CS 3015 Midterm Review - PowerPoint PPT Presentation

1 / 30

About This Presentation

Title:

CS 3015 Midterm Review

Description:

(list (car l) Exercise ... (square (car things) (iter items nil)) Exercise ... (cons ((car fns) item) (apply-all (cdr fns) item)))) Exercise ... – PowerPoint PPT presentation

Number of Views:15

Avg rating:3.0/5.0

Slides: 31

Provided by: jeffreyv

Category:

more less

Transcript and Presenter's Notes

Title: CS 3015 Midterm Review

1
CS 3015 Midterm Review
2
Exercise

Write a procedure called product that returns the
product of the values of a function at points
over a given range.
Show how to define factorial in terms of product.

3
Solution

(define (product f a next b)
(if (gt a b)
1
( (f a)
(product f (next a) next b))))
(define (fact x)
(product (lambda (x) x)
1
(lambda (x) ( x 1))
x))

4
Problem

Write iterative version of product

5
Problem

Write iterative version of product
(define (product f a next b)
(define (prod-iter a result)
(if (gt a b) result
(prod-iter (next a)
( a result))))
(prod-iter a 1))

6
Exercise

Define a procedure reverse that takes a list as
argument and returns a list of the same elements
in reverse order.

7
Solution

Define a procedure reverse that takes a list as
argument and returns a list of the same elements
in reverse order.
(define (reverse l)
(if (null? l) nil
(append (reverse (cdr l))
(list (car l)))))

8
Exercise

Modify your reverse procedure to produce a
deep-reverse procedure that takes a list as
argument and returns as its value the list with
its elements reversed and with all sublists
deep-reversed as well.

9
Solution

(define (deep-reverse l)
(cond ((null? l) nil)
((pair? l)
(append (deep-reverse (cdr l))
(list (deep-reverse
(car l)))))
(else l)))

10
Exercise

Write a function that takes a value and a number
and returns a list of that value repeated that
number of times.

11
Solution

Write a function that takes an value and a number
and returns a list of that value repeated that
number of times.
(define (repeat v n)
(if ( n 1) (list v)
(cons v (repeat n (- n 1))))

12
Exercise

Write a function that takes a number and returns
a function that takes a value and returns a list
of that value repeated that number of times

13
Solution

Write a function that take a number and returns a
function that takes a value and returns a list of
that value repeated that number of times
(define (make-repeater n)
(lambda (v)
(define (helper n)
(if ( n 1) (list v)
(cons v (helper (- n 1)))))
(helper n)))

14
Exercise

If f is a numerical function and n is a positive
integer, then we can form the nth repeated
application of f, which is defined to be the
function whose value at x is f(f(...(f(x))...)).

15
Solution

If f is a numerical function and n is a positive
integer, then we can form the nth repeated
application of f, which is defined to be the
function whose value at x is f(f(...(f(x))...)).
(define (repeated f n)
(lambda (x)
(define (helper n)
(if (lt n 2) (f x)
(f (helper (- n 1))))
(helper n)))

16
Exercise

If f is a function and dx is some small number,
then the smoothed version of f is the function
whose value at a point x is the average of f(x -
dx), f(x), and f(x dx). Write a procedure
smooth that takes as input a procedure that
computes f and a dx and returns a procedure that
computes the smoothed f.

17
Solution

(define (smooth f dx)
(lambda (x)
(/ ( (f (- x dx))
(f x)
(f ( x dx)))
3)))

18
Exercise

Show how to generate the n-fold smoothed function
of any given function using smooth and repeated
from exercise 1.43.
(define (nfold f dx n)
(repeated (smooth f dx) n)))

19
Exercise

Write square-list iteratively
(define (square-list items)(define (iter things a
nswer)  (if (null? things)      answer      (it
er (cdr things)             (cons (square(car thi
ngs))                  answer)))) (iter items ni
l))

20
Exercise

Write square-list iteratively
(define (square-list items)(define (iter things a
nswer)  (if (null? things)      answer      (it
er (cdr things)             (cons (square(car thi
ngs))                  answer)))) (iter items ni
l))
Is this right?

21
How about the following?

(define (square-list items)(define (iter things a
nswer)  (if (null? things)      answer      (it
er (cdr things)            (cons answer
         (square (car things))))))(iter items nil
))

22
Exercise

Write a procedure apply-all that takes a list of
procedures and an item as arguments and returns a
list of results of applying each procedure to the
item.

23
Solution

Write a procedure apply-all that takes a list of
procedures and an item as arguments and returns a
list of results of applying each procedure to the
item.
(define (apply-all fns item)
(if (null? fns) nil
(cons ((car fns) item)
(apply-all (cdr fns) item))))

24
Exercise

Write a procedure apply-composition that takes as
arguments a list of procedures that compute f1fn
and an argument appropriate for fn, and returns
the value of the composition of those function at
that argument.

25
Solution