# Class 14: Repetition with Recursion

Reading: Repetition with Recursion. Back to CGI Scripting, Continued. On to Recursion with Lists.

Held Wednesday, February 14, 2001

Summary

Today we begin to consider one of the most powerful tools in Scheme, recursion. Recursion allows you to repeat operations.

Notes

• Are there questions on homework 2?
• Happy valentines day!
• We'll spend a few days on recursion, so don't worry if you don't get it all today.

Overview

• Repetition
• Recursion
• Recursion in Scheme
• Examples: Sum

## 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 almost all of these things, except for repetition.
• Examples of repetition from baking:
• Stir the mix 50 times
• 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?

## Recursion

• In Scheme, the most common mechanism for repetition is recursion.
• To do something that involves repeated actions, you
• Do one action
• Repeat the rest
• 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 its 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

• Here's a typical recursive procedure:
```(define proc
(lambda (val)
(if (base-case-test)
(base-case val)
(combine (partof val)
(proc (update 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 (onestep (car val))
(proc (cdr val))))))
```
• For example, consider `sum` (see the reading).

## History

Friday, 12 January 2001

• Created generic outline format for class.

Wednesday, 14 February 2001

• Filled in the details. All new!

Back to CGI Scripting, Continued. On to Recursion with Lists.

Disclaimer: I usually create these pages on the fly. This means that they are rarely proofread and may contain bad grammar and incorrect details. It also means that I may update them regularly (see the history for more details). Feel free to contact me with any suggestions for changes.

This page was generated by Siteweaver on Wed May 5 12:14:53 2004.
This page may be found at `http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2001S/outline.14.html`.