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#ifndef VECTOR_HH

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#define VECTOR_HH

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#include <iostream>

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#include <cmath>

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/**

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 * A 2D Vector class. Implements standard vector operations.

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 */

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template <typename T>

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class _Vector {

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public:

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    T x;

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    T y;

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    /**

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     * Default constructor.

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     */

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    _Vector() : x(0), y(0) {}

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    /**

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     * Constuctor.

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     *

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     * @param x Initial x-coordinate

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     * @param y Initial y-coordinate

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     */

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    _Vector(T x, T y) : x(x), y(y) {}

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    /**

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     * Copy constructor.

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     *

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     * @param v Vector to be copied.

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     */

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    _Vector(const _Vector &v) : x(v.x), y(v.y) {}

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    // Operator declarations

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    void operator=(const _Vector &v) {

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        this->x = v.x;

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        this->y = v.y;

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    }

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    _Vector operator+(const _Vector &v) const {

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        return _Vector(this->x+v.x, this->y+v.y);

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    }

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    _Vector operator-(const _Vector &v) const {

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        return _Vector(this->x-v.x, this->y-v.y);

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    }

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    _Vector operator*(const T &scalar) const {

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        return _Vector(this->x*scalar, this->y*scalar);

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    }

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    T operator*(const _Vector &v) const {

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        return (this->x*v.x + this->y*v.y);

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    }

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    _Vector operator/(const T &d) const {

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        return _Vector(this->x/d, this->y/d);

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    }

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    void operator+=(const _Vector &v) {

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        *this = *this + v;

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    }

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    void operator-=(const _Vector &v) {

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        *this = *this - v;

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    }

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    void operator*=(const T &scalar) {

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        *this = *this * scalar;

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    }

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    void operator/=(const T &scalar) {

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        *this = *this / scalar;

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    }

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    // Other operations

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    T length() const {

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        return sqrt(sqrLength());

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    }

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    T sqrLength() const {

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        return (this->x * this->x) + (this->y * this->y);

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    }

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    _Vector roundToInt() const {

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        return _Vector((int)(x), (int)(y));

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    }

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};

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// Unary operators

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template<typename T>

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_Vector<T> operator*(const T &scalar, const _Vector<T> v) {

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    return (v * scalar);

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} 

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// Comparison operators

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template<typename T>

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bool operator==(const _Vector<T> &v1, const _Vector<T> &v2) {

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    return ((v1.x == v2.x) && (v1.y == v2.y));

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}

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template<typename T>

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bool operator!=(const _Vector<T> &v1, const _Vector<T> &v2) {

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    return !(v1 == v2);

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}

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// Output operator

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template<typename T>

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std::ostream& operator<<(std::ostream &s, const _Vector<T> &v) {

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    return s<<"("<<v.x<<", "<<v.y<<")";

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}

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// Standard vector

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typedef _Vector<float> Vector;

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#endif