Note: Due to time constraints, "Collections" has been dropped from our list of topics and Recursion is now the topic of Honors Assignment 4 rather than Honors Assignment 5. There will be no honors assignments 5 or 6.

As discussed in class, recursion is an elegant and powerful algorithm design pattern that matches well with many types of structured information, such as mathematical equations and hierarchical directories of computer files. However, recursion can also be terribly inefficient, as exemplified by the naive Fibonacci function shown in class. In some cases, an iterative approach to the same problem can be much more efficient than a recursive approach, even if the iterative approach does not match as nicely with the concept underlying the structured information.

This assignment explores an example of this design trade-off between recursion and iteration.

Consider again the naive Fibonacci function we covered in class, as well as the two iterative Fibonacci functions we covered (one that stores the values in an array and one that stores values in two temporary variables). Write a paper comparing these three functions. In your paper, be sure to compare the following:

• The maximum amount of memory required as a function of the parameter n. (For this, you may make the simplifying assumption that each primitive data type occupies a single word of memory, regardless of whether it is an int, instruction pointer, etc.)
• The number of times each Fibonacci number less than n needs to be calculated in order to calculate n.
• The time it takes for the function to run as a function of the parameter n. (For this, you may make the simplifying assumptions that each assignment statement and each basic arithmetic operation such as addition, subtraction, and comparison takes one time unit while memory allocation takes five.)

You may cover these points in any order that clearly conveys the information required.

Your comparison paper should be approximately three to five pages in length (roughly 80 characters per line, 50 lines per page). Note that this is a guideline range. Values somewhat outside this range are acceptable. However, if you go much over five pages, I may take off points for being excessively verbose. This page range does not include figures used in your explanations, which are encouraged and may take up any amount of space.

Turn in an electronic copy of this document as a PDF file by submitting it to the appropriate droxbox in D2L and a paper copy of this document at or prior to the start of the class period on the due date.