Held: Tuesday, 29 October 2013

Back to Outline 30 - Naming Local Procedures. On to Outline 32 - Geometric Art Through Numeric Recursion.

Summary

We visit a slightly different kind of recursion, numeric recursion. In this technique, we once again have procedures call themselves. However, the parameter that we "simplify" at every step is a number, rather than a list.

Related Pages

• Reading: Numeric Recursion
• Lab: Numeric Recursion
• EBoard (Raw) (HTML) (PDF)

Overview

• Recursion, generalized.
• Numeric recursion.
• Lab.

Administrivia

• Our grader cannot manage grading and classwork. I'm working on a solution.
  • Of course, it's not clear that I can manage grading and class prep either.
• Reminder: HW 7 is due on Wednesday.
• Reminder: Exam 2 will be distributed tomorrow.
• Upcoming extra credit opportunities:
  • Tuesday, 7pm, Talk on The Hopkins Touch
  • Wednesday, Noon, Science 3821: Learn about study-abroad opportunities in CS in Budapest.
  • Friday, Noon, CS Table; Ambient Belonging
  • Any one Grinnell prize event next week

Patterns of Recursion

While we've seen and written a variety of examples of direct recursion, they typically have the following form:

(define *recursive-proc*
  (lambda (*params*)
    (if (*base-case-test*)
        (*base-case* *params*)
        (*combine* (*partof* *params*)
                   (*recursive-proc* (*simplify* *params*))))))

For lists, the simplification was almost always "take the cdr" and the "part-of" was almost always "take the car".

Recursion with Numbers

• While most of the recursion we've been doing has used lists as the structure to recurse over, you can recurse with many different kinds of values.
• It is fairly common to recurse using numbers.
• The natural base cases for integers are when you hit 0 or when you hit 1.
• The natural simplification step for recursive procedure using numbers calls typically involves subtracting 1 from the argument.
  • Other simplifications, such as dividing in half, are also possible.

Lab

• Do the lab