CPS 1 (Ramm)                        Page 1 of 5

22 February              Spring Semester,  1995			Section _____

CLOSED BOOK                    Hour Test            NAME_____________________

A. The following Pascal program has had most of its punctuation	    (5)
marks removed.  Restore all of these in their proper position.	    A	_____

	program greetings					    (5)
	var							    B	_____
        	i,  n:  integer
	begin							    (10)
	writeln(  Enter starting count  ) 			    C	_____
	readln(  n  ) 				
	i  :=  n           					    (15)
	while  i  >  0  do					    D	_____
		begin       	
		writeln(  i  )					    (5)
		i  :=  i  -  1					    E	_____
		end		
	while  i  <  n  do					    (10)
		begin						    F	_____
		i  :=  i  +  1		
	        writeln(  i  )					    (5)
		end						    G	_____
	end
								    (5)
B. In the program above, circle all of the names and data fields    H	_____
that are the choice of the programmer.  In other words, circle
those words that are not part of the Pascal language.		    (10)
								    I	_____

								    (5)
C. The following Pascal program was run.  The user typed the	    J	_____
following string as input:  ABCQXYZ
Show exactly what output the program produced.  (Remember that	    (10)
for these purposes, upper and lower case characters are different.) K	_____

	program tm1;		     OUTPUT(show next to writeln's) (10)
	var			     ----------------------------   L	_____
	    stra, strb, strc: string;
	    i, lng: integer;					    (15)
	begin							    M	_____
	readln(stra);						    ---------
	strb := copy(stra, 3, 2);
	writeln(strb);
	strc := strb + ' << ' + stra;
	writeln(strc);
	i := pos('X', stra);
	lng := length(stra);
	writeln(lng, ' ', i);
	strc := copy(stra, i+1, lng - i) + copy(stra, 1, i - 1);
	writeln(strc);

	writeln('stra + - + stra');

	writeln(stra + '-' + stra);
	readln;
	end.
                                 Hour Test                       Page 2 of 5

D. Here are some simple rules defining Pascal objects.
	(Use the back of page 1 for your answer)
						
#1 <identifier> -> //a sequence of letters//	
				(where // indicates italics)
#2 <string expression> -> '//any string of printable characters//'

#3 <statement> -> readln(<identifier>)	

#4 <statement> -> writeln(<string expression>)
						
#5 <compound statement> -> begin
			   //a sequence of <statement>s each
				followed by a semicolon//
			   end

Show how these rules can be used to generate the following Pascal program
fragment.  Identify the rule used at each stage.

	begin
  	writeln('Please enter number.');
	readln(n);
  	writeln('Thanks for that number.');
	end

Start with: #5	<compound statement> ->


E. Trace the following program with four columns: one for the statement
number,  one for i, one for T/F (for the while statement), and one for
output.  The first four are done.  Quit after 7 additional steps have been
traced.

 {#}	program again;		      stmt#	i      T/F	output
 	var				1	64	?
 		i: integer;		2
 		str: string;		3		T
 	begin				4			||  64||
 {1}	i := 64;
 {2}	str := '||';
 {3}	while i <> 0 do
 		begin
 {4}		writeln(str, i:4, str);
 {5}		i :=  -1 * i div 2;
 		end;
 	end.


F. On the back of the next page, write a complete Pascal program that
reads in a positive integer N, and then prints a table of the integers
from N+6 down to the smallest number greater than 0, by threes. Also
prints their corresponding squares.  For example, if your program reads
in a 5, it should print out the following:

 11   121
  8    64
  5    25
  2     4
                                 Hour Test                        Page 3 of 5

G. Below is the first part of a Pascal program.  Assume that it reads in
the numbers shown to the right of the program.  Show the contents of
array t by writing the numbers in the box below representing t in memory.

							DATA
program ara;					|	30
type						|	40
	t10 = array[1..10] of integer;		|	10
var						|	20
	t: t10;					|	80
	i, j, n, inc, num: integer;		|	55
	heat, cool, total: integer;		|	75
begin						|	20
n := 10;					|	85
i := 0;						|	25
while i < n do					|
	begin					|
	i := i + 1;
	writeln('Enter T:');			
	readln(t[i]);
	end;
			   1    2    3    4    5    6    7    8    9   10
			 ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
		    t	|    |    |    |    |    |    |    |    |    |    |
			 ---- ---- ---- ---- ---- ---- ---- ---- ---- ----

H. Assume that the program above continues with the code that follows.
What output does it produce?

	inc := 2;
	i := 5;
	while i <= n do
		begin
		writeln(t[i]:5);
		i := i + inc;
		end;

I. Next, the program concludes with the following code.  What is the output? 

	i := 0;
	cutoff := 70;
	total := 0;
	cool := 0;
	num := 0;
	while i < n do
		begin
		i := i + 1;
		if t[i] > cutoff then
			begin
			cool := cool + t[i];
			num := num + 1;
			end;
		total := total + t[i];
		end;
	writeln('sum =', total:6);
	writeln('cooling load of', cool:5, ' over', num:4, 'days');
	readln;
	end.
                                 Hour Test                       Page 4 of 5

J. What OUTPUT will the following program print?

					NOTE: FORMATTING IS IMPORTANT
						    OUTPUT 
					---------------------------------
	program one;
	var
		i: integer;
		c: string;
	begin
	i := 1;
	c := 'XX';
	while i <= 3 do
		begin
		c := c + '*' + c;
		i := i + 1;
		writeln(i, ' ', c);
		end;
	writeln(i);
	end.







K. What output does the following program produce?

	program multistr;
	var
		a, b: string;

	procedure putlines(var line:string);
		var
			i:integer;
		begin
		i := 1;
		while i <= 3 do
			begin
			writeln(copy(line,1, 7 - 2*i));
                	i := i + 1;
			end;
		end;

	begin
	a := '*****';
	putlines(a);
	writeln('Wow!');
	b := '+++++'
	putlines(b);
	readln;
	end.





                                 Hour Test                        Page 5 of 5

L.  Irrational numbers are numbers which have an infinite number of digits
after the decimal point with no repeating pattern.  Pi is such a number.
It starts with 3.14159265... but goes on forever.  One third ( 0.333333... )
goes on for an infinite number of places but does not qualify because it has
a repeating pattern.

Prove that there are an uncountable infinity of irrational numbers by using
arguments that are similar to those used in the text about functions of
integers to integers.  Assume we have a list claiming to include all of them,
one after the other, as suggested below.  (Note that Pi happens to be the
first one, using only digits after the decimal point.)  Prove that such
an infinite list could not include all irrational numbers.

          	col 1	col 2	col 3 	col 4	...  infinity	
1st # (Pi)	1	4	1	5	...	?
2nd #		3	7	4	7	...	?
3rd #		4	8	3	6	...	?
4th #           7       3       0       6       ...     ?
...		...	...	...	...	...	...
infinity	?	?	?	?	...	?










M.  On the back of the previous page, write a complete Pascal program that
prints out a table of integers, their negatives, their double, and their
cubes.  The number of rows in the table should be controlled by a number
read in from the user of the program.  Make sure the format is neat and that
the user is prompted to enter the numbers setting the length of the table.
The program should print a heading and "ruled lines" for the table.  For
example, if the user entered 4, the program would print out:

	   N     -N    2*N  N*N*N
    ===============================
    |      1     -1      2      1 |
    |-----------------------------|
    |	   2     -2  	 4      8 |
    |-----------------------------|
    |	   3  	 -3  	 6     27 |
    |-----------------------------|
    |	   4     -4  	 8     64 |
    |-----------------------------|

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HONOR CODE

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