#pragma once

#include <iostream>
#include <string>

class Rational;

  ///////////////////////////
 // Function declarations //
///////////////////////////

// Calculate n + p.
Rational operator+( int const n, Rational const &p );

// Calculate n - p.
Rational operator-( int const n, Rational const &p );

// Calculate n*p.
Rational operator*( int const n, Rational const &p );

// Calculate n/p.
Rational operator/( int const n, Rational const &p );

// Determine whether n == p.
bool operator==( int const n, Rational const &p );

// Determine whether n != p.
bool operator!=( int const n, Rational const &p );

// Determine whether n < p.
bool operator<( int const n, Rational const &p );

// Determine whether n <= p.
bool operator<=( int const n, Rational const &p );

// Determine whether n >= p.
bool operator>=( int const n, Rational const &p );

// Determine whether n > p.
bool operator>( int const n, Rational const &p );

// Insert p into an output stream.
std::ostream &operator<<( std::ostream &out,
                          Rational const &p );

  //////////////////////
 // Class definition //
///////////////////////

class Rational {
  public:

    // NEW: Construct a rational number and put it into
    // normal form.
    Rational( int const numerator = 0,
              int const denominator = 1 );

    // NEW: Return the numerator.
    int numer() const;

    // NEW: Return the denominator.
    int denom() const;

    // Calculate this + q.
    Rational operator+( Rational const &q ) const;

    // Calculate this + n.
    Rational operator+( int const n ) const;

    // Calculate this - q.
    Rational operator-( Rational const &q ) const;

    // Calculate this - n.
    Rational operator-( int const n ) const;

    // Calculate this*q.
    Rational operator*( Rational const &q ) const;

    // Calculate this*n.
    Rational operator*( int const n ) const;

    // Calculate this/q.
    Rational operator/( Rational const &q ) const;

    // Calculate this/n.
    Rational operator/( int const n ) const;

    // Return this rational number unchanged.
    Rational operator+() const;

    // Return the additive inverse of this rational number.
    Rational operator-() const;

    // Determine whether this == q.
    bool operator==( Rational const &q ) const;

    // Determine whether this == n.
    bool operator==( int const n ) const;

    // Determine whether this != q.
    bool operator!=( Rational const &q ) const;

    // Determine whether this != n.
    bool operator!=( int const n ) const;

    // Determine whether this < q.
    bool operator<( Rational const &q ) const;

    // Determine whether this < n.
    bool operator<( int const n ) const;

    // Determine whether this <= q.
    bool operator<=( Rational const &q ) const;

    // Determine whether this <= n.
    bool operator<=( int const n ) const;

    // Determine whether this >= q.
    bool operator>=( Rational const &q ) const;

    // Determine whether this >= n.
    bool operator>=( int const n ) const;

    // Determine whether this > q.
    bool operator>( Rational const &q ) const;

    // Determine whether this > n.
    bool operator>( int const n ) const;

    // Return the multiplicative inverse.
    Rational inverse() const;

    // Return the absolute value.
    Rational abs() const;

    // Return this rational number as a double.
    double real() const;

    // Return a string representation.
    std::string to_string() const;

  private:

    // NEW: The numerator and denominator are private so
    // users cannot place the object into an invalid or
    // non-normal form.
    //  - Because the user now uses numer() and denom(),
    //    these can be given clearer identifiers.
    int numerator_;
    int denominator_;

    // NEW: Calculate the greatest common divisor of m and n.
    //
    // This is static because calculating a GCD does not
    // require a particular Rational object.
    static int gcd( int m, int n );
};