Vectors

Exercise 1

Start DrScheme and tell it not to print the lengths of vectors.

Exercise 2

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?

Exercise3

Develop a vector-sum procedure that takes one argument, a vector of numbers, and returns the sum of the elements of that vector. (You can use our-vector->list as a pattern for vector-sum -- only a few judicious changes are needed.)

Exercise 4

Develop a Scheme procedure join-strings that takes two arguments, both vectors of strings, equal in length, and returns a third vector of the same length, containing the results of concatenating corresponding elements of the argument vectors.

> (join-strings (vector "sect" "ram" "wee") (vector "ion" "pant" "knights"))
#("section" "rampant" "weeknights")

Exercise 5

Develop a Scheme procedure reverse-vector that takes any vector as argument and returns a vector of the same length, containing the same elements, but in reverse order.

Exercise 6

The dot product of two equally long vectors of numbers is the sum of the products of corresponding elements of those vectors. Develop a Scheme procedure dot-product that computes the dot product of two given vectors of numbers.

> (dot-product '#(2 3 4) '#(5 6 7))
56  ; (2 x 5) + (3 x 6) + (4 x 7) = 56
> (dot-product '#(3 1 4 1 6) '#(2 7 1 8 3))
43
> (dot-product '#() '#())
0

(Thanks to Alison McQuillan 2004 for pointing out an error in a previous version of this exercise.)

I am indebted to Professor Ben Gum for his contributions to the development of this lab.