A1081. Rational Sum
Given N rational numbers in the form "numerator/denominator", you are supposed to calculate their sum.
Input Specification:
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.
Output Specification:
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.
Sample Input 1:
5 2/5 4/15 1/30 -2/60 8/3
Sample Output 1:
3 1/3
Sample Input 2:
2 4/3 2/3
Sample Output 2:
2
Sample Input 3:
3 1/3 -1/6 1/8
Sample Output 3:
7/24
1 #include<cstdio> 2 #include<iostream> 3 #include<algorithm> 4 using namespace std; 5 typedef struct{ 6 long long up, down; 7 }fra; 8 long long gcd(long long a, long long b){ 9 a = abs(a); 10 b = abs(b); 11 if(b == 0) 12 return a; 13 else return gcd(b, a % b); 14 } 15 fra cacul(fra a, fra b){ 16 fra temp; 17 temp.down = a.down * b.down; 18 temp.up = a.down * b.up + b.down * a.up; 19 long long fact = gcd(temp.up, temp.down); 20 temp.down = temp.down / fact; 21 temp.up = temp.up / fact; 22 return temp; 23 } 24 int main(){ 25 int N; 26 fra re = {0,1}, temp = {0, 1}; 27 scanf("%d", &N); 28 for(int i = 0; i < N; i++){ 29 scanf("%lld/%lld", &temp.up, &temp.down); 30 re = cacul(re, temp); 31 } 32 if(re.up == 0){ 33 printf("0"); 34 }else if(abs(re.up) == abs(re.down)){ 35 printf("%lld", re.up / re.down); 36 }else if(abs(re.up) > abs(re.down)){ 37 if(re.up % re.down == 0) 38 printf("%d", re.up / re.down); 39 else 40 printf("%lld %lld/%lld", re.up / re.down, re.up % re.down, re.down); 41 }else{ 42 printf("%lld/%lld", re.up, re.down); 43 } 44 cin >> N; 45 return 0; 46 }
总结:
1、分数运算化简:化简时分子分母同除最大公因数。 输出时考虑:分子为0时直接输出0;分子>=分母时(用绝对值比较,是>=而非>),可以整除则输出整数,否则输出代分数(4/1直接输出4);
2、gcd函数:
int gcd(int a, int b){
if(b == 0) return a; else return gcd(b, a % b); }