.fm * r2.fz;
            long newFz = r1.fz * r2.fm;
            return new Rational(newFz, newFm);
        }
    }
}

c++：