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import java.util.Hashtable;
 
public class Poly implements Cloneable {
 
    //the first integer is the degree, the second integer is the coefficient
    Hashtable<Integer, Integer> poly = new Hashtable<Integer, Integer>();
     
    @Override
    //print this as a polynomial
    public String toString()
    {
        String str = "";
        int degree = 0;
        for (int i = 0; i < this.poly.size(); i++)
        {
            //find next degree
            while (! this.poly.containsKey(degree))
            {
                degree++;
            }
            //construct output
            str += this.poly.get(degree) + " x^" + degree;
            //append + if needed
            if (i != (this.poly.size() - 1))
            {
                str += " + ";
            }
            //increment degree
            degree++;
        }
        return str;
    }
     
    //constructor for 0*x^0
    public Poly()
    {
        //initialise polynomial
        this.poly.clear();
        this.poly.put(0, 0);
    }
     
    //constructor for c*x^n
    public Poly(int c, int n) throws Exception
    {
        //throw less than 0 exception
        if (n<0)
        {
            throw new Exception("n must be greater or equal to 0");
        }
        //initialise polynomial
        this.poly.clear();
        this.poly.put(n, c);
    }
     
    //return the degree of the polynomial
    public int degree()
    {
        int degree = 0;
        for (int i = 0; i < this.poly.size(); i++)
        {
            //find next degree
            while (! this.poly.containsKey(degree))
            {
                degree++;
            }
            //increment degree if needed
            if (i != (this.poly.size() - 1))
            {
                degree++;
            }
        }
        return degree;
    }
     
    //return coefficient with exponent n
    public int coeff(int n) throws Exception
    {
        //throw less than 0 exception
        if (n<0)
        {
            throw new Exception("n must be greater or equal to 0");
        }
        //return coefficient
        if (this.poly.containsKey(n))
        {
            return this.poly.get(n);
        }
        //return 0 otherwise
        else
        {
            return 0;
        }
    }
     
    //sum of this and a polynomial
    public Poly add(Poly q) throws Exception
    {
        Poly sum = new Poly();
        sum.poly.clear();
        //throw null exception
        if (q.poly.isEmpty())
        {
            throw new Exception("q must not be null");
        }
        //get degree of polynomials
        int qdeg = q.degree();
        int thisdeg = this.degree();
        //find highest degree
        int maxdeg = qdeg;
        if (maxdeg < thisdeg) {maxdeg = thisdeg;}
        //add polynomials
        for (int i = 0; i < (maxdeg + 1); i++)
        {
            //addition will take place iff q has a coef with such degree
            if (q.poly.containsKey(i))
            {
                //case where this and q have coef with same degree
                if (this.poly.containsKey(i))
                {
                    int s = this.poly.get(i) + q.poly.get(i);
                    sum.poly.put(i, s);
                }
                //case where this doesn't have a coef q does
                else
                {
                    sum.poly.put(i, q.poly.get(i));
                }
            }
            //case where q doesn't have a coef this does
            if (this.poly.containsKey(i))
            {
                sum.poly.put(i, this.poly.get(i));
            }
        }
        return sum;
    }
     
    //difference of this and a polynomial
    public Poly sub(Poly q) throws Exception
    {
        Poly diff = new Poly();
        diff.poly.clear();
        //throw null exception
        if (q.poly.isEmpty())
        {
            throw new Exception("q must not be null");
        }
        //get degree of polynomials
        int qdeg = q.degree();
        int thisdeg = this.degree();
        //find highest degree
        int maxdeg = qdeg;
        if (maxdeg < thisdeg) {maxdeg = thisdeg;}
        //sub polynomials
        for (int i = 0; i < (maxdeg + 1); i++)
        {
            //addition will take place iff q has a coef with such degree
            if (q.poly.containsKey(i))
            {
                //case where this and q have coef with same degree
                if (this.poly.containsKey(i))
                {
                    int s = this.poly.get(i) - q.poly.get(i);
                    diff.poly.put(i, s);
                }
                //case where this doesn't have a coef q does
                else
                {
                    diff.poly.put(i, q.poly.get(i));
                }
            }
            //case where q doesn't have a coef this does
            else if (this.poly.containsKey(i))
            {
                diff.poly.put(i, this.poly.get(i));
            }
        }
        return diff;
    }
     
    public boolean equals(Poly q)
    {
        //find degree of polynomials
        int qdeg = q.degree();
        int thisdeg = this.degree();
        //polynomials are not equal if they don't have the same degree
        if (qdeg != thisdeg)
        {
            return false;
        }
        //compare polynomials
        else
        {
            for (int i = 0; i < (thisdeg + 1); i++)
            {
                //this has a coef
                if (this.poly.containsKey(i))
                {
                    if (! q.poly.containsKey(i))
                    {
                        return false;
                    }
                    else
                    {
                        if (this.poly.get(i) != q.poly.get(i))
                        {
                            return false;
                        }
                    }
                }
                //q has a coef
                if (q.poly.containsKey(i))
                {
                    if (! this.poly.containsKey(i))
                    {
                        return false;
                    }
                    else
                    {
                        if (this.poly.get(i) != q.poly.get(i))
                        {
                            return false;
                        }
                    }
                }
                //skip if no coef
            }
        }
        return true;
    }
     
    @Override
    public Poly clone()
    {
        Poly clone;
        //try to clone
        try {
            clone = (Poly) super.clone();
        } catch(CloneNotSupportedException e) {
            System.out.println("Cannot clone this");
            return null;
        }
        return clone;
    }
     
    public static void main(String[] args)
    {
    //start of code execution. You can have some test code in
    //here that you may have written to test your class.
        try {
        Poly p1 = new Poly(); //0 x^0
        Poly p2 = new Poly(2, 4); //2 x^4
        Poly p3 = p1.add(p2); //0 x^0 + 2 x^4
        Poly p4 = new Poly(-1, 4); //-1 x^4
        Poly p5 = p2.sub(p4); //3 x^4
        System.out.println(p1.toString());
        System.out.println(p2.toString());
        System.out.println(p3.toString());
        System.out.println(p4.toString());
        System.out.println(p5.toString());
        } catch (Exception e) {
            System.out.println("invalid action");
        }
    }
 
}