/* A Polynomial has all its coefficients in an array coeffs */
class Polynomial{
  
  // coeffs[i] is the coefficient of the term x^i
  protected double[] coeffs;
  
  /* This Polynomial has coefficients as specified in the array*/
  public Polynomial(double[] coefficients){
    coeffs = new double[coefficients.length];
    for(int i=0; i<coeffs.length; i++)
      coeffs[i] = coefficients[i];
  }
  
  /* =degree of this Polynomial */
  public int getDegree(){
    int d = coeffs.length-1;
    while((coeffs[d] == 0) && (d > 0))
      d--;
    return d;
  }
  
  /* ={This Polynomial is the same as Polynomial  p}, true or false */
  public boolean equals(Polynomial p){
    if(getDegree() != p.getDegree())
      return false;
    for(int i=0; i<=getDegree(); i++)
      if(coeffs[i] != p.coeffs[i])
        return false;
    return true;
  }
  
  /* = The value of this polynomial evaluated at x */
  public double evaluate(double x) {
    double sum = 0;
    double input = 1;
    for(int k=0; k<coeffs.length; k++) {
      sum += coeffs[k]*input;
      input *= x;
    }
    return sum;
  }

  /* Add this Polynomial to Polynomial p */
  public Polynomial add(Polynomial p){
    int degree = getDegree();
    if(p.getDegree() > degree){
      degree = p.getDegree();
    }
    double[] coefficients = new double[degree];
    for(int i=0; i<getDegree(); i++)
      coefficients[i] += coeffs[i];
    for(int i=0; i<p.getDegree(); i++)
      coefficients[i] += p.coeffs[i];
    return new Polynomial(coefficients);
  }
  
  /* =Polynomial that is the derivative of this Polynomial */
  public Polynomial derivative(){
    double[] coefficients = new double[getDegree()];
    for(int i=0; i<getDegree(); i++){
      coefficients[i] = (i+1)*coefficients[i+1];
    }
    return new Polynomial(coefficients);
  }
}