Your name: 	

	A 1

	A


CS 3 (Clancy)	Exam 1
October 5, 1992
Read and fill in this page now.
Do NOT turn the page until you are told to do so.
Your name:		
	(please printÑlast name, first name)
Your lab section day and time:		
Your lab t.a.:		
Name of the person sitting to your left:		
Name of the person sitting to your right:		
Problem 0			Total:  	/30
Problem 1		
Problem 2		
Problem 3		
Problem 4		
Problem 5						
This is an open-book test. You have approximately fifty minutes to 
complete it. You may consult any books, notes, or other inanimate objects 
available to you. To avoid confusion, read the problems carefully. If you find 
it hard to understand a problem, ask us to explain it. If you have a question 
during the test, please come to the front or the side of the room to ask it.
This exam comprises 15% of the points on which your final grade 
will be based. Partial credit will be given for wrong answers. 
You are not to use setf within functions. Any other Lisp construct 
described in Touretzky chapters 1-6, in part I of the ÒDifference Between 
DatesÓ case study, or in ÒInteger Division and its UsesÓ is ok, though. 
Your exam should contain 6 problems (numbered 0 through 5) on 8 
pages. Appendix A and Appendix B from part I of the ÒDifference Between 
DatesÓ case study appear on the last page of the exam. Please write your 
answers in the spaces provided in the test; in particular, we will not grade 
anything on the back of an exam page unless we are clearly told on the front 
of the page to look there. 
RelaxÑthis exam is not worth having heart failure about.

Problem 0 (2 points; 1 minute)
Put your name on each page. Also make sure you have provided the 
information requested on the first page.
Problem 1 (4 points; 5 minutes)
Given below is the definition for a function called pair-up1 and 
several possible calls to pair-up1. For each function call, determine if it 
will produce an error. For every error-free call, state the result of 
evaluation. For every call that will produce an error, describe the error 
message that results.
(defun pair-up1 (L1 L2)
	(list
		(list (first L1) (second L2))
		(list (first L2) (second L1)) ) )
	okay? yes or no	result if yes, or error message if no
(pair-up1 (a b) (1 2))		
(pair-up1 '(a b) (1 2))		
(pair-up1 '(a b) '(1 2))		
(pair-up1 '((a b) (1 2)))		


Problem 2 (3 points; 4 minutes)
Given below is the definition for a function called pair-up2. Write an 
error-free sample call to pair-up2 and show what you expect evaluation of 
your sample call to return.
(defun pair-up2 (x L)
	(list x (+ (first L) (second L))) )

Problem 3 (2 points; 5 minutes)
Complete the function below, so that when given the index of a month 
in the Islamic calendar as inputÑan integer between 1 and 12Ñthe 
function returns the number of days in that month.
(defun islam-days-in-month (month-num)
	(second
		(assoc
			month-num
		) ) )

Problem 4 (9 points; 15 minutes)
Write a function islam-date-after that takes a single input, a date 
in the Islamic calendar, and returns the date thatÕs one day later. Recall 
that the Islamic calendar has twelve months, alternately 30 and 29 days as 
follows:
30  29  30  29  30  29  30  29  30  29  30  29
The input to islam-date-after will be a legal date in the Islamic calendar, 
as was the input to your islam-day-of-year from homework assignment 
2. 
Here are some examples of what islam-date-after should return.
input	value to return
(1 1)	(1 2)
(11 15)	(11 16)
(3 30)	(4 1)
(12 29)	(1 1)
You may use the function islam-days-in-month from the previous 
problem without redefining it. Your solution may also include other 
auxiliary functions, whose definitions you must provide.

Problem 5 (10 points; 20 minutes)
Code for the ÒDifference Between DatesÓ case study programs 
appears at the end of this exam.
Part a
A programmer decides to compute the number of days between two 
dates by subtracting the number of days not between those dates from 365. 
This process is represented in the diagram below.
                                    
# days between date1 and date2
= 365 Ð # days in the shaded area
The programmer codes this computation as follows:
(defun new-days-between (date1 date2)
	(- 365
		(+ (days-between '(january 1) date1)
			(days-between date2 '(december 31)) ) ) )
Used with the program in Appendix B of the ÒDifference Between DatesÓ 
case study, this function produces the following results.
first input date	second input date	result returned
(january 1)	(december 31)	363
(january 1)	(january 1)	-1
The bug can be fixed by changing the 365 in new-days-between to a 
different value. Make this fix by completing the following sentence.
The 365 should be changed to 	 in order to fix the bug.

Part b
Suppose that a version of new-days-between with the bug fixed is 
used with the program in Appendix A instead of the program in Appendix 
B. (Recall that the program in Appendix A is incomplete, since it is 
missing the function days-btwn-in-general.) 
Give a pair of dates for which new-days-between would return a 
value and days-between would not, and another pair of dates for which 
days-between would return a value and new-days-between would not.
A pair of date inputs for which new-days-between returns a value and 
days-between does not (using the incomplete program in Appendix A)
A pair of date inputs for which days-between returns a value and new-
days-between does not (using the incomplete program in Appendix A)
Part c
Again assume that the version of new-days-between with the bug 
fixed is used with the incomplete program in Appendix A. Compare the 
number of pairs of date inputs for which new-days-between returns a 
value to the number of pairs for which days-between returns a value: does 
new-days-between return a result for more pairs of dates, fewer, or the 
same number of pairs of dates as days-between? Explain.