1088. Rational Arithmetic (20)

1.注意在数字和string转化过程中，需要考虑数字不是只有一位的，如300转为“300”，一开始卡在里这里，

测试用例：

24/8 100/10

24/11 300/11

2.该题用到了欧几里德算法求最小公约数gcd(a,b)

算法如下：

//欧几里德算法求最大公约数gcd，其中a>b
long long gcd(long long a, long long b)
{
	return b == 0 ? a : gcd(b, a%b);
}

AC代码如下：

//#include<string>
//#include <iomanip>
#include<vector>
#include <algorithm>
//#include<stack>
#include<set>
#include<queue>
#include<map>
//#include<unordered_set>
#include<unordered_map>
//#include <sstream>
//#include "func.h"
//#include <list>
#include<stdio.h>
#include<iostream>
#include<string>
#include<memory.h>
#include<limits.h>
using namespace std;

/*
24/8 100/10
24/11 300/11
*/

//欧几里德算法求最大公约数gcd
long long gcd(long long a, long long b)
{
	return b == 0 ? a : gcd(b, a%b);
}
void str2num(string str, long long&top, long long&bot, int&sign)
{
	bool first = true;
	for (int i = 0; i < str.size(); i++)
	{
		if (str[i] == '-')
			sign = -1;
		else if (str[i] != '/'&&first)
			top = top * 10 + str[i] - '0';
		else if (str[i] == '/')
			first = false;
		else if (str[i] != '/'&&!first)
			bot = bot * 10 + str[i] - '0';
	}
}
string i2s(long long a)
{
	string ans = "";
	if (a == 0) return "0";
	else
	{
		while (a != 0)
		{
			char c = a % 10 + '0';
			ans = c + ans;
			a /= 10;
		}
	}
	return ans;
}
string int2Str(long long top, long long bot, bool sign)
{
	long long tmpGCD = gcd(top, bot);
	top /= tmpGCD;
	bot /= tmpGCD;
	long long tmpInt = top / bot;
	long long tmpRat = top%bot;
	string ans = "";
	if (tmpInt != 0)
	{
		ans = i2s(tmpInt);
	}
	if (tmpRat == 0 && ans.size() != 0)
		;
	else if (tmpRat == 0 && ans.size() == 0)
	{
		return "0";
	}
	else if (tmpRat != 0 && ans.size() != 0)
	{//整数和分数同时存在
		ans += " "+i2s(tmpRat) + "/" + i2s(bot);
	}
	else if (tmpRat != 0 && ans.size() == 0)
	{//仅存在分数
		ans += i2s(tmpRat) + "/" + i2s(bot);
	}
	if (!sign)
		ans = "(-" + ans + ")";
	return ans;
}
int main(void)
{
	string a, b;
	cin >> a >> b;
	long long aTop = 0, aBot = 0, bTop = 0, bBot = 0;
	int aSign = 1;
	int bSign = 1;
	str2num(a, aTop, aBot, aSign);
	str2num(b, bTop, bBot, bSign);
	string aAns;
	string bAns;
	if (aTop != 0)
	{
		int aGCD = gcd(aTop, aBot);
		aTop /= aGCD;
		aBot /= aGCD;
		aAns = int2Str(aTop, aBot, aSign == 1);
	}
	else aAns = "0";
	if (aTop != 0)
	{
		int bGCD = gcd(bTop, bBot);
		bTop /= bGCD;
		bBot /= bGCD;
		bAns = int2Str(bTop, bBot, bSign == 1);
	}
	else
		bAns = "0";

	//加法：
	long long addBot = aBot*bBot;
	long long addTop = aSign*aTop*bBot + bSign*bTop*aBot;
	bool addSign = (addTop >= 0 ? true : false);
	addTop = labs(addTop);
	long long addInt = addTop / addBot;
	string addAns = int2Str(addTop, addBot, addSign);
	cout << aAns << " + " << bAns << " = " << addAns << endl;

	//减法：
	long long diffBot = aBot*bBot;
	long long diffTop = aSign*aTop*bBot - bSign*bTop*aBot;
	bool diffSign = (diffTop >= 0 ? true : false);
	diffTop = labs(diffTop);
	long long diffInt = diffTop / diffBot;
	string diffAns = int2Str(diffTop, diffBot, diffSign);
	cout << aAns << " - " << bAns << " = " << diffAns << endl;

	//乘法
	long long proBot = aBot*bBot;
	long long proTop = aSign*bSign*aTop*bTop;
	bool proSign = (proTop >= 0 ? true : false);
	proTop = labs(proTop);
	long long proInt = proTop / proBot;
	string proAns = int2Str(proTop, proBot, proSign);
	cout << aAns << " * " << bAns << " = " << proAns << endl;

	//除法
	long long quoBot = aBot*bTop;
	long long quoTop = aSign*bSign*aTop*bBot;
	string quoAns;
	if (quoBot != 0)
	{
		bool quoSign = (quoTop >= 0 ? true : false);
		quoTop = labs(quoTop);
		long long quoInt = quoTop / quoBot;
		quoAns = int2Str(quoTop, quoBot, quoSign);
	}
	else
		quoAns = "Inf";
	cout << aAns << " / " << bAns << " = " << quoAns << endl;

	return 0;
}