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  1. #include <iostream>
  2. #include <stdexcept>
  3. #include <sstream>
  4.  
  5. struct IComparable {
  6. 	virtual bool Equal(const IComparable&) const = 0;
  7. };
  8.  
  9. template <typename T>
  10. T gcd (const T& m, const T& n) {
  11.    return n == 0 ? m : gcd (n, m % n);
  12. }
  13.  
  14. class Frac : public IComparable {
  15.   int p, q;
  16.  
  17.   void reduce () {
  18.      int d = gcd (p,q);
  19.      p /= d;
  20.      q /= d;
  21.      if (q < 0) {
  22.        q = -q;
  23.        p = -p;
  24.      }
  25.   }
  26.  
  27. public:
  28.   Frac (int p=0,int q=1) : p(p), q(q) { 
  29.   	if (q == 0) throw std::invalid_argument("Делитель равен 0");
  30.   	reduce ();
  31.   }
  32.  
  33.   std::string ToString() const { 
  34.   	std::stringstream s;
  35.   	if (q!=1) s << '(';
  36.   	if (p>q && p%q)
  37.   	  s << p/q << ' ' << p%q;
  38.   	else
  39.   	  s << p;
  40.   	if (q!=1) s << '/' << q << ')';
  41.   	return s.str();
  42.   }
  43.  
  44.   bool operator==(const Frac& other) const {
  45.   	return p == other.p && q == other.q;
  46.   }
  47.  
  48.   bool operator!=(const Frac& other) const {
  49.   	return !(*this == other);
  50.   }
  51.  
  52.   bool Equal(const IComparable& other) const {
  53.   	const Frac* o = dynamic_cast<const Frac*>(&other);
  54.   	return o ? *o == *this : false;
  55.   }
  56.  
  57.   explicit operator double() const { return double(p)/q; }
  58.  
  59.   Frac operator ~() const { return Frac(q,p); }
  60.   Frac operator -() const { return Frac(-p,q); }
  61.  
  62.   Frac& operator +=(const Frac& other) { 
  63.   	p = p*other.q + other.p*q;
  64.   	q *= other.q;
  65.   	reduce();
  66.   	return *this;
  67.   }
  68.   Frac& operator -=(const Frac& other) { 
  69.   	return *this += -other;
  70.   }
  71.   Frac& operator *=(const Frac& other) { 
  72.   	p *= other.p;
  73.   	q *= other.q;
  74.   	reduce();
  75.   	return *this;
  76.   }
  77.   Frac& operator /=(const Frac& other) { 
  78.   	return *this *= ~other;
  79.   }
  80. };
  81.  
  82. Frac operator+(const Frac& lhs, const Frac& rhs) { return Frac (lhs) += rhs; }
  83. Frac operator-(const Frac& lhs, const Frac& rhs) { return Frac (lhs) -= rhs; }
  84. Frac operator*(const Frac& lhs, const Frac& rhs) { return Frac (lhs) *= rhs; }
  85. Frac operator/(const Frac& lhs, const Frac& rhs) { return Frac (lhs) /= rhs; }
  86.  
  87. Frac polynomial (Frac coef[], size_t n, const Frac& x) {
  88.   if (n==0) return 0;
  89.   Frac result=coef[n-1];
  90.   for (size_t i=n-2; i < n; --i) {
  91.   	result *= x;
  92.   	result += coef[i];
  93.   }
  94.   return result;
  95. }
  96.  
  97. std::string PolynomialToString (Frac poly[], size_t n) {
  98.   std::stringstream s;
  99.   for (size_t i=n-1; i < n; --i) {
  100.   	if (poly[i] != 0) {
  101.   	  if (poly[i] != 1 || i == 0) {
  102.   	  	s << poly[i].ToString();
  103.   	  	if (i > 0)
  104.   	  	  s << '*';
  105.   	  }
  106.       if (i > 0) {
  107.         s << 'x';
  108.         if (i > 1)
  109.           s << "^" << i;
  110.         s << "+";
  111.       }
  112.   	}
  113.   }
  114.   return s.str();
  115. }
  116.  
  117. int main () {
  118.  
  119.   Frac poly[] = { Frac(3,2), Frac(1,-3), 0, -Frac (2,7) };
  120.   const size_t n = sizeof poly / sizeof poly[0];
  121.  
  122.   Frac x(2,8); 
  123.  
  124.   Frac result = polynomial (poly, n, x);
  125.  
  126.   std::cout << PolynomialToString (poly, n) << '=' << result.ToString();
  127.   std::cout << '=' << static_cast<double>(result);
  128.   std::cout << " при x=" << x.ToString();
  129.  
  130.   std::cout << "\n" << (Frac(2,3)/Frac(2,3)).ToString();
  131. }
Success #stdin #stdout 0s 3440KB
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(-2/7)*x^3+(-1/3)*x+(1 1/2)=(1 277/672)=1.4122 при x=(1/4)
1
https://ideone.com/OHZ2ph
language:
C++14 (gcc 8.3)
created:
11 years ago
visibility:
public

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