poly.cpp

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#include <algorithm>
#include <functional>
#include <iostream>
#include <vector>
using namespace std;

template <typename T>
class Polynomial {
public:
  typedef T value_type, &reference;
  typedef const T &const_reference, &param_type;
  typedef std::vector<T> coef_type;
  typedef typename coef_type::size_type size_type;
  
  Polynomial (param_type x = T()) : myCoef(1, x) { }
  Polynomial (size_type n, param_type x = T()) : myCoef(n, x) { }

  template <typename It>
  Polynomial (It first, It last) : myCoef(first, last) { }

  size_type degree () const { return myCoef.size() - 1; }
  void degree (size_type n, param_type x = T()) { myCoef.resize(n + 1, x); }

  T &operator[] (size_type i) { return myCoef[i]; }
  T operator[] (size_type i) const { return myCoef[i]; }

  Polynomial &operator+= (const Polynomial &p) {
    size_type size = p.myCoef.size();
    if (myCoef.size() < size) myCoef.resize(size);
    std::transform(myCoef.begin(),
		   myCoef.begin() + std::min(degree() + 1, p.degree() + 1),
		   p.myCoef.begin(), myCoef.begin(),
		   std::plus<T>());
    normalize();
    return *this;
  }

  Polynomial &operator-= (const Polynomial &p) {
    size_type size = p.myCoef.size();
    if (myCoef.size() < size) myCoef.resize(size);
    std::transform(myCoef.begin(),
		   myCoef.begin() + std::min(degree() + 1, p.degree() + 1),
		   p.myCoef.begin(), myCoef.begin(),
		   std::minus<T>());
    normalize();
    return *this;
  }

  Polynomial &operator*= (const Polynomial &p) {
    coef_type coef(myCoef.size() + p.myCoef.size());

    for (size_type i = 0, j = myCoef.size(); i < j; ++i) {
      for (size_type m = 0, n = p.myCoef.size(); m < n; ++m) {
	coef[i + m] += myCoef[i] * p.myCoef[m];
      }
    }

    coef.swap(myCoef);
    normalize();
    return *this;
  }

  void swap (Polynomial &p) {
    myCoef.swap(p.myCoef);
  }

  T operator() (const T &x) const {
    T result = 0;
    for (size_type i = myCoef.size(); i > 0; --i) {
      result = result * x + myCoef[i - 1];
    }
    return result;
  }

private:
  std::vector<T> myCoef;

  void normalize () {
    myCoef.erase(std::find_if(myCoef.rbegin(),
			      myCoef.rend(),
			      std::bind2nd(std::not_equal_to<T>(), T())).base(),
		 myCoef.end());
  }
};

template <typename T> Polynomial<T> operator+ (const Polynomial<T> &p, const Polynomial<T> &q) {
  return Polynomial<T>(p) += q;
}

template <typename T> Polynomial<T> operator+ (const Polynomial<T> &p, T q) {
  return Polynomial<T>(p) += q;
}

template <typename T> Polynomial<T> operator+ (T p, const Polynomial<T> &q) {
  return Polynomial<T>(p) += q;
}

template <typename T> Polynomial<T> operator- (const Polynomial<T> &p, const Polynomial<T> &q) {
  return Polynomial<T>(p) -= q;
}

template <typename T> Polynomial<T> operator- (const Polynomial<T> &p, T q) {
  return Polynomial<T>(p) -= q;
}

template <typename T> Polynomial<T> operator- (T p, const Polynomial<T> &q) {
  return Polynomial<T>(p) -= q;
}

template <typename T> Polynomial<T> operator* (const Polynomial<T> &p, const Polynomial<T> &q) {
  return Polynomial<T>(p) *= q;
}

template <typename T> Polynomial<T> operator* (const Polynomial<T> &p, T q) {
  return Polynomial<T>(p) *= q;
}

template <typename T> Polynomial<T> operator* (T p, const Polynomial<T> &q) {
  return Polynomial<T>(p) *= q;
}

template <typename T>
std::ostream &
operator<< (std::ostream &os, const Polynomial<T> &p) {
  os << '(';
  bool printed = false;
  
  for (typename Polynomial<T>::size_type ip1 = p.degree() + 1; ip1 > 0; --ip1) {
    typename Polynomial<T>::size_type i = ip1 - 1;

    if (T coeff = p[i]) {
      if (coeff < 0) {
	os << " - ";
	coeff = -coeff;
      }

      else if (printed) {
	os << " + ";
      }

      if (coeff != 1) os << coeff;
      if (coeff != 0 && i > 0) os << 'x';
      if (i > 1) os << '^' << i;
      printed = true;
    }
  }

  if (!printed) os << '0';
  return os << ')';
}

template <typename T, int N> int n_elements (T (&) [N]) { return N; }

int main () {
  {
    int parray[] = { 0, 1, 2, 3 };
    Polynomial<int> p(parray, parray + n_elements(parray));

    cout << (p) << endl;
    cout << (5 + p) << endl;
    cout << (p + 5) << endl;
    cout << (5 + p + 5) << endl;
    cout << (p - p) << endl;
    cout << (p(6)) << endl;
  }

  {
    int parray[] = { 2, 2 };
    Polynomial<int> p(parray, parray + n_elements(parray));
    cout << (p) << endl;
    cout << (p * p) << endl;
  }
}