Fundamentals of Computer Science I (CS151 2003F)
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Summary: In this laboratory, you will reflect on the appropriate and inappropriate uses of tail recursion.
Contents:
a. Review the reading on tail recursion.
b. Start DrScheme.
Identify three (or more) tailrecursive procedures you've already written.
In DrScheme, you can find out how long it takes to evaluate an
expression by using (time expression)
,
which prints out the time it takes to evaluate
and then returns the value computed.
Please scan the reading on using
time
before continuing this exercise.
a. Try the two versions of factorial
on some large numbers.
Does one seem to be faster than the other? You can find the two versions
of factorial in the notes on this problem.
b. Try the three versions of addtoall
on some lists
of varying sizes (you'll probably need at least a hundred values in
each list, and possibly more) until you can determine a difference
in running times. Note that you should make sure to build the list
before you start timing.
Note that you can easily create a long list of using makevector
and vector>list
.
Here's an attempt to write a tailrecursive version of the
select
procedure that selects all the values in a list for
which a predicate holds.
;;; Procedure: ;;; select ;;; Parameters: ;;; pred?, a unary predicate ;;; lst, a list of values ;;; Purpose: ;;; Selects all values in lst for which pred? holds. ;;; Produces: ;;; selected, a list ;;; Preconditions: ;;; pred? can be applied to any element of lst. ;;; Postconditions: ;;; every value in selected appears in lst. ;;; (pred? val) holds for every val in selected. ;;; (pred? val) holds for every val in lst not in selected. ;;; values in selected appear in the same order in which they appear in lst. (define select (lambda (pred? lst) (let kernel ((lst lst) (selected null)) (cond ; If nothing's left in the original list, use selected ((null? lst) selected) ; If the predicate holds for the first value in lst, ; select it and continue ((pred? (car lst)) (kernel (cdr lst) (cons (car lst) selected))) ; Otherwise, skip it and continue (else (kernel (cdr lst) selected))))))
a. What do you expect the results of the following two expression to be?
(select odd? (list 1 2 3 4 5 6 7)) (select even? (list 1 2 3 4 5 6 7))
b. Verify your answer through experimentation.
c. Correct any errors in select
that you observed in a or b.
Write a tailrecursive longeststringonlist
procedure which,
given a list of strings as a parameter, returns the longest string in
the list.
Note that you can use stringlength
to find the length of
a string.
Define a tailrecursive procedure (index val
lst)
that returns the index of val
in lst. That is, it should return zerobased location of
val
in lst
. If the item is not in the list,
the procedure should return 1. Test your procedure on:
(index 3 (list 1 2 3 4 5 6)) => 2 (index 'so (list 'do 're 'mi 'fa 'so 'la 'ti 'do)) => 4 (index "a" (list "b" "c" "d")) => 1 (index 'cat null) => 1
Recall that (iota n)
is to be the list of all
nonnegative integers less than n in increasing order.
Define and test a tailrecursive version of iota
.
Write your own tailrecursive version of reverse
.
Here's a nontailrecursive version of append
.
(define append (lambda (listone listtwo) (if (null? listone) listtwo (cons (car listone) (append (cdr listone) listtwo)))))
a. Write your own tailrecursive version.
b. Determine experimentally which of the three versions (builtin, given above, tailrecursive) is fastest.
Here are the two versions of factorial
.
;;; Procedures: ;;; factorial ;;; factorialtr ;;; Parameters: ;;; n, a nonnegative integer ;;; Purpose: ;;; Computes n! = 1*2*3*...*n ;;; Produces: ;;; result, a positive integer ;;; Preconditions: ;;; n is a nonnegative integer [unchecked] ;;; Postconditions: ;;; result = 1*2*3*...*n (define factorial (lambda (n) (if (<= n 0) 1 (* n (factorial ( n 1)))))) (define factorialtr (lambda (n) (letrec ((kernel (lambda (m acc) (if (<= m 0) acc (kernel ( m 1) (* acc m)))))) (kernel n 1))))
Here are the three versions of addtoall
.
;;; Procedures: ;;; addtoall1 ;;; addtoall2 ;;; addtoall3 ;;; Parameters: ;;; value, a number ;;; values, a list of numbers ;;; Purpose: ;;; Creates a new list by adding value to each member of values. ;;; Produces: ;;; newvalues, a list of numbers ;;; Preconditiosn: ;;; value is a number [unchecked] ;;; values is a list of numbers [unchecked] ;;; Postconditions: ;;; (listref newvalues i) equals (+ value (listref values i)) ;;; for all reasonable values of i. (define addtoall1 (lambda (value values) (if (null? values) null (cons (+ value (car values)) (addtoall1 value (cdr values)))))) (define addtoall2 (lambda (value values) (let kernel ((valuesremaining values) (valuesprocessed null)) (if (null? valuesremaining) valuesprocessed (kernel (cdr valuesremaining) (append valuesprocessed (list (+ value (car valuesremaining))))))))) (define addtoall3 (lambda (value values) (let kernel ((valuesremaining values) (valuesprocessed null)) ; If we've run out of values to process, (if (null? valuesremaining) (reverse valuesprocessed) (kernel (cdr valuesremaining) (cons (+ value (car valuesremaining)) valuesprocessed))))))
Monday, 30 October 2000 [Samuel A. Rebelsky]
Labs/tailrecursion.html
Sunday, 8 April 2001 [Samuel A. Rebelsky]
addtoend
after adding the answer to the reading.
reverse
and append
.
Labs/tailrecursion.html
.
Thursday, 7 November 2002 [Samuel A. Rebelsky]
select
.
append
to if you have time.
Monday, 11 November 2002 [Samuel A. Rebelsky]
factorial
and
the three versions of addtoall
.
Labs/tailrecursion.html
.
Sunday, 11 April 2003 [Samuel A. Rebelsky]
Thursday, 13 November 2003 [Samuel A. Rebelsky]
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[SamR]
Disclaimer:
I usually create these pages on the fly
, which means that I rarely
proofread them and they may contain bad grammar and incorrect details.
It also means that I tend to update them regularly (see the history for
more details). Feel free to contact me with any suggestions for changes.
This document was generated by
Siteweaver on Tue Dec 9 13:59:23 2003.
The source to the document was last modified on Thu Nov 13 12:54:45 2003.
This document may be found at http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2003F/Labs/tailrecursion.html
.
; ; Check with Bobby
Samuel A. Rebelsky, rebelsky@grinnell.edu