Held: Wednesday, 8 October 2014

Back to Outline 23 - Revisiting Lists. On to Outline 25 - Recursion Basics, Continued.

Summary

We begin our exploration of recursion, the most general form of repetition available in Scheme. You can use recursion to both build and iterate over different kinds of values.

Related Pages

• Reading: Recursion Basics
• Lab: Recursion Basics
• EBoard 24 (Source 24) (HTML 24)

Overview

• Some challenges.
• The idea of recursion.
• Some sample recursive procedures.
• Expressing recursion in Scheme.

Administrivia

• Continue partners
• Office hours
  • Normal (MThF 1:45-3:15; walking 1:15-1:45)
  • In the Grill 8:00-9:30 am Fri
  • In my office 8:00-9:30 am Tue and Thu
• Evening review sessions tonight at 8pm and Thursday at 8pm
• Daytime review session Thursday at 10:00 a.m.

Topics for Friday's Quiz

My quiz policies will continue through this week. You may bring a page of notes. You will not have a time limit, although I will encourage you to try to finish in ten minutes.

• Lists, particularly cons, car, cdr, and null?
  • We might ask you to write instructions to build a list.
  • We might give you some instructions and ask yo to interpret them.
  • We might challenge you to think about lists and non-lists (issues raised by the now-renamed one-two, won-too, and want-to)
• image-compute!
  • We might ask you to interpret some code. ("Sketch the image that this code creates ...")
  • We might ask you to write instructions to create a particular image (given verbally or pictorially).
  • We might do a hybrid ("Fill in the blanks to achieve ...")
• Local bindings with let and let*
  • The relationship(s) between the two
  • Ordering of let and lambda
• Any previous topics are also fair game, although they will probably be incorporated in the previous kinds of problems.
  • We might ask for an anonymous procedure
  • We might have problems that require conditionals
  • We might combine the earlier list procedures with the newer ones
  • ...

Upcoming Work

• No writeup today! (There will be a writeup on this lab, but it will be assigned Friday.)
• Exam 2
• Reading for Friday:
  • Reread Recursion Basics

Cool Things Coming to Campus

• Two versions of Anna Christie!
• Live Streaming of Verdi's Macbeth, Saturday at 11:55 a.m.
• Pop-up Exhibit, Thursday October 9th, all day in BCA 132

Extra Credit Opportunities

Academic

• Grinnell Prize events this week (particularly events related to the prize winners whose project involves Web tools)
• Artist Talk, Wednesday October 8th at 4:15pm in BCA 152 Rewriting the Application Programming Interface (API) for Art Making
• BCC Faculty Chat, Tuesday, October 14, 7pm

Peer Support

• Football (Saturday at 1pm)
• Swimming October 18: Alumni Weekend
• Karan's radio show 11pm Thursday nights on KDIC
• Evan's radio show 5pm Friday nights on KDIC
• Donna's radio show Sunday midnight on KDIC
• The College's version of Anna Christie, Oct. 9-12 (SB plays Marthy)
• Men's Tennis (???)
• Women's Tennis (???)

Misc

• Fill in the GC External Web Survey at http://bit.ly/1ncPO5V

Repetition

• You may recall that when we first considered algorithms we identified a number of key aspects of algortihms:
  • variables: the ability to name things;
  • conditions: the ability to choose between things;
  • procedures: the ability to name (and parameterize) collections of steps;
  • repetition: the ability to do something multiple times;
  • input and output: the ability to get and report values.
• We've already seen how to do all of these things.
• Examples of repetition from baking:
  • Stir the mix 50 times
  • Knead the bread dough until it feels like your earlobe
  • Bake until golden-brown.
• Examples of repetition from mathematics:
  • Sum these values
  • Find the smallest of these values
• Examples of repetition from everyday life:
  • Naively find a name in the phone book
  • Do I have a CD by Van Morrison?
• We know a few ways to repeat actions:
  • Using lists: map
  • Using images: image-variant, image-transform!, and image-compute-pixels!.
• Today we begin to consider more general forms of repetition.

Some Challenges

• You may recall that one of the issues in writing algorithms is that we are often limited to a few basic operations. Let's explore how we might accomplish some more challenging tasks with only a few basic operations and a powerful helper function.
• We will develop some functions to answer questions about lists under the following assumptions:
  • You get a collection of values
  • You may assess only the first item in the collection (assuming there is such an item)
  • You may pass the rest of the collection to the person next to you and ask one question of that person
  • You have answer to give if there are no items in the collection
• Here are some possibilities
  • Counting the number of values we have
  • Determining whether a collection contains a value
  • Finding the alphabetically first thing in a collection
  • Finding all values in a collection that meet some criteria
  • (Maybe) summing some values
• After I've done a few, I'll have you write a few
• If we do this right, you'll see some interesting patterns

Recursion

• In Scheme, the most common mechanism for repetition is recursion.
• To do something that involves repeated actions, you
  • Do one action, computing a result
  • Do the remaining actions, computing a result
  • Combine the results if necessary.
• For example, to stir your cake mix 50 times, you stir it one time and then stir it 49 more times.
• More generally, to stir a cake mix n times, you stir it one time and then n-1 more times.
• Similarly, to knead dough until it's the right consistency, you knead it a little, check the consistency, and, if it's not the right consistency, knead it until its the right consistency.
• In the case of mathematics, to sum a list we might add the first value to the sum of the remaining values (or add the last value to the sum of the initial values).
• There are a few key aspects to recursive design:
  • You need to know when you're done (and what to do when you're done).
    This aspect of recursive design is called the base case.
  • You need to know what to do when you're not done. Here, you should do a little, try again, and then perhaps combine the results. This aspect of recursive design is called the recursive case.
  • You need to be sure that you're getting closer to the base case (otherwise you'll never stop).

Recursion in Scheme

Remember that I tend to think in abstractions first. But we'll look at some concrete forms, too.

Here's the form of a typical recursive procedure:

(define PROC
  (lambda (VAL)
    (if (BASE-CASE-TEST)
        (COMPUTE-BASE-CASE VAL)
        (COMBINE (EXTRACT-DATA VAL)
                 (PROC (SIMPLIFY VAL))))))

When the value you're working with is a list and your base case is the null list, the form is somewhat simpler:

(define PROC
  (lambda (LST)
    (if (null? LST)
        NULL-CASE
        (COMBINE (EXTRACT-DATA (car LST))
                 (PROC (cdr LST))))))

Sometimes it's useful to grab the recursive result first, particularly if you're going to use it in multiple ways.

(define PROC
  (lambda (LST)
    (if (null? LST)
        NULL-CASE
        (let ((recursive-result (PROC (cdr LST))))
          (if (TEST)
              (COMBINE-1 (EXTRACT-DATA-1 (car LST)) recursive-result)
              (COMBINE-2 (EXTRACT_DATA-2 (car LST)) recursive-result))))))

Lab

• Start the lab on recursion
• We will continue this lab in the next class session.
• Be prepared to reflect and to ask questions.