Multiple Choices

1. What is the simplest definition of recursion?

   • A method is recursive if it does not take arguments.
   • A property is recursive if it has a backing field.
   • A method is recursive if it calls itself.
   • A method is recursive if it calls a constructor.
   • A class is recursive if it inherits from another class.

2. Consider the following code:

   void Test(int n)
       {
       if (n != 0){
           Console.Write($"{n} ");
           Test(n - 1);
           }
       }
   Test(3);

   What will it display?

   • Nothing
   • n
   • 3 2 1
   • 3 2 1 0
   • 3 2 1 0 -1 -2 -3 -4 -5 … until the program crashes.
   • 2 1 0 -1 -2 -3 -4 -5 … until the program crashes.
   • 1 2 3
   • 0 1 2 3

3. Consider the following code:

   void Test(int n)
       {
           Console.Write($"{n} ");
           Test(n - 1);
       }
   Test(3);

   What will it display?

   • Nothing
   • n
   • 3 2 1
   • 3 2 1 0
   • 3 2 1 0 -1 -2 -3 -4 -5 … until the program crashes.
   • 2 1 0 -1 -2 -3 -4 -5 … until the program crashes.
   • 1 2 3
   • 0 1 2 3

4. Consider the following code:

   void Test(int n)
       {
           Test(n - 1);
           Console.Write($"{n} ");
       }
   Test(3);

   What will it display?

   • Nothing
   • n
   • 3 2 1
   • 3 2 1 0
   • 3 2 1 0 -1 -2 -3 -4 -5 … until the program crashes.
   • 2 1 0 -1 -2 -3 -4 -5 … until the program crashes.
   • 1 2 3
   • 0 1 2 3

Exercises

1. What would the following code display?

   int Myst1(int n)
   {
       if (n != 0)
       {
           return n + Myst1(n - 1);
       }
       else
       {
           return n;
       }
   }
    
   Console.WriteLine(Myst1(4));

   Solution

   10

2. What would the following code display?

   void Myst2(int n)
   {
       if (n == 0) { Console.WriteLine("Done"); }
       else if (n < 0)
       {
           Console.Write($"{n} ");
           Myst2(-n);
       }
       else
       {
           Console.Write($"{n} ");
           Myst2(-(n - 1));
       }
   }
   Myst2(3);

   Solution

   3 -2 2 -1 1 Done

3. What would the following code display?

   void Myst3(int len)
   {
       MystH(0, 1, 1, len);
   }
   void MystH(int axP, int bxP, int counter, int len)
   {
       if (counter <= len)
       {
           Console.Write($"{axP} ");
           MystH(bxP, axP + bxP, counter + 1, len);
       }
   }
   Myst3(6);

   Solution

   0 1 1 2 3 5

   Those are the first 6 digits of the Fibonacci sequence.

4. Write a recursive method that takes an int as argument, generates a random int between 0 and this argument, displays it and calls itself with that number. The method should stop when the int generated is 0.

   Solution

    void RandomTo0(int n)
    {
        Random seed = new Random();
        int randomNumber = seed.Next(0, n);
        if (randomNumber == 0) { Console.WriteLine("Done"); }
        else
        {
            Console.WriteLine($"Number: {randomNumber}");
            RandomTo0(randomNumber);
        }
    }

5. Write a recursive method that takes a string as argument and returns true if it is a palindrome. Your method should return true on input "civic", "noon", "radar" and "" (empty string), and false on input "test" and "not a palindrome".

   Hint

   Use Length - 1 to access the last index of the string, and the Substring method to create a string without the first and last characters.

   Solution

    bool Palindrome(string s)
    {
        if (s.Length <= 1) return true;
        else
        {
            if (s[0] == s[s.Length - 1]) return Palindrome(s.Substring(1, s.Length - 2));
            else return false;
        }
    }
    
    List<string> palindrome_test = new List<string> { "radar", "civic", "noon", "", "test", "not a palindrome"};
    foreach (string test in palindrome_test)
    {
        Console.WriteLine(test + " is a palindrome: " + Palindrome(test));
    }

6. Write a recursive method that takes an int as argument and returns the number of even digits in it. For example, on input 631, the method should return 1 since only 6 is even.

   Hint

   The % 10 operation gives the last digit of a number (631 % 10 gives 1), and the / 10 operation (on integers) removes the last digit from an int (631 / 10 gives 63).

   Solution

    int CountEven(int n)
    {
        if (n == 0) { return 0; }
        else if (n % 10 % 2 == 0) { return 1 + CountEven(n / 10); }
        else { return CountEven(n / 10); }
    }