Contents:

• Overview
• Practice Problems
• Problems to be Submitted
• Extra Credit

Topic: Recursion
Related Reading: Ch. 2.5.1, 4.1, 10.1.1, 10.3
Due: Tuesday, 28 March 2006, 1:10pm

Please make sure you adhere to the policies on academic integrity.

• Reinforcement Exercise R-2.12 of the text.

• Reinforcement Exercise R-4.4 of the text.

1. (6 points)

   Describe a recursive algorithm to compute the product of two positive integers, m and n, using only additions. (thus you should not use the binary * operator). Your code should have a signature:

         int Product(int m, int n);
         

2. (7 points)

   Reinforcement Exercise R-4.6 of the text (page 196).

3. (7 points)

   Ch 2.5.1 describes a recursive procedure drawTicks(int tickLength). For this problem, we are interested in determining the number of lines of output which are generated by a call drawTicks(L) for a given integer L, including all of the recursive calls it generates.

   1. As a function of L, how many lines of output are generated?
      (Hint: You might wish to try out a few small values by hand)

   2. Give a proof of your result!

3. (2 points)

   Creativitiy Exercise C-4.3 (page 197) of the text (though you need not discuss the running time).