The exam covers Chapter 1 in SICP and material in the lectures. The exam is closed book.
In outline, the exam is as below. No further information on the exam will be given.

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Spring 2002

91.301, Section 201                                             Name: _____________________
 

                                                                                    Quiz 1
 
 

1. Consider the following inductive definition of unary function f defined on the natural numbers:
     (i) f(0) =
    (ii) f(succ(n)) =
For example, f(1) =      .
        (1) (5 points) Write a Scheme procedure fr(n) that computes f(n) using a recursive process.
        (2) (15 points) Write a Scheme procedure fi(n) that computes f(n) using an iterative process.
        (3) (15 points) Give a closed form cff(n) for f(n).
        (4) (20 points) Prove that your closed form is correct --- that is, for every n³ 0, cff(n) = f(n).
        (5) (5 points) Write a Scheme procedure fc(n) that computes f(n) in constant time and space.

        (6) (20 points) Write a Scheme procedure that
        (7) (20 points) Write a Scheme procedure (function) that