算法笔记5.3 分数四则运算

5.3.1分数的表示和化简

#include<iostream>     
#include<cmath>
using namespace std;

struct Fraction{
  int up,down;
};

int gcd(int a,int b){
  if(b==0) return a;
  return gcd(b,a%b);
}

//分数规范化 化简
void reduction(Fraction& result){
  if(result.down<0){//规定分母必须为正数
    result.down=-result.down;
    result.up=-result.up;
  }
  if(result.up==0){//分子为0时分母为1
    result.down=1;
  }else{
    int d=gcd(abs(result.down),abs(result.up));
    result.down/=d;
    result.up/=d;
  }
}

void showFra(Fraction a){
  cout<<a.up<<"/"<<a.down<<endl;
}

int main(){
  int m,n;
  Fraction fra;
  while(cin>>fra.up>>fra.down){
    reduction(fra);
    showFra(fra);
  }
  return 0;
}

 

分数的四则运算以及输出

#include<iostream>     
#include<cmath>
using namespace std;

struct Fraction{
  int up,down;
};

int gcd(int a,int b){
  if(b==0) return a;
  return gcd(b,a%b);
}

//分数规范化 化简
void reduction(Fraction& result){
  if(result.down<0){//规定分母必须为正数
    result.down=-result.down;
    result.up=-result.up;
  }
  if(result.up==0){//分子为0时分母为1
    result.down=1;
  }else{
    int d=gcd(abs(result.down),abs(result.up));
    result.down/=d;
    result.up/=d;
  }
}

//分数加法
Fraction add(Fraction f1,Fraction f2){
  Fraction result;
  result.up=f1.down*f2.up+f1.up*f2.down;
  result.down=f1.down*f2.down;
  reduction(result);
  return result;
}

//分数减法
Fraction minu(Fraction f1,Fraction f2){
  Fraction result;
  result.up=f1.up*f2.down-f2.up*f1.down;
  result.down=f1.down*f2.down;
  reduction(result);
  return result;
}

//分数乘法
Fraction multi(Fraction f1,Fraction f2){
  Fraction result;
  result.up=f2.up*f1.up;
  result.down=f1.down*f2.down;
  reduction(result);
  return result;
}

//分数除法
Fraction divide(Fraction f1,Fraction f2){
  Fraction result;
  result.up=f1.up*f2.down;
  result.down=f1.down*f2.up;
  reduction(result);
  return result;
}

//分数输出
void showResult(Fraction r){
  reduction(r);
  if(r.down==1){//整数
    cout<<r.up;
  }else if(abs(r.up)>r.down){//分母一定正数  假分数以带分数形式输出
    cout<<r.up/r.down<<" "<<abs(r.up)%r.down<<"/"<<r.down;
  }else{
    cout<<r.up<<"/"<<r.down;
  }
  cout<<endl;
}

int main(){
  int m,n;
  Fraction f1,f2,result;
  f1.up=10;f1.down=-15;
  f2.up=-20;f2.down=-25;
  cout<<"加:";showResult(add(f1,f2));
  cout<<"减:";showResult(minu(f1,f2));
  cout<<"乘:";showResult(multi(f1,f2));
  cout<<"除:";showResult(divide(f1,f2));
  return 0;
}