Contents:

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

Topic: Recursion
Related Reading: Ch. 2.5.1 and 4.1
Due: Monday, 31 January 2005, 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.

• Reinforcement Exercise R-4.6 of the text.

1. (10 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!

2. (10 points)

   Give a C++ implementation of a recursive algorithm for finding the maximum element in an array A of n elements? For the sake of outward appearance, you must support a routine with signature as follows:

   int max(int A[], int n)

   though certainly you may choose to define an additional routine if you wish.

   Note: You do not necessarily need to type/execute this code. Doing it on paper is fine. But we ask that you use C++ in describing your answer for the sake of precision.

3. (2 points)

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