Comp 210 Lab 3: Lists

This lab is mainly practice with lists. There are too many examples here to do all during lab. Instead, do some from each group during lab, and the rest on your own. We may revisit some of these examples in next week's lab, also.

Important for all examples:

Index: Definition and Design Recipe Review, Lots of Examples

Definition and Design Recipe Review

First, a quick review of what a list is. A list is a common data structure for keeping track of an arbitrary amount of information. Lists use all three of the basic building blocks we've seen:

Data definition questions
How are lists defined?
What are the constructors, selectors, and predicates?
See the definition and functions.

Now, let's quickly review our latest design recipe. We know our programs should take advantage of the structure of the data. Now that we know about compound (or structured) data, let's use that knowledge in our methodology.

  1. Data definition.
  2. Data examples.
  3. Function's contract, purpose, and header.
  4. Function's example uses.
  5. Function's template.

    The template should remind you how to take advantage of the structure in the data definition.

    Template question
    What are the steps for developing the template?
    See the steps and an example.
  6. Function body.
  7. Function testing.

Lots of examples

There are many more examples here than you can do in lab. Labbies can pick and choose what to present. Students should look over the rest on their own.

Lists of numbers

Series of list-of-numbers exercises
Do at least the first 5 parts in lab:
  1. Make the data definition for list-of-numbers. (Extremely similar to list-of-symbols.)
  2. Make some examples of list-of-numbers.
  3. Make the template for list-of-numbers. Make sure you understand what each step of the design recipe wants.
  4. Develop a program which takes a list-of-numbers and returns the length of the list, i.e., a count of the items in the list. (Of course, also first make some test cases, e.g. How many numbers are in (cons 3 (cons 1 empty))?)
  5. Once your function works, use the stepper, and step through the program on a list of length 2. How many times is your function called (counting both the initial call plus recursive calls)?
  6. Develop a program which takes a list-of-numbers and returns the sum of all the numbers. (Yes, this includes test cases. We'll stop reminding you now.)
  7. Develop a program which takes a list-of-numbers and returns the product of all the numbers.

Databases

Let's build an example using lists of more interesting data. This just uses ideas you've already learned, but in new contexts. Stick to the design recipe, to avoid confusion!

Series of database exercises
  1. Copy the following into DrScheme: 
         ; A record is
     ;   (make-record name age salary)
     ; where name is a symbol, and age and salary are numbers.

     (define-struct record (name age salary))

     ; A database is a list of database records, i.e., either
     ;   - empty
     ;   - (cons f r)
     ; where f is a record, and r is a database (or, equivalently, a list-of-records).
  2. Create some example records (not databases -- just records).
  3. Create a template for records.
  4. Write the function eligible?, which takes in a single record, and returns whether or not it represents somebody who earns more than 60000 and is younger than 53.
  5. Create an example database.
  6. Write the template for functions which handle entire databases.
  7. Develop number-eligible, which takes a database and returns a count of those employees who are younger than 53 and earn more than 60000.
  8. For the curious... Develop db-search, which takes a database and returns a list of those employees' names (in the order they appear in the database).

Functions returning lists

Of course, since lists are just another form of data, we can also return lists from functions. As always, use the template corresponding to the input (also lists in these examples), not the output.

Series of exercises
Do at least one of these in lab:
  1. Develop a program which consumes a list of numbers and another number n, and returns a list where each element is n bigger. E.g., 
         (add-numbers (cons 1 (cons 3 (cons 4 empty))) 2)
     =
     (cons 3 (cons 5 (cons 6 empty)))
  2. Develop a program which consumes a list of numbers and returns a list of all of those numbers which are positive.

Mixed data (heterogenous) lists

Sometimes we would like to have multiple kinds of data stored intermingled within a single list. Technically, these are called heterogenous lists.

Series of heterogenous list exercises
  1. Make a data definition for a value which is a symbol or a number.
  2. Make a data definition for lists containing symbols and/or numbers. Examples would include 
         empty
     (cons 1 (cons 5 (cons 0 empty)))
     (cons 1 (cons 'hi empty))
     (cons 'hello (cons 'there empty))
  3. Develop a program which computes the product of all the numbers in a such a list. The structure of your program should correspond with your choice of data definition.
There are two reasonable ways to do this, although we hinted at the usually preferable one.

Non-empty lists -- Optional

Sometimes we would like to work with lists that are guaranteed to be non-empty. Rather than just stating this restriction as a side note, we can encode it into a separate data definition. This allows our code to be more explicit in what kind of data it uses.

Series of non-empty list exercises
  1. Make a data definition for non-empty lists of numbers. Hint: The base case should not be empty, since that is not a non-empty list of numbers! What is a description of the shortest non-empty lists of numbers?
  2. Develop a program which takes a non-empty list of numbers and returns the average (aka, arithmetic mean) of all the numbers.
  3. Develop a program which takes a list of numbers and returns the average of all the numbers. For this example, arbitrarily define the average of an empty list to be false.
There are actually two reasonable solutions to this, although we hinted towards the usually preferable one.