Fundamentals of Computer Science I (CS151 2003F)
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Summary: In this laboratory, you will further explore issues of deep recursion introduced in the reading on pairs and pair structures.
Contents:
a. Review the material from the reading on pairs and pair structures.
b. Start DrScheme.
Recall that a list is a data structure defined recursively as follows:
Write a similar recursive definition for number trees, trees built from only numbers and cons cells.
Using your recursive definition of number trees from the previous probelm,
write a procedure, (numbertree? val)
that returns
true if val is a number tree and false otherwise.
Consider again the sumofnumbertree
procedure from the
reading, which you can find repeated at the
end of this lab.
a. Verify that it works as advertised on the first example.
(sumofnumbertree (cons (cons (cons 0 1) (cons 2 3)) (cons (cons 4 5) (cons 6 7))))
b. What do you expect sumofnumbertree
to return when
given (cons 10 11)
as a parameter? Verify your answer
experimentally.
c. Verify that it works as advertised on a single number.
d. Verify that it works as advertised on a pair of numbers.
e. What do you expect sumofnumbertree
to return when
given the empty list as a parameter? Verify your answer experimentally.
f. What do you expect sumofnumbertree
to return when
given (list 1 2 3 4 5)
as a parameter? Verify your answer
experimentally.
a. What preconditions should sumofnumbertree
have?
b. Rewrite sumofnumbertree
so that it reports an appropriate error if its preconditions are not met.
c. Some programmers consider it inappropriate to scan a tree twice, once to make sure that it's valid and once to compute a value based on the tree. Rewrite sumofnumbertree
so that it checks for and reports errors only when it is at one of the nonpair nodes.
a. Define and test a procedure named conscellcount
that takes
any Scheme value and determines how many boxes would appear in its
boxandpointer diagram. (The data structure that is represented by such a
box, or the region of a computer's memory in which such a structure is
stored is called a cons cell
. Every time the cons
procedure is used, explicitly or implicitly, in the construction of a
Scheme value, a new cons cell is allocated, to store information about the
car and the cdr. Thus conscellcount
also tallies the number
of times cons
was invoked during the construction of its
argument.)
For example, the structure in the following boxandpointer diagram
contains seven conscells, so when you apply conscellcount
to that structure, it should return 7. On the other hand, the string
"sample"
contains no conscells, so the value of
(conscellcount "sample")
is 0.
b. Use conscellcount
to find out how many cons cells are needed
to construct the list
(0 (1 (2 (3 (4)))))
See the notes at the end of the lab if you have trouble creating that list.
c. Draw a boxandpointer diagram of this list to check the answer.
If you find that you have extra time, you might want to attempt one or more of the following problems.
Write a procedure, numsyms
, that counts the number
of symbols in a tree of mixed values.
In case you don't want to switch documents, here is the code for
sumofnumbertree
.
;;; Procedure: ;;; sumofnumbertree ;;; Parameters: ;;; ntree, a number tree ;;; Purpose: ;;; Sums all the numbers in ntree. ;;; Produces: ;;; sum, a number ;;; Preconditions: ;;; ntree is a number tree. That is, it consists only of numbers ;;; and cons cells. ;;; Postconditions: ;;; sum is the sum of all numbers in ntree. (define sumofnumbertree (lambda (ntree) (if (pair? ntree) (+ (sumofnumbertree (car ntree)) (sumofnumbertree (cdr ntree))) ntree)))
If, for some reason, you are having trouble creating the list
(0 (1 (2 (3 (4)))))
try
(list 0 (list 1 (list 2 (list 3 (list 4)))))
Thursday, 16 October 2003 [Samuel A. Rebelsky]
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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.
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