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==) return a;
     else return gcd(b,a%b);
 }

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

     for(int i=;i<N;++i)
     {
         long int a = ;//输入分子
         long int b = ;//输入分母
         char c;
         cin >> a >> c >> b; 

         int f = ;
         if(a<)
         {
             a = a*-;
             f = -;
         }
         Inter += a/b; //简化
         a = a-b*(a/b);

         long int Div = ;//最大公约数
         long int Mul = ;//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== && resa==)
         cout <<  << endl;
     else if(Inter !=  && resa == )
         cout << Inter << endl;
     else if(Inter ==  && resa !=  )
         cout << resa << "/" << resb << endl;
     else
         cout << Inter << " " << resa << "/" << resb << endl;

     return ;
 }