Week 6: Exercises

1. Exceptions

What will this program print?

class MyException : Exception { }

static class Test {
  static int foo(int i) {
    try {
      WriteLine("a " + i);
      if (i == 0)
        throw new MyException();
      WriteLine("b " + i);
      return foo(i - 1);
    } catch (MyException e) {
      WriteLine("c " + i);
      if (i < 2)
        throw e;
      return i;
    } finally {
      WriteLine("d " + i);
    }
  }  
  
  static void Main(string[] args) {
    WriteLine("e " + foo(3));
  }
}

2. Polynomials

Design and implement a C# class Polynomial representing a polynomial of a single variable. Your class should include the following:

• a constructor that takes a variable number of arguments of type double, yielding a polynomial with those coefficients. For example,

      new Polynomial(1.0, 4.0, 5.0)

  should yield the polynomial x² + 4x + 5.

• an overloaded operator + that adds two polynomials

• an overloaded operator - that subtracts two polynomials

• an overloaded operator * that multiplies two polynomials, or a polynomial and a scalar

• a method that evaluates a polynomial for a given value of x

• a method that returns the first derivative of a polynomial

• a method that finds an approximate zero of a polynomial, i.e. a value x for which the polynomial evaluates to zero

• a ToString() method that yields a string such as "x^2 + 4x + 5"

• a static method Parse() that parses a string such as "x^2 + 4x + 5", yielding a polynomial. Throw a ParseException if you cannot parse the string.