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;
}
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