Class 17: Recursion with Natural Numbers

Held Monday, February 19, 2001

Summary

Today we consider recursion over a different domain, the natural numbers.

Assignments

• Lab Writeup 1.
• Read Pairs and Pair Structures.

Handouts

• Required format for laboratory writeups.

Notes

• How long are the labs taking you? I've heard some reports that some of you spent about five hours on the recursion lab in addition to the three class periods we spent on the lab.
• Some of you have shown some frustration that Anne and I tend to say "okay, let's reflect on XXX" rather than "just put X here" (and, admittedly, Anne's better at it than I am).
  • There's a reason we don't just give you the answer: If we give you the answer, you're not likely to learn much; if we show you how to solve it, you'll be able to solve similar problems.
  • Remember the philosophy that someone who receives a fish eats for a day; someone who learns to fish eats for a lifetime. (Apologies to vegetarians.)
• Are there questions on homework 3?
• I'm guest-teaching Mr. Walker's CSC153 class this week (at 8am; yech), so I may seem even more harried than normal. Sorry.
• This Thursday at 4:15, a group of my summer research students will be speaking about their research project, which involves changing other people's Web pages. It's some pretty cool stuff, and I hope to see you there.
• For those of you interested in taking a peek at what your colleagues did for homework 2, here's what I know about (if you're not listed, send me your URL).
  • http://www.math.grin.edu/~hodgman/story.html (Amanda and Brad)
  • http://www.cs.grinnell.edu/~pervaiza/storypage.html (Ammar and Muhammad)
  • http://www.math.grinnell.edu/~armahke/cgi-bin/webpage.html (George and Kabenla)
  • http://www.cs.grinnell.edu/~makinen/entryform.html (Laura and Greg)
  • http://www.math.grinnell.edu/~porter/dragon.html (Marie and Audrey)
  • http://www.cs.grinnell.edu/~likarish/ananta/homework2.html (Peter, Ananta, Sammy (Samarth) and Katya)
  • http://www.cs.grinnell.edu/~waymouth/cgistory/index.html (Rob and Aaron)
  • http://www.cs.grinnell.edu/hw2/story.html (Sarah, Anna, and Matt)
  • http//www.math.grin.edu/~walkerxh/adventures.html (Xylina and Patty)
  • http://www.cs.grinnell.edu/~smithg/pizza.html (Tony and Brandon) (Not working at last count)

Overview

• Reflections on recursion
• Introduction to numeric recursion
• Lab

Reflections on List Recursion

Patterns

• Let's try to identify some patterns of recursion over lists.
  • That is, the general structure of kinds of Scheme procedures that work on lists.
• Here's one category of recursion that we did a few times: apply some operation to every element of a list.
• How do we express the general form of that category?
• What other kinds of things do you do to lists?
• What is the general form for those things?

Problems

• What things are likely to be difficult or wrong in one of your recursive procedures?
• I see many people having trouble with the base case. It may help to think about what kind of thing the procedure should return.
• I know that you sometimes write procedures that run forever (I do, too; I wrote one yesterday). Make sure that when you do the recursive call, you're using something closer to the base case.

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 parameter for recursive procedure calls typically involves subtracting 1 from the argument.

Lab

• Do the lab.