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  1. #include <string>
  2. #include <iostream>
  3. #include <iomanip>
  4. #include <type_traits>
  5.  
  6. template<typename T, typename = std::enable_if_t<std::is_integral<T>::value>>
  7.     T gcd(T m, T n)
  8. {
  9.     while(m && n) if (m < n) n %= m; else m %= n;
  10.     return m + n;
  11. }
  12.  
  13. template<typename T, typename = std::enable_if_t<std::is_integral<T>::value>>
  14. T lcm(T m, T n)
  15. {
  16.     return (m/gcd(m,n))*n;
  17. }
  18.  
  19. class frac
  20. {
  21. public:
  22.     frac(long long d, unsigned long long q = 1ull);
  23.     frac(const frac&)            = default;
  24.     frac& operator=(const frac&) = default;
  25.  
  26.     operator std::string() const;
  27.  
  28.  
  29. private:
  30.     unsigned long long d, q;
  31.     int sign;
  32.     void norm();
  33.  
  34.     friend frac operator +(const frac&a, const frac&b);
  35.     friend frac operator -(const frac&a, const frac&b);
  36.     friend frac operator *(const frac&a, const frac&b);
  37.     friend frac operator /(const frac&a, const frac&b);
  38.  
  39.     friend bool operator ==(const frac&a, const frac&b);
  40.     friend bool operator !=(const frac&a, const frac&b);
  41.  
  42. };
  43.  
  44. frac::frac(long long dd, unsigned long long qq)
  45. {
  46.     sign = (dd < 0) ? -1 : +1;
  47.     d = dd*sign;
  48.     q = qq;
  49.     norm();
  50. };
  51.  
  52. void frac::norm()
  53. {
  54.     unsigned long long g = gcd(d,q);
  55.     if (g != 1) { d /= g; q /= g; }
  56. }
  57.  
  58.  
  59. frac operator +(const frac&a, const frac&b)
  60. {
  61.     long long dd;
  62.     unsigned long long qq;
  63.     if (a.q == b.q)
  64.     {
  65.         dd = a.d*a.sign + b.d*b.sign;
  66.         qq = a.q;
  67.     }
  68.     else
  69.     {
  70.         qq = lcm(a.q,b.q);
  71.         dd = a.d*a.sign*(qq/a.q) + b.d*b.sign*(qq/b.q);
  72.     }
  73.     return frac(dd,qq);
  74. }
  75.  
  76. frac operator -(const frac&a, const frac&b)
  77. {
  78.     long long dd;
  79.     unsigned long long qq;
  80.     if (a.q == b.q)
  81.     {
  82.         dd = a.d*a.sign - b.d*b.sign;
  83.         qq = a.q;
  84.     }
  85.     else
  86.     {
  87.         qq = lcm(a.q,b.q);
  88.         dd = a.d*a.sign*(qq/a.q) - b.d*b.sign*(qq/b.q);
  89.     }
  90.     return frac(dd,qq);
  91. }
  92.  
  93. frac operator *(const frac&a, const frac&b)
  94. {
  95.     return frac(a.d*a.sign*b.d*b.sign,a.q*b.q);
  96. }
  97.  
  98. frac operator /(const frac&a, const frac&b)
  99. {
  100.     return frac(a.sign*b.sign*a.d*b.q,a.q*b.d);
  101. }
  102.  
  103. bool operator ==(const frac&a, const frac&b)
  104. {
  105.     return a.d==b.d && a.q == b.q && a.sign == b.sign;
  106. }
  107.  
  108. bool operator !=(const frac&a, const frac&b)
  109. {
  110.     return !(a==b);
  111. }
  112.  
  113. frac::operator std::string() const
  114. {
  115.     std::string s = (sign > 0) ? "" : "-";
  116.     s = s + std::to_string(d) + "/" + std::to_string(q);
  117.     return s;
  118. }
  119.  
  120.  
  121. using namespace std;
  122.  
  123.  
  124. int main(int argc, const char * argv[])
  125. {
  126.     int n;
  127.     cin >> n;
  128.     frac f(0);
  129.     for(int i = 1; i <= n; ++i)
  130.     {
  131.         frac t(i-1,i*(i+1));
  132.         f = f + t;
  133.     }
  134.     cout << string(f) << endl;
  135. }
  136.  
  137.  
Success #stdin #stdout 0s 5652KB
comments (?)
stdin 
45
stdout 
3281281745920812427/1345655451257488800
https://ideone.com/eMVr8d
language:
C++14 (gcc 8.3)
created:
4 years ago
visibility:
public

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