Laboratory 24: Vectors

Summary: In this laboratory, you will explore various aspects of the Vector data type that Scheme provides as an alternative to lists.

Contents:

• Exercises
  • Exercise 0: Preparation
  • Exercise 1: Create a Simple Vector
  • Exercise 2: Modifying Lists and Vectors
  • Exercise 3: Specifying Vector Length
  • Exercise 4: Summing Vectors
  • Exercise 5: Filling Vectors
• If You Have Extra Time
• Extra 1: Rotating Vectors
• Extra 2: Reversing Vectors
• Extra 3: Rotating Vectors, Revisited
• Notes
  • Notes on Exercise 5: Filling Vectors

Exercises

Exercise 0: Preparation

Tell DrScheme not to print the lengths of vectors by entering (print-vector-length #f).

Exercise 1: Create a Simple Vector

a. In DrScheme's interaction window, type in a vector literal that denotes a vector containing just the two elements 3.14159 and 2.71828. How does DrScheme display the value of this vector?

b. Create a vector that contains the same two values by using the vector procedure.

c. Create a vector that contains the same two values by using the make-vector and vector-set! procedures.

Exercise 2: Modifying Lists and Vectors

Consider the following code.

> (define aardvark (list 1 2 3 4))
> (define baboon aardvark)
> (define aardvark (cons 5 (cdr aardvark)))
> (define chinchilla (vector 1 2 3 4))
> (define dingo chinchilla)
> (vector-set! chinchilla 0 5)

a. What do you expect the output of the following commands to be?

> (list-ref aardvark 0)

_____

> (list-ref baboon 0)

_____

b. Verify your answer experimentally.

c. What do your results suggest about Scheme?

d. What do you expect the output of the following commands to be?

> (vector-ref chinchilla 0)

_____

> (vector-ref dingo 0)

_____

e. Verify your answer experimentally.

f. What do your results suggest about Scheme?

Exercise 3: Specifying Vector Length

a. Tell DrScheme to print the length of vectors by entering (print-vector-length #t).

b. Enter each of the following vector expressions in DrScheme; consider the result (perhaps by examining individual elements with vector-ref); and indicate what vector has been created.

• #4(0)
• #4(1)
• #4(1 2)
• #2(1 2 3 4)
• (make-vector 4 0)

c. Tell DrScheme not to print the lengths of vectors and reenter each expression. Do your results differ? What do the differences suggest?

Exercise 4: Summing Vectors

Write a procedure, (vector-sum numbers), which takes one argument, a vector of numbers, and returns the sum of the elements of that vector.

You can use vector->list from the reading as a pattern for vector-sum -- only a few judicious changes are needed. However, you should not use vector->list as a helper. (That's inefficient -- and besides, we want you to learn how to do recursion over vectors.)

Exercise 5: Filling Vectors

In the reading on vectors, we saw that it was possible to implement list->vector and vector->list by using more primitive operations (particularly vector-set! and vector-length).

Write your own version of the vector-fill! procedure. Recall that vector-fill! takes two parameters, a vector and a value, and puts that value in every position of the vector.

If You Have Extra Time

If you have extra time, you may wish to finish the lab on deep recursion. Or, try one or more of the following exercises.

Extra 1: Rotating Vectors

Write a procedure, (rotate! vec) that rotates the elements in vec. That is, rotate! puts the initial element of vec at the end, the element at position 1 in position 0, the element at position 2 in position 1, and so on and so forth.

Extra 2: Reversing Vectors

a. Write a procedure, (reverse-vector vec), that creates a new vector whose elements appear in the reverse order of the elements in vec.

b. Write a procedure, (reverse-vector! vec), that reverses vec in place. That is, instead of producing a new vector, it rearranges the elements within vec.

Extra 3: Rotating Vectors, Revisited

Write a procedure, (rotate! vec amt), that rotates the values in vec by amt positions. That is, the first amt values in vec move to the end, the value in position amt moves to position 0, the value in position amt+1 moves to position 1, and so on and so forth.

Notes

Notes on Exercise 5: Filling Vectors

Just as in the case of list->vector, you will probably want to define a helper procedure that fills only part of the vector. Your termination condition will certainly be different and should probably involve the length of the vector.

Janet Davis (davisjan@cs.grinnell.edu)