1088.Rational Arithmetic

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本文介绍了一种实现分数加减乘除运算的方法，并通过最大公约数算法将结果分数简化到最简形式。代码中使用了自定义函数来处理分数的输入、运算及输出。

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【题意】

对两个分数进行四则运算，并用最简形式表示结果

【思路】

通过求最大公约数约分，别的就没啥好说的了

#include <iostream>
#include <string>
#include <cstring>
#include <cstdio>
#include <sstream>
#include <cmath>
using namespace std;

#define ll long long

ll gcd(ll a, ll b){
	if(a<b){
		return gcd(b,a);
	}
	else if(a%b==0){
		return b;
	}
	else{
		return gcd(b,a%b);
	}
}

string ll2str(ll num){
	string res = "";

	while(num){
		res.insert(res.begin(),num%10+'0');
		num /= 10;
	}

	return res;
}

string simplestForm(ll numerator, ll denominator){
	if(denominator==0){
		return "Inf";
	}
	else if(numerator==0){
		return "0";
	}
	else{
		string res = "";
		bool nf = false;

		if((numerator<0 && denominator>0) || (numerator>0 && denominator<0)){
			nf = true;
			res.append("(-");
		}
		numerator = abs(numerator);
		denominator = abs(denominator);

		ll tmp = gcd(numerator,denominator);
		numerator /= tmp;
		denominator /= tmp;
		if(numerator/denominator){
			ll tmp = numerator/denominator;
			numerator %= denominator;

			res.append(ll2str(tmp));

			if(numerator==0){
				if(nf){
					res.insert(res.end(),')');
				}
				return res;
			}
			else{
				res.append(" ");
			}
		}
		res.append(ll2str(numerator)+"/"+ll2str(denominator));
		if(nf){
			res.insert(res.end(),')');
		}

		return res;
	}
}

int main(int argc, char const *argv[])
{
	ll numerator[3],denominator[3];
	
	for(int i=0; i<2; i++){
		scanf("%lld/%lld", &numerator[i], &denominator[i]);
	}

	string newForm[3];
	for(int i=0; i<2; i++){
		newForm[i] = simplestForm(numerator[i], denominator[i]);
	}

	cout << newForm[0] << " + " << newForm[1] << " = ";
	numerator[2] = numerator[0]*denominator[1]+numerator[1]*denominator[0];
	denominator[2] = denominator[0]*denominator[1];
	newForm[2] = simplestForm(numerator[2], denominator[2]);
	cout << newForm[2] << endl;
	
	cout << newForm[0] << " - " << newForm[1] << " = ";
	numerator[2] = numerator[0]*denominator[1]-numerator[1]*denominator[0];
	denominator[2] = denominator[0]*denominator[1];
	newForm[2] = simplestForm(numerator[2], denominator[2]);
	cout << newForm[2] << endl;

	cout << newForm[0] << " * " << newForm[1] << " = ";
	numerator[2] = numerator[0]*numerator[1];
	denominator[2] = denominator[0]*denominator[1];
	newForm[2] = simplestForm(numerator[2], denominator[2]);
	cout << newForm[2] << endl;

	cout << newForm[0] << " / " << newForm[1] << " = ";
	numerator[2] = numerator[0]*denominator[1];
	denominator[2] = denominator[0]*numerator[1];
	newForm[2] = simplestForm(numerator[2], denominator[2]);
	cout << newForm[2];

	system("pause");
	return 0;
}