Class 13: Recursion with Natural Numbers

Held Friday, September 15, 2000

Summary

In recent classes, we've studied recursive procedures in which the argument is a list and the result a list, a number, or a boolean value. We now turn our attention to recursive procedures in which the argument is a number.

Notes

• Today's reading: Recursion with numbers
• Today's lab: Recursion with numbers
• Monday's reading: Preconditions and Postconditions
• Due today: homework 2
  • I was surprised that so few of you took advantage of email and the discussion boards.
  • How long did it take?
• Monday's brown-bag lunch seems interesting. I encourage you to attend.
• This weekend is the science student research poster session. Come and see interesting summer and academic-year research.
• Today is the last day to drop a course. Please talk to me if you plan to drop 151.
• It's probably time to reflect on how the class is going.
  • Are the introductory announcements helpful?
  • Are you feeling comfortable with the pace?
  • What kinds of sessions do you prefer?
  • What can I do to help you get through the material?

Overview

• Basic aspects of recursion
• Recursion on other kinds of values
• Examples
  • Factorial
  • Sum of squares
• Lab: Recursion with numbers

Can we recurse on values other than lists? Certainly. One natural set of values to recurse on is the natural numbers.

• What do you expect are typical base cases?
• What are typical ways of making things smaller?

Some examples: factorial, sum-of-squares.