题目：https://pintia.cn/problem-sets/994805260223102976/problems/994805287624491008

注意点

有个地方我一开始没注意，导致分子和分母的正负一直有问题
就是求最大公约数的d时，gcd里面要传绝对值，一定要注意约数的求法！！

  1. Fraction reduction(Fraction a){
  2.     if(a.down < 0){
  3.         a.up *= -1;
  4.         a.down *= -1;
  5.     }
  6.     if(a.up == 0) a.down = 1;
  7.     else {
  8.         ll d = gcd(abs(a.up), abs(a.down));
  9.         a.up /= d;
  10.         a.down /= d;
  11.     }
  12.     return a;
  13. }

代码

  1. #include<algorithm>
  2. #include<vector>
  3. #include<iostream>
  4. #include<cstdio>
  5. using namespace std;
  6. typedef long long ll;
  8. struct Fraction{
  9.     ll up, down;
  10. };
  12. ll gcd(ll a, ll b){
  13.     return b == 0 ? a : gcd(b, a % b);    
  14. }
  16. Fraction reduction(Fraction a){
  17.     if(a.down < 0){
  18.         a.up *= -1;
  19.         a.down *= -1;
  20.     }
  21.     if(a.up == 0) a.down = 1;
  22.     else {
  23.         ll d = gcd(abs(a.up), abs(a.down));
  24.         a.up /= d;
  25.         a.down /= d;
  26.     }
  27.     return a;
  28. }
  30. Fraction add(Fraction a, Fraction b){
  31.     Fraction temp;
  32.     temp.up = a.up * b.down + b.up * a.down;
  33.     temp.down = a.down * b.down;
  34.     return reduction(temp);
  35. }
  37. Fraction minu(Fraction a, Fraction b){
  38.     Fraction temp;
  39.     temp.up = a.up * b.down - b.up * a.down;
  40.     temp.down = a.down * b.down;
  41.     return reduction(temp);
  42. }
  44. Fraction multiply(Fraction a, Fraction b){
  45.     Fraction temp;
  46.     temp.up = a.up * b.up;
  47.     temp.down = a.down * b.down;
  48.     return reduction(temp);
  49. }
  51. Fraction divide(Fraction a, Fraction b){
  52.     Fraction temp;
  53.     temp.up = a.up * b.down;
  54.     temp.down = a.down * b.up;
  55.     return reduction(temp);
  56. }
  58. void show_Fra(Fraction a){
  59.     a = reduction(a);
  60.     if(a.up < 0) printf("(");
  61.     if(a.down == 1) printf("%lld",a.up);
  62.     else if(abs(a.up) > a.down) printf("%lld %lld/%lld",a.up / a.down, abs(a.up) % a.down, a.down);
  63.     else printf("%lld/%lld", a.up, a.down);
  64.     if(a.up < 0) printf(")");
  65. }
  67. int main(){
  68.     Fraction a, b;
  69.     scanf("%lld/%lld %lld/%lld", &a.up, &a.down, &b.up, &b.down);
  70.     show_Fra(a);
  71.     printf(" + ");
  72.     show_Fra(b);
  73.     printf(" = ");
  74.     show_Fra(add(a, b));
  75.     printf("\n");
  77.     show_Fra(a);
  78.     printf(" - ");
  79.     show_Fra(b);
  80.     printf(" = ");
  81.     show_Fra(minu(a, b));
  82.     printf("\n");
  84.     show_Fra(a);
  85.     printf(" * ");
  86.     show_Fra(b);
  87.     printf(" = ");
  88.     show_Fra(multiply(a, b));
  89.     printf("\n");
  91.     show_Fra(a);
  92.     printf(" / ");
  93.     show_Fra(b);
  94.     printf(" = ");
  95.     if(b.up != 0) show_Fra(divide(a, b));
  96.     else printf("Inf");
  97.     printf("\n");
  98. }