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

 1 #include <iostream>
 2 #include <vector>
 3 #include <math.h>
 4 
 5 using namespace std;
 6 
 7 long int  gcd(long int a, long int b)
 8 {
 9     if(b==0) return a;
10     else return gcd(b,a%b);    
11 }
12 
13 int main()
14 {
15     double N;
16     cin>>N;
17     long int Inter = 0;//整数
18     long int resa = 0;//答案分子 
19     long int resb = 1;//答案分母 
20 
21     for(int i=0;i<N;++i)
22     {
23         long int a = 0;//输入分子 
24         long int b = 0;//输入分母 
25         char c;
26         cin >> a >> c >> b; 
27         
28         int f = 1;
29         if(a<0)
30         {
31             a = a*-1;
32             f = -1;        
33         } 
34         Inter += a/b; //简化 
35         a = a-b*(a/b);
36         
37         long int Div = 0;//最大公约数 
38         long int Mul = 0;//最小公倍数 
39         //化简输入的分数 
40         Div = gcd(b,a);
41         a = a/Div;
42         b = b/Div;                
43         
44         //求最大公倍数 
45         if(resb > b)
46         {
47             Div = gcd(resb,b);
48             Mul = resb / Div * b;
49         }
50         else
51         {
52             Div = gcd(b, resb);
53             Mul = b / Div * resb;
54         }
55         //相加        
56         resa = resa * (Mul/resb) + f * a * (Mul/b);
57         resb = Mul;
58         //化简有理数 
59         Inter += resa / resb;        
60         resa = resa - (resa / resb)*resb;        
61         
62         //化简最简分数 
63         Div = gcd(resb, fabs(resa));
64         resa = resa/Div;
65         resb = resb/Div;
66     }
67     if(Inter==0 && resa==0)
68         cout << 0 << endl;
69     else if(Inter != 0 && resa == 0)
70         cout << Inter << endl;
71     else if(Inter == 0 && resa != 0 )
72         cout << resa << "/" << resb << endl;
73     else
74         cout << Inter << " " << resa << "/" << resb << endl;
75     
76     return 0;
77 }