PAT甲级——【牛客练习题100】

题目描述

Given N rational numbers in the form "numerator/denominator", you are supposed to calculate their sum.

输入描述:

Each input file contains one test case. Each case starts with a positive integer N (<=100), followed in the next line N rational numbers "a1/b1 a2/b2 ..." where all the numerators and denominators are in the range of "long int".  If there is a negative number, then the sign must appear in front of the numerator.

输出描述:

For each test case, output the sum in the simplest form "integer numerator/denominator" where "integer" is the integer part of the sum, "numerator" < "denominator", and the numerator and the denominator have no common factor.  You must output only the fractional part if the integer part is 0.

输入例子:

5
2/5 4/15 1/30 -2/60 8/3

输出例子:

3 1/3

#include <iostream>
#include <vector>
#include <math.h>

using namespace std;

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

int main()
{
    double N;
    cin>>N;
    long int Inter = 0;//整数
    long int resa = 0;//答案分子 
    long int resb = 1;//答案分母 

    for(int i=0;i<N;++i)
    {
        long int a = 0;//输入分子 
        long int b = 0;//输入分母 
        char c;
        cin >> a >> c >> b; 
        
        int f = 1;
        if(a<0)
        {
            a = a*-1;
            f = -1;        
        } 
        Inter += a/b; //简化 
        a = a-b*(a/b);
        
        long int Div = 0;//最大公约数 
        long int Mul = 0;//最小公倍数 
        //化简输入的分数 
        Div = gcd(b,a);
        a = a/Div;
        b = b/Div;                
        
        //求最大公倍数 
        if(resb > b)
        {
            Div = gcd(resb,b);
            Mul = resb / Div * b;
        }
        else
        {
            Div = gcd(b, resb);
            Mul = b / Div * resb;
        }
        //相加        
        resa = resa * (Mul/resb) + f * a * (Mul/b);
        resb = Mul;
        //化简有理数 
        Inter += resa / resb;        
        resa = resa - (resa / resb)*resb;        
        
        //化简最简分数 
        Div = gcd(resb, fabs(resa));
        resa = resa/Div;
        resb = resb/Div;
    }
    if(Inter==0 && resa==0)
        cout << 0 << endl;
    else if(Inter != 0 && resa == 0)
        cout << Inter << endl;
    else if(Inter == 0 && resa != 0 )
        cout << resa << "/" << resb << endl;
    else
        cout << Inter << " " << resa << "/" << resb << endl;
    
    return 0;
}